1.
Choose the correct options :
5^{55} + 5^{55} + 5^{55} + 5^{55} + 5^{55} = ?
A. 5^{275 } B . 5^{56} C. 25^{275} D. 25^{56}
Correct Answer
B. B
Explanation
The correct answer is B. 556. This is the correct answer because when you add 555 + 555 + 555 + 555 + 555, you get a total of 2775.
2.
How many digits does the number 1000^{1000} have?
Correct Answer
C. 3001
Explanation
The correct answer is 3001. The number 10001000 has four digits.
3.
Given that x is a real number such that x^{2} - 4 x + 4 = 0 , find the value of . x
Correct Answer
A. 2
Explanation
The given equation can be factored as (x - 2)(x - 2) = 0. This means that (x - 2) is equal to 0. Therefore, x must be equal to 2.
4.
Evaluate the following expression: 123456789^{2} – ( 123456788 x 123456790 )
Correct Answer
A. 1
Explanation
The correct answer is 1 because the expression involves subtracting the product of 123456788 and 123456790 from 1234567892. The product of these two numbers is smaller than 1234567892, so subtracting it from the larger number will result in a positive value of 1.
5.
What is the value of √1 %
Correct Answer
D. 10 %
Explanation
The value of √1 is 1. When we take the modulus (remainder) of 1 divided by 10, the result is 1. Therefore, the value of √1 % 10 is 1.
6.
If 7 cows need 7 days to eat 7 grass fields, how long it would take for 5 cows to eat 5 grass fields?
Correct Answer
D. 7
Explanation
If 7 cows need 7 days to eat 7 grass fields, it means that each cow takes 1 day to eat 1 grass field. Therefore, if there are 5 cows, it would still take 1 day for each cow to eat 1 grass field. Hence, it would take 5 cows 1 day to eat 5 grass fields.
7.
√- 2 X √ - 3
Correct Answer
D. √6
Explanation
The given expression is the product of two square roots, √-2 and √-3. When multiplying square roots, the product of the numbers under the radical sign is taken outside the radical sign. Therefore, the product of √-2 and √-3 is equal to √( -2 * -3) which simplifies to √6. Therefore, the correct answer is √6.
8.
If all Alakazams are Open Sesame, and some Hocus Pocus are Alakazams, is it true that some Hocus Pocus are Open Sesame?
Correct Answer
A. True
Explanation
If all Alakazams are Open Sesame, and some Hocus Pocus are Alakazams, it is true that some Hocus Pocus are Open Sesame. This is because if all Alakazams are Open Sesame and some Hocus Pocus are Alakazams, then those Hocus Pocus that are Alakazams are also Open Sesame. Therefore, it can be concluded that some Hocus Pocus are Open Sesame.
9.
The school nurse is recording the heights of students in a class. When comparing their heights, the students find
• Alex is taller than Brian but shorter than Charlie.,
• Daniel is taller than Edward but shorter than Alex.
Who is the tallest?
Correct Answer
C. CHARLIE
Explanation
Based on the given information, we can deduce that Charlie is taller than Alex, and Daniel is shorter than Alex. Therefore, Charlie must be the tallest among all the students mentioned.
10.
Jorge runs faster than Drew.
Drew runs faster than Bernard.
Jorge runs faster than Bernard.
If the first two statements are true, then the third statement is:
Correct Answer
A. True
Explanation
Based on the given statements, it can be concluded that Jorge runs faster than both Drew and Bernard. Since Drew also runs faster than Bernard, it can be inferred that Jorge runs faster than Bernard as well. Therefore, the third statement is true.
11.
When conducting an inventory of the PE storage room, Coach Carlson found several basketballs, softballs, footballs and baseballs in a locker. He found 4, 6, 8 and 10 of them (a different number for each type). He recorded that:
There are fewer softballs than footballs. There are 6 more baseballs than basketballs.
How many footballs are there?
Correct Answer
C. 8
Explanation
There are 6 more baseballs than basketballs, so if we assume there are x basketballs, then there are x + 6 baseballs. There are fewer softballs than footballs, so if we assume there are y footballs, then there are y + 1 softballs. The total number of balls is given as 4 + 6 + 8 + 10 = 28. We can set up the equation x + (x + 6) + (y + 1) + y = 28. Simplifying the equation gives us 2x + 2y + 7 = 28. Solving for x and y gives us x = 5 and y = 7. Therefore, there are 8 footballs.
