Math Exam - 1 (Number Theory)
(95).webp "Math Exam - 1 (Number Theory) - Quiz")
This Math Exam - 1 focuses on Number Theory, including problems on divisibility, consecutive integers, and properties of prime numbers.
- 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
Correct Answer
B. N/10Explanation
n is not divided by 5, how can n be divided by 10? So, n/10 can not be integer ever.Rate this question:
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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
Correct Answer
C. 58Explanation
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=58Rate this question:
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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
Correct Answer
B. 9x-3Explanation
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).Rate this question:
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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
Correct Answer
E. None of theseExplanation
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.Rate this question:
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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
Correct Answer
C. 3Explanation
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.Rate this question:
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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
Correct Answer
D. A-10Explanation
Just take the multiples of 11 such as 22,33,44 etc. & replace a by any of them in the choice options.Rate this question:
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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
Correct Answer
C. 13Explanation
Only 13 is a prime among them which is odd(strange).Rate this question:
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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
Correct Answer
D. (c-b)/aExplanation
Very simple, just a+b=c, or a=c-b & so (c-b)/a=a/a=1.Rate this question:
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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
Correct Answer
C. 7Explanation
If 10 is being divided by 7, then the remainder is 3 which is 7-4 that means n-4.Rate this question:
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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
Correct Answer
C. 2Explanation
Here, n=3p+1 = 3(5q+2)+1=15q+6+1=(15q+5)+2; (15q+5) is divisible by 5, so remainder is 2.Rate this question:
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May 22, 2024Quiz Edited by
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Feb 25, 2016Quiz Created by
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