Math Exam - 1 (Number Theory)

1. Turn the odd man out: 4, 9, 10, 12, 13, 18, 21

4

12

13

21

None of these

Only 13 is a prime among them which is odd(strange).

Explanation

Only 13 is a prime among them which is odd(strange).

2. If a, b, and c are nonzero numbers and a+b=c, which of the following is equal to 1?

(a-b)/c

(a-c)/b

(b-c)/a

(c-b)/a

None of these

Very simple, just a+b=c, or a=c-b & so (c-b)/a=a/a=1.

Explanation

Very simple, just a+b=c, or a=c-b & so (c-b)/a=a/a=1.

3. When the integers x id divided by 5, the remainder is 2. Which of the following can be multiple of (x+3)

8x+7

9x-3

11x-4

13x+1

13x

we have to find out a number divisible by (x+3), Given that the remainder is 2 if x is divided by 5, then we may guess the value of x such as 7 (5+2), 12(5*2+2), 17(5*3+2) ..so on. Then (x+3) means 10(7+3), 15(12+3) & so on. Thus (9x-3)=9*7-3=60 which is divisible by 10 means ( x+3).

Explanation

we have to find out a number divisible by (x+3), Given that the remainder is 2 if x is divided by 5, then we may guess the value of x such as 7 (5+2), 12(5*2+2), 17(5*3+2) ..so on. Then (x+3) means 10(7+3), 15(12+3) & so on. Thus (9x-3)=9*7-3=60 which is divisible by 10 means ( x+3).

4. A certain integer when divided by 5 yields a remainder of 4. Which of these can not be an integer?

N/9

N/10

N/14

N/19

None of these

n is not divided by 5, how can n be divided by 10? So, n/10 can not be integer ever.

Explanation

n is not divided by 5, how can n be divided by 10? So, n/10 can not be integer ever.

5. When 10 is divided by the positive integer n, the remainder is n-4. Which of the following could be value of n?

3

4

7

8

12

If 10 is being divided by 7, then the remainder is 3 which is 7-4 that means n-4.

Explanation

If 10 is being divided by 7, then the remainder is 3 which is 7-4 that means n-4.

6. When the integer n is divided by 3, the quotient is p and the remainder is 1. When p is divided by 5, the quotient is q and the remainder is 2. What will be the remainder when n is divided by 5.

4

3

2

1

None of these

Here, n=3p+1 = 3(5q+2)+1=15q+6+1=(15q+5)+2; (15q+5) is divisible by 5, so remainder is 2.

Explanation

Here, n=3p+1 = 3(5q+2)+1=15q+6+1=(15q+5)+2; (15q+5) is divisible by 5, so remainder is 2.

7. If the average of 5 consecutive odd integer is 55. what is the average of the last two integers?

56

57

58

60

None of these

55 is the average of 5 (which is an odd number) numbers, so 55 is in the middle of those numbers. Hence, 51,53,55,57,59 will those numbers & (57+59)/2=58

Explanation

55 is the average of 5 (which is an odd number) numbers, so 55 is in the middle of those numbers. Hence, 51,53,55,57,59 will those numbers & (57+59)/2=58

8. Q is a prime number larger than 10. What is the smallest positive number (except 1) that 3Q can be equally divided by?

3Q

Q

3

Q+3

None of these

Q is a prime number so it can be divided equally by 3Q, by 1 and by the components of 3 & Q. So the smallest number is 3 except 1.

Explanation

Q is a prime number so it can be divided equally by 3Q, by 1 and by the components of 3 & Q. So the smallest number is 3 except 1.

9. A can be divided by 11. Which of the following expressions can be divided by 11 leaving a remainder of 1?

A-20

A-12

A-9

A-10

None of these

Just take the multiples of 11 such as 22,33,44 etc. & replace a by any of them in the choice options.

Explanation

Just take the multiples of 11 such as 22,33,44 etc. & replace a by any of them in the choice options.

10. P is divisible by 4. Q is divisible by 3. Which of the following is definitely odd?

Q(P+1)

2P+3Q

PQ2

P2Q3

None of these

P is divisible by 4, so P is an even number but Q is divisible by 3, so Q may be odd(3,9,15 etc.) or even (6,12,18 etc.). hence if we think from our concept, we find we can not say about any option definitely.

Explanation

P is divisible by 4, so P is an even number but Q is divisible by 3, so Q may be odd(3,9,15 etc.) or even (6,12,18 etc.). hence if we think from our concept, we find we can not say about any option definitely.