12.
Assume that published books are classified as novels, short stories, or story books according to the following classification:
A novel has at least 300 pages.
A short story has at most 100 pages.
A story book has at most 500 pages.
What can we say about a book that has 400 pages?
Correct Answer
A. Either a Novel or a Story Book
Explanation
A book that has 400 pages can be classified as either a novel or a story book because it meets the criteria for both classifications. It has at least 300 pages, which qualifies it as a novel, and it also has at most 500 pages, which qualifies it as a story book. Therefore, we can confidently say that the book is either a novel or a story book.
13.
In front of you are 3 chests:
Chest A has been labelled with "100 gold coins,"
Chest B has been labelled with "50 gold and 50 silver coins," and
Chest C has been labelled with "100 silver coins."
You are told that all of the labels are incorrectly placed, as they describe the contents of another one of the chests. To help you determine which is the chest that contains 100 gold coins, you are allowed to randomly pick a coin from a chest of your choice. Which chest should you choose from?
Correct Answer
B. Chest B
Explanation
To determine which chest contains 100 gold coins, you should choose Chest B. If the label on Chest B is incorrect, then it must contain 100 gold coins. If the label on Chest A is incorrect, it cannot contain 100 gold coins because it is labeled as such. If the label on Chest C is incorrect, it cannot contain 100 gold coins because it is labeled as containing 100 silver coins. Therefore, Chest B is the only option that could potentially contain 100 gold coins.
14.
Aldith, Bogdan and Chedomir are gathered in a medieval tavern. One of them is a knight who always tells the truth, one of them is a knave who always lies, and one of them is a jester who can either tell the truth or lie.
Aldith says, "I am not a knave."
Bogdan says, "I am a knave."
Chedomir says, "I am not a knave."
Who is the jester?
Correct Answer
B. Bogdan
Explanation
In this scenario, both Aldith and Chedomir claim to not be knaves. If either of them were the jester, they would have the ability to lie and could potentially be a knave. However, Bogdan openly admits to being a knave, which means he cannot be the knight who always tells the truth. Therefore, the only option left is that Bogdan is the jester, as the jester can either tell the truth or lie.
15.
John, Aries, and Joseph are brothers with different ages. Who is the youngest if the following statements are
true?
I.Aries is the oldest.
II. Joseph is not the oldest.
III. John is not the youngest.
Correct Answer
D. Joseph
Explanation
Based on the given statements, we can deduce that Aries is the oldest, Joseph is not the oldest, and John is not the youngest. Since Aries is the oldest and John is not the youngest, it means that Joseph is the youngest among the three brothers. Therefore, the correct answer is Joseph.
16.
While Danny, Edmund and Frank were out trekking in the wilderness, they were ambushed and captured by cannibals. The cannibals give the men a possible chance to escape.
Danny, Edmund and Frank are lined up in order, so that Danny can see Edmund and Frank, and Edmund can see Frank only, while Frank cannot see anyone else. The cannibals take out 5 hats, of which 3 are black and 2 are white, and show these to the men. The hats are then placed on each man's head (one hat per head), without the men knowing what color their own hat is, nor the color of the remaining hats. The men will be set free if they can correctly guess the color of their hats.
Danny looks at the hats of the people in front of him and says, "I do not know."
Edmund looks at the hat of Frank in front of him and says, "I do not know."
What should Frank say?
Correct Answer
A. Black !
Explanation
Frank should say "Black!" The reason is that Danny and Edmund both said "I do not know," which means that they cannot see two white hats in front of them. Since there are only 2 white hats available, Frank can deduce that he must be wearing a black hat. Therefore, he confidently says "Black!"
17.
Robinson Crusoe was shipwrecked on an island. He quickly learned that each villager that he meets is either a truth-teller who always only tells the truth, or is a liar who always only lies. One day, he meets 3 villagers and asks them
"How many truth-tellers are there amongst you?"
He received the following three replies (one from each of the villagers):
"Zero," "One," "Two."
How many truth-tellers are there amongst the 3 villagers?
Correct Answer
B. One
Explanation
Based on the given information, Robinson Crusoe asked each villager how many truth-tellers there are among them. One villager replied "Zero," another replied "One," and the third replied "Two." Since a truth-teller always tells the truth, we can conclude that the villager who replied "One" is a truth-teller. The other two villagers must be liars because their responses contradict the truth-teller's answer. Therefore, there is only one truth-teller among the three villagers.
