1.
The first term in a certain sequence is 1, and for all integers n ≥ 2, the nth term in the sequence is the sum of 1 plus the reciprocal of the previous term in the sequence. What is the value of the sixth term in this sequence?Give your answer as a fraction.
Correct Answer
D. 13/8
Explanation
The nth term in the sequence is the sum of 1 plus the reciprocal of the previous term. Starting with the first term as 1, the second term would be 1 + 1/1 = 2. The third term would be 1 + 1/2 = 3/2. The fourth term would be 1 + 2/3 = 5/3. The fifth term would be 1 + 3/5 = 8/5. Therefore, the sixth term would be 1 + 5/8 = 13/8.
2.
If p and q are the solutions to x^{2} + 13x = 48, then what is the value of (p − q)^{2}?
Correct Answer
B. 361
Explanation
The value of (p - q)Â² can be found by substituting the values of p and q into the equation. To find the values of p and q, we can solve the given quadratic equation xÂ² + 13x = 48. By factoring the equation, we get (x + 16)(x - 3) = 0. Therefore, the solutions are x = -16 and x = 3. Substituting these values into (p - q)Â², we get (-16 - 3)Â² = (-19)Â² = 361.
3.
In the diagram, BC = CD = BD, angle FDE = 40°, angle EFD = 75°, and line BG is parallel to line DF. What is the measure of angle A in degrees?
Correct Answer
D. 55
Explanation
In the given diagram, we know that BC = CD = BD, which means that triangle BCD is an equilateral triangle. Since all angles in an equilateral triangle are equal, angle BCD = angle BDC = angle CBD = 60Â°.
We also know that line BG is parallel to line DF, which means that angle FDE = angle EBG. Since angle FDE = 40Â°, angle EBG must also be 40Â°.
Now, we can find angle BDE by subtracting angle EBG (40Â°) from angle BCD (60Â°). Therefore, angle BDE = 60Â° - 40Â° = 20Â°.
Since angle BDE = angle BDA, angle BDA is also 20Â°.
Finally, we can find angle A by subtracting angle BDA (20Â°) from angle EFD (75Â°). Therefore, angle A = 75Â° - 20Â° = 55Â°.
4.
A clock has the numbers 1 to 12 arranged equidistantly, in order, around the circumference of its circular face. If the clock’s minute hand starts out pointing at the number 1 and is adjusted counterclockwise until it points at 8 instead, what is the measure of the arc in degrees traversed by the minute hand’s tip?
Correct Answer
150
Explanation
When the minute hand starts at the number 1 and is adjusted counterclockwise until it points at 8, it traverses an arc on the clock face. Since there are 12 numbers arranged equidistantly around the circumference of the clock, each number represents an arc of 30 degrees (360 degrees divided by 12). Therefore, the minute hand traverses an arc of 7 numbers, which is equal to 7 times 30 degrees, resulting in 210 degrees. However, the question asks for the measure of the arc from the number 1 to 8, which is only 7 numbers. So, the correct measure of the arc traversed by the minute hand is 7 times 30 degrees, which is 210 degrees.
5.
In a given sequence, each term after the first one is found by multiplying the preceding term by the constant c. If a1 * a2 * a3 = 512, what is the value of a2?
Correct Answer
8
Explanation
In this sequence, each term is obtained by multiplying the preceding term by a constant "c". Given that a1 * a2 * a3 = 512, we can deduce that a2 is the square root of 512 (since a2 * a2 = 512). The square root of 512 is 8, so the value of a2 is 8.
6.
What is the value of 2*x in below equation?
Correct Answer
A. 26
Explanation
The value of 2*x in the equation is 26.
7.
What is the value of n?
Correct Answer
B. 2
Explanation
The value of n is 2 because it is the only whole number option provided. The other options, 3 and 2.5, are not whole numbers and therefore cannot be the value of n.
8.
A weighs 10 KG more than B, C weighs 5 KG less than A, and D weighs 10 KG more than C. If D weighs 60 KG, what is B's weight?
Correct Answer
45
Explanation
Based on the given information, we can determine the weights of A, C, and B. D weighs 10KG more than C, so C weighs 60KG - 10KG = 50KG. C weighs 5KG less than A, so A weighs 50KG + 5KG = 55KG. A weighs 10KG more than B, so B weighs 55KG - 10KG = 45KG. Therefore, B's weight is 45KG.
9.
Whenever a Dealer sells a toy, he earns a 20 percent commission on the first Rs.10,000 of the sale price plus 10 percent of the sale price in excess of Rs.10,000. If Art earned a Rs.3,000 commission on the sale of a certain sculpture, what was the sale price?
Correct Answer
B. 20000
Explanation
The question states that the dealer earns a 20% commission on the first Rs.10,000 of the sale price and an additional 10% commission on the remaining amount. Since Art earned a Rs.3,000 commission, we can calculate the total commission earned by dividing it into the two parts - 20% commission on Rs.10,000 and 10% commission on the remaining amount.
Let's assume the sale price is x.
20% commission on Rs.10,000 = (20/100) * 10,000 = Rs.2,000
10% commission on (x - 10,000) = (10/100) * (x - 10,000)
The total commission earned is Rs.3,000, so we have the equation:
2,000 + (10/100) * (x - 10,000) = 3,000
Simplifying the equation, we get:
(10/100) * (x - 10,000) = 3,000 - 2,000
(10/100) * (x - 10,000) = 1,000
(x - 10,000) = 1,000 * (100/10)
(x - 10,000) = 10,000
x = 10,000 + 10,000
x = 20,000
Therefore, the sale price of the sculpture was Rs.20,000.
10.
A was driving on a straight highway, from Noida to Agra, at 60 KMPH. B was driving faster than A, on the same highway, in the same direction. B started behind A. B passed A at 6:20 AM. At 8:20 AM, B arrived in Agra, and A arrived 50 minutes later, at 9:10 AM. Assume both drivers kept up constant speeds without stops. What was B's speed, in KMPH?
Correct Answer
D. 85
Explanation
Since B passed A at 6:20 AM and A arrived in Agra at 9:10 AM, the time difference between them is 2 hours and 50 minutes.
A arrived 50 minutes later than B, so A took 2 hours and 50 minutes + 50 minutes = 3 hours and 40 minutes to reach Agra.
Since A was driving at 60 KMPH, the distance between Noida and Agra is 60 KMPH * 3 hours and 40 minutes = 220 KM.
B arrived in Agra at 8:20 AM, which means B took 2 hours and 20 minutes to reach Agra.
Therefore, B's speed is 220 KM / 2 hours and 20 minutes = 94.78 KMPH, which rounds to 95 KMPH.
11.
A right triangle has legs of 6 and x, and a hypotenuse of r. If 5r = 5x + 9, what is the value of r + x?
Correct Answer
20
12.
4 years ago, A was 4 times as old as B. In 4 years, A will be twice as old as B. What is A’s present age?
Correct Answer
20
Explanation
Let's assume A's present age is x and B's present age is y. According to the given information, 4 years ago, A was 4 times as old as B. So, we can write the equation x-4 = 4(y-4). Simplifying this equation, we get x-4 = 4y-16. Further simplifying, we have x-4y = -12. In 4 years, A will be twice as old as B, so we can write the equation x+4 = 2(y+4). Simplifying this equation, we get x+4 = 2y+8. Further simplifying, we have x-2y = 4. Solving these two equations simultaneously, we find x = 20. Therefore, A's present age is 20.