# Math Exam - 1 (Number Theory)

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Quizzes Created: 1 | Total Attempts: 160
Questions: 10 | Attempts: 160

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• 1.

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

• A.

N/9

• B.

N/10

• C.

N/14

• D.

N/19

• E.

None of these

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

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• 2.

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

• A.

56

• B.

57

• C.

58

• D.

60

• E.

None of these

C. 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

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• 3.

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

• A.

8x+7

• B.

9x-3

• C.

11x-4

• D.

13x+1

• E.

13x

B. 9x-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).

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• 4.

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

• A.

Q(P+1)

• B.

2P+3Q

• C.

​PQ<sup style="color: rgb(102, 102, 102);">2

• D.

P2Q3

• E.

None of these

E. None of these
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.

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• 5.

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

• A.

3Q

• B.

Q

• C.

3

• D.

Q+3

• E.

None of these

C. 3
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.

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• 6.

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

• A.

A-20

• B.

A-12

• C.

A-9

• D.

A-10

• E.

None of these

D. A-10
Explanation
Just take the multiples of 11 such as 22,33,44 etc. & replace a by any of them in the choice options.

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• 7.

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

• A.

4

• B.

12

• C.

13

• D.

21

• E.

None of these

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

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• 8.

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

• A.

(a-b)/c

• B.

(a-c)/b

• C.

(b-c)/a

• D.

(c-b)/a

• E.

None of these

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

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• 9.

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

• A.

3

• B.

4

• C.

7

• D.

8

• E.

12

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

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• 10.

### 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.

• A.

4

• B.

3

• C.

2

• D.

1

• E.

None of these

C. 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.

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