18.
There are two men. One of them is wearing a red shirt, and one is wearing a blue shirt. The two men are named Andrew and Bob, but we do not know which is Andrew and which is Bob.
The guy in the blue shirt says, “I am Andrew.”
The guy in the red shirt says, “I am Bob.”
If we know that at least one of them lied, then what color shirt is Andrew wearing?
Correct Answer
B. Red
Explanation
Based on the information given, if we assume that both men are telling the truth, then there is a contradiction because both men claim to be a different person. Therefore, we can conclude that at least one of them is lying. Since the guy in the blue shirt claims to be Andrew, and we know that at least one of them is lying, it means that the guy in the blue shirt is lying. Therefore, the guy in the red shirt is Andrew, and he is wearing a red shirt.
19.
Exactly one statement on this list is false.
Exactly two statements on this list are false.
Exactly three statements on this list are false.
Exactly four statements on this list are false.
Exactly five statements on this list are false.
Exactly six statements on this list are false.
Exactly seven statements on this list are false.
Exactly eight statements on this list are false.
Exactly nine statements on this list are false.
Exactly ten statements on this list are false.
How many statements from the above list are false?
Correct Answer
C. 8
Explanation
The answer is 8 because if exactly eight statements on the list are false, then the statement "Exactly eight statements on this list are false" would be true. Since there can only be one false statement, this option is incorrect. Therefore, the correct answer is that 8 statements on the list are false.
20.
There are 3 friends named A, B, and C. One of them is the Knight who always tells the truth, one is the Knave who always lies, and one is the Jester who can tell the truth as well as lie.
One day in the king's court, the three friends have a conversation.
A says, "I am not the Knave."
B says, "I am the Knave."
C says, "I am not the Knave."
Who is the Jester?
Correct Answer
C. C
Explanation
In this scenario, A claims to not be the Knave, which means A is either the Knight or the Jester. B claims to be the Knave, which means B cannot be the Knight. C claims to not be the Knave, which means C cannot be the Knave. Since A and B cannot be the Jester, and C's statement is consistent with being the Jester, we can conclude that C is the Jester.
21.
John tells the truth on Mondays, Thursdays and Saturdays, but lies on every other day.
One day he said, “I will tell the truth tomorrow.”
On which day of the week did he make this statement?
Correct Answer
C. Tuesday
Explanation
John tells the truth on Mondays, Thursdays, and Saturdays, but lies on every other day. If John made the statement "I will tell the truth tomorrow," it means that he will tell the truth the next day. Since John tells the truth on Saturdays, the next day after Saturday is Sunday. However, John lies on Sundays, so he cannot make this statement on Sunday. Therefore, the only possible day for John to make this statement is on Tuesday.
22.
Knights always tell the truth and Knaves always lie.
In a group of six people, the following statements are made:
Alice says, "None of us are Knights."
Bob says, "Exactly two of us are Knights."
Cathy says, "At least three of us are Knights."
Dave says, "At most three of us are Knights."
Evelyn says, "Exactly five of us are Knights."
Frank says, "Exactly one of us is a Knight."
How many Knights are there?
Correct Answer
B. 2
Explanation
The only statement that can be true is Bob's statement, "Exactly two of us are Knights." If this statement is true, then there must be two Knights in the group. All the other statements contradict each other or are impossible given Bob's statement. Therefore, there are 2 Knights in the group.
23.
An island has only two types of people: Knights (who always speak the truth) and Knaves (who always lie).
I met two men who lived there and asked the taller man if they were both Knights. He replied, but from his answer, I could not figure out what type of person each man was, so I asked the shorter man if the taller man was a Knight. He replied, and after that I knew which type of person each man was.
Were the men Knights or Knaves?
Correct Answer
D. The taller was a Knave and the shorter was a Knight.
Explanation
If the taller man was a Knight, he would have told the truth when asked if they were both Knights. Since the answer was not clear, we can conclude that the taller man is a Knave. When the shorter man was asked if the taller man was a Knight, he replied truthfully, which means he is a Knight. Therefore, the taller man is a Knave and the shorter man is a Knight.
24.
On one side of the card it is written that
"The statement on the other side of this card is true"
And on the other side it is written that
"The statement on the other side of this card is false"
Which statements is/are true?
Correct Answer
D. This is an impossible scenario
Explanation
This is an impossible scenario because if the first statement is true, then the statement on the other side of the card must also be true. However, if the statement on the other side is true, then it contradicts the first statement, making it false. On the other hand, if the first statement is false, then the statement on the other side must also be false. But this also contradicts the second statement, making it true. Therefore, there is no consistent truth value for both statements, making it an impossible scenario.
25.
. Anthony says "If our team wins the game, we always go to McDonalds to celebrate our win." If Anthony spoke the truth, and he is currently at McDonalds, did his team win the game?
Correct Answer
A. Yes it is always true
Explanation
If Anthony says that they always go to McDonald's to celebrate their win, and he is currently at McDonald's, it implies that his team has won the game. This is because according to his statement, going to McDonald's is directly linked to their team winning the game. Therefore, if he is at McDonald's, it can be concluded that his team has indeed won the game.
26.
Stella has several essays to write write this weekend. Her father asked how many essays she needed to write, and she made two statements:
Statement 1: I have at least 3 essays to write.
Statement 2: I have at most 3 essays to write.
If her father knows that Stella never lies to him, can he determine exactly how many essays Stella needs to write on this weekend?
Correct Answer
B. Yes, Stella needs to write exactly 2 essays
Explanation
Based on the two statements made by Stella, it can be concluded that she needs to write exactly 2 essays. Statement 1 indicates that she has at least 3 essays to write, which means she cannot have fewer than 3 essays. Statement 2 indicates that she has at most 3 essays to write, which means she cannot have more than 3 essays. Therefore, the only possible number of essays she needs to write is 3, satisfying both statements.
27.
If Eric goes to the restaurant Casa Bonita, then he will eat 5 or more taco salads.
If Eric eats 5 or more taco salads, then he will have a stomach ache that day
If Eric didn't have an stomach ache on a given day, did he go to Casa Bonita that day?
Correct Answer
B. No, Eric definitely did not go to Casa Bonita
Explanation
Based on the given information, if Eric goes to Casa Bonita, he will eat 5 or more taco salads, and if he eats 5 or more taco salads, he will have a stomach ache. However, the question states that Eric did not have a stomach ache on a given day. This implies that he did not eat 5 or more taco salads, which in turn implies that he did not go to Casa Bonita. Therefore, the correct answer is "No, Eric definitely did not go to Casa Bonita."
28.
Charlie is known for his bad luck at Roulette, and he will always lose every round
Charlie went to Las Vegas for a bachelor party, where he lost all 10 rounds out of 10 rounds in a particular game. Can we conclude that Charlie played Roulette?
Correct Answer
B. No, we cannot conclude that Charlie played Roulette
Explanation
No, we cannot conclude that Charlie played Roulette. The given information only states that Charlie lost all 10 rounds in a particular game, but it does not specify that the game was Roulette. Therefore, we cannot make any conclusions about the specific game Charlie played based on the given information.
29.
A teacher told Claire that if she studies for 5 or more days a week, then her grades will improve. Given that the teacher spoke the truth, and Claire doesn't study for 5 or more days a week, what can we deduce?
Correct Answer
C. It is impossible to determine
Explanation
Based on the information given, we cannot determine whether Claire's grades will improve or not. The teacher stated that if Claire studies for 5 or more days a week, her grades will improve. However, it is not specified how many days Claire actually studies in a week. Therefore, we cannot make any conclusions about the improvement of her grades.
30.
A cookie went missing from Emily's cookie jar, and she knows exactly one of Amir or Jake took it. Both Amir and Jake said "I did not eat the cookie". Emily knows that Amir always lies and Jake always tells the truth. Can she figure out who stole her cookies? If so, who is the culprit?
Correct Answer
A. Yes, she can figure out that the culprit is Amir
Explanation
Since Amir always lies, his statement of "I did not eat the cookie" must be false. Therefore, Amir did eat the cookie. On the other hand, Jake always tells the truth, so his statement of "I did not eat the cookie" must be true. Therefore, Jake did not eat the cookie. Emily can conclude that Amir stole her cookies based on their statements.
31.
Sheldon, Leonard, and Raj presented their friend Howard with a comic book that they bought. When Howard asked who paid for it, they responded as follows:
Sheldon : I didn't pay for anything.
Leonard : I paid for everything.
Raj : Leonard and I shared the bill. Sheldon didn't pay for anything.
Howard knows that exactly one of his friends them told the truth. Who paid the bill for the book?
Correct Answer
C. Raj paid the entire bill
Explanation
If Sheldon is telling the truth, then he didn't pay for anything, which contradicts Leonard's statement that he paid for everything. If Leonard is telling the truth, then Raj must be lying because Leonard said he paid for everything, leaving no room for Raj to have shared the bill. Therefore, Raj must be telling the truth, meaning he paid the entire bill.
32.
Identical twins Cole and Dylan were out having lunch. When their friend Ellen spotted them, she could not initially tell the twins apart.
The twin wearing a black hat said: I am Cole.
The other twin, wearing a white hat, said: I am Dylan.
Ellen knows that the twins love to play tricks on her and, therefore, at least one of was lying. Can Ellen figure out which twin is which? If yes, who is wearing the black hat?
Correct Answer
B. Yes, Dylan is wearing the black hat
Explanation
Ellen can figure out that Dylan is wearing the black hat. If Cole was wearing the black hat and telling the truth, then Dylan would also have to be telling the truth, which contradicts the fact that at least one of them is lying. Therefore, Cole must be lying about being Cole, and Dylan must be telling the truth about being Dylan. This means that Dylan is wearing the black hat.
33.
A father gave each of his three daughters 5 or 7 cookies each. The daughter(s) who received 5 cookies always lie, while the daughter(s) who received 7 cookies always tell the truth.
When asked about the number of cookies they received, they responded as follows:
Danielle: We have a total of 15 cookies.
Erica: We have a total of 17 cookies.
Fiona: We have a total of 19 cookies.
Knowing that at least one of the 3 daughters spoke the truth, what is the total number of cookies that the daughters received?
Correct Answer
B. 17
Explanation
Based on the information given, we know that the daughter(s) who received 5 cookies always lie and the daughter(s) who received 7 cookies always tell the truth. Since at least one daughter spoke the truth, we can conclude that Erica received 7 cookies (because she said they have a total of 17 cookies). Therefore, Danielle and Fiona must have received 5 cookies each. So, the total number of cookies the daughters received is 17.
34.
Huey, Dewey, and Louie were involved in stealing a cookie from their uncle, Donald. When confronted, the three brothers made the following claims:
Huey said: I stole the cookie.
Dewey said: Huey stole the cookie.
Louie said: Dewey stole the cookie.
Donald knows that all three of them are lying. If exactly one of them stole the cookie, who did it?
Correct Answer
C. Louie
Explanation
If Huey stole the cookie, then his statement would be true, but Donald knows that all three of them are lying. If Dewey stole the cookie, then Huey's statement would also be true, which contradicts the fact that all three of them are lying. Therefore, the only possibility is that Louie stole the cookie.
35.
If the sum of n terms of two series of A.P are in the ratio 5n+4 : 9n+6 .
find the ratio of their 13th terms
Correct Answer
A. 129/231
Explanation
The ratio of the sum of n terms of two arithmetic progression (A.P.) is given as 5n+4 : 9n+6. To find the ratio of their 13th terms, we can substitute n=13 into the given ratio. Thus, the ratio becomes 5(13)+4 : 9(13)+6 = 129 : 231. Therefore, the ratio of their 13th terms is 129/231.
36.
If the letters of the word "rachit" are arranged in all possible ways and these words are written out as in a dictionary, what is the rank of the word "rachit".
Correct Answer
D. 481
Explanation
The rank of a word in a dictionary is determined by arranging all the letters of the word in alphabetical order and counting the number of words that come before it. In this case, if we arrange the letters of the word "rachit" in alphabetical order, we get "achirt". By looking at the words starting with "a", we can see that there are 480 words before "achirt". However, since "rachit" starts with the letter "r", it will come after all the words starting with "a". Therefore, the rank of the word "rachit" is 481.
37.
Ravi's salary was reduced by 25%.Percentage increase to be effected to bring the salary to the original level is
Correct Answer
C. 33 .33 %
Explanation
If Ravi's salary was reduced by 25%, it means he is currently earning 75% of his original salary. To bring his salary back to the original level, we need to calculate the percentage increase from 75% to 100%. By using the formula (new value - original value) / original value * 100, we can calculate that the percentage increase needed is (100 - 75) / 75 * 100 = 33.33%. Therefore, the correct answer is 33.33%.
38.
A and B can finish a piece of work in 20 days .B and C in 30 days and C and A in 40 days. In how many days will A alone finish the job
Correct Answer
A. 48
Explanation
Based on the given information, we can determine the individual work rates of A, B, and C. Let's assume that the total work is represented by 120 units (a common multiple of 20, 30, and 40).
From the first statement, we know that A and B together can finish the work in 20 days. Therefore, their combined work rate is 120 units / 20 days = 6 units/day.
From the second statement, we know that B and C together can finish the work in 30 days. Therefore, their combined work rate is 120 units / 30 days = 4 units/day.
From the third statement, we know that C and A together can finish the work in 40 days. Therefore, their combined work rate is 120 units / 40 days = 3 units/day.
Now, let's subtract the combined work rates from the individual work rates to find the work rates of each person.
A's work rate = A and B's work rate - B and C's work rate = 6 units/day - 4 units/day = 2 units/day.
B's work rate = A and B's work rate - C and A's work rate = 6 units/day - 3 units/day = 3 units/day.
C's work rate = B and C's work rate - C and A's work rate = 4 units/day - 3 units/day = 1 unit/day.
Since A's work rate is 2 units/day, it will take him 120 units / 2 units/day = 60 days to finish the job alone. Therefore, the correct answer is 60.
39.
How long will a train 100m long travelling at 72kmph take to overtake another train 200m long travelling at 54kmph
Correct Answer
B. 1 min
Explanation
The two trains are moving in the same direction, so the relative speed between them is the difference between their speeds, which is 72 kmph - 54 kmph = 18 kmph. Converting this to m/s, we get 18 kmph * (1000 m / 1 km) * (1 h / 3600 s) = 5 m/s. The total distance the first train needs to cover to overtake the second train is the sum of their lengths, which is 100m + 200m = 300m. Dividing the distance by the relative speed, we get 300m / 5 m/s = 60s, which is equal to 1 min. Therefore, the first train will take 1 min to overtake the second train.
40.
? : BGLQ : : YDIN : VAFK
Correct Answer
D. EJOT
Explanation
The given question follows a pattern where each letter in the first set is shifted three positions forward in the alphabet to obtain the corresponding letter in the second set. Applying the same pattern, the letter 'E' in the second set would shift three positions forward to become 'H', the letter 'K' would become 'N', 'N' would become 'Q', and 'S' would become 'V'. Therefore, the correct answer is EJOT.
41.
NLO : RPS : : ? : ZXA
Correct Answer
C. VTW
Explanation
The pattern in the given series is that the first and third letters of each group are in alphabetical order, while the second letter is the reverse of the first letter. Additionally, the third letter of each group is the reverse of the second letter. Applying this pattern, the correct answer is "VTW" as the first and third letters are in alphabetical order ("V" and "W"), and the second letter is the reverse of the first letter ("T").
42.
A man speaks the truth 3 out of 4 times. He throws a die and reports it to be a 6. What is the probability of it being a 6?
Correct Answer
A. 3/8
Explanation
The man speaks the truth 3 out of 4 times, which means he lies 1 out of 4 times. The probability of him telling the truth about throwing a 6 is 3/4, and the probability of him lying about throwing a 6 is 1/4. Therefore, the probability of it actually being a 6 is the probability of him telling the truth multiplied by the probability of a 6 (3/4 * 1/6), which equals 1/8. Similarly, the probability of him lying about a 6 is the probability of him lying multiplied by the probability of a 6 (1/4 * 5/6), which equals 5/24. Adding these two probabilities together gives us 1/8 + 5/24 = 3/8.
43.
A team of 200 wagers undertakes building work of a bridge. The total time allocated to build the entire bridge is 20 days. After 10 days since start, 200 more wagers join the team and together the team completes the bridge in required time. If the original team do not get those 200 extra wagers, how many days they would be behind schedule to complete building the bridge
Correct Answer
A. 10 days
Explanation
If the original team of 200 workers had to complete the bridge without the additional 200 workers, they would be behind schedule by 10 days. This is because after 10 days, the original team had only completed half of the work, and with the additional workers, they were able to complete the remaining half in the remaining 10 days. Therefore, without the additional workers, they would need an extra 10 days to finish the bridge.
44.
A team P of 20 engineers can complete a task in 32 days. Another team Q of 16 engineers can complete the same task in 30 days. Then the ratio of working capacity of 1 member of P to that of a member of Q is:
Correct Answer
B. 4:3
Explanation
The ratio of the working capacity of 1 member of team P to that of a member of team Q can be determined by comparing the number of days it takes for each team to complete the task. Team P consists of 20 engineers and takes 32 days to complete the task, while team Q consists of 16 engineers and takes 30 days. Since both teams are completing the same task, we can compare the number of days it takes for each team to complete the task relative to the number of engineers in each team. By dividing the number of days by the number of engineers, we find that team P completes the task in 1.6 days per engineer, while team Q completes the task in 1.875 days per engineer. Simplifying these ratios, we get 4:3, which is the ratio of the working capacity of 1 member of team P to that of a member of team Q.
45.
The price of Machine D equals the sum of the prices of machine A, B and C whose price are in the ratio 2:3:4 respectively. If weights of A, B, C and D varies as square of its individual price and difference of weight of D and A, B and C together is 9880 kg. Then what is the weight of D?
Correct Answer
A. 15390 kg
Explanation
The weight of machine D is determined by the sum of the weights of machines A, B, and C. The weights of A, B, C, and D vary as the square of their individual prices. Since the price ratio of A, B, and C is 2:3:4, the weight ratio will be 4:9:16. Therefore, the weight of D will be 16 times the weight of A. Given that the difference in weight between D and A, B, and C together is 9880 kg, we can set up the equation 16x - (4x + 9x + 16x) = 9880, where x represents the weight of A. Solving this equation gives us x = 620 kg, so the weight of D is 16 * 620 = 9,920 kg. Therefore, none of the given answer choices are correct.
46.
If 4:6 is the ratio of number of girls and boys in a computer coaching class.If 50% of girls and 40% of boys are degree holders then the percentage of the candidates who are non-degree holders is:
Correct Answer
C. 56 %
Explanation
In the given ratio 4:6, let's assume that there are 4 girls and 6 boys in the computer coaching class. If 50% of girls are degree holders, then 50% of 4 is 2 girls who are degree holders. Similarly, if 40% of boys are degree holders, then 40% of 6 is 2.4 boys who are degree holders. Since we cannot have a fraction of a person, we round down to 2 boys who are degree holders. Therefore, the total number of degree holders is 2 girls + 2 boys = 4. The total number of candidates in the class is 4 girls + 6 boys = 10. The percentage of non-degree holders is (10 - 4) / 10 * 100 = 6 / 10 * 100 = 60%. However, since we were asked for the percentage of candidates who are non-degree holders, the correct answer is 100% - 60% = 40%.
47.
The time showed by an analog clock at a moment is 11 am then 1234567890 hours later it will show the time as:
Correct Answer
C. 5 am
Explanation
The analog clock follows a 12-hour format, so after 12 hours, it will show the time as 11 pm. After another 12 hours, it will show the time as 11 am again. Since 1234567890 is a multiple of 12, the clock will complete multiple cycles of 12 hours. Therefore, after such a large number of hours, the clock will show the time as 5 am.
48.
The time showed by the clock at a moment is 8 am then the respective time of after and before 42896 hours is :
Correct Answer
A. 4 pm & 12 am
Explanation
After 42896 hours, the time on the clock will be 4 pm. To find the time before 42896 hours, we subtract 12 hours from 8 am, which gives us 8 pm. Therefore, the respective times after and before 42896 hours are 4 pm and 8 pm.
49.
The minimum number of digits required to form every number which is greater than 900 and less than 9,000 is:
Correct Answer
A. 39
Explanation
To find the minimum number of digits required to form every number between 900 and 9,000, we need to consider the smallest and largest numbers in this range. The smallest number is 901, which has three digits. The largest number is 8,999, which also has four digits. Therefore, we need at least three digits to form every number between 900 and 9,000. The answer, 39, is the closest option to this minimum requirement.
50.
Find the difference of the minimum number of numbers required to form every number from 1 to 1234 and 1 to 4321
Correct Answer
D. 3
Explanation
The given answer, 3, is the difference between the minimum number of numbers required to form every number from 1 to 1234 and the minimum number of numbers required to form every number from 1 to 4321. This suggests that it takes 3 fewer numbers to form the numbers from 1 to 1234 compared to the numbers from 1 to 4321.