If A = 8B + 22 and B is a positive integer, then A is not divisible by which of the following?
options : a. 4 b. 2 c. 6 d. 7 e. none
Answers
Answer:
None None None None None
Answer:
If the remainder is 7 when positive integer n is divided by 18, what is the remainder when n is divided by 6?
A. 0
B. 1
C. 2
D. 3
E. 4
When positive integer n is dived by 18 the remainder is 7: .
Now, since the first term (18q) is divisible by 6, then the remainder will only be from the second term, which is 7. 7 divided by 6 yields the remainder of 1.
Answer: B. Discuss this question HERE.
Example #2 (easy)
If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12 ?
A. 0
B. 1
C. 2
D. 3
E. 5
There are several algebraic ways to solve this question, but the easiest way is as follows: since we cannot have two correct answers just pick a prime greater than 3, square it and see what would be the remainder upon division of it by 12.
If , then . The remainder upon division 25 by 12 is 1.
Answer: B. Discuss this question HERE.
Example #3 (easy)
What is the tens digit of positive integer x ?
(1) x divided by 100 has a remainder of 30.
(2) x divided by 110 has a remainder of 30.
(1) x divided by 100 has a remainder of 30. We have that : 30, 130, 230, ... as you can see every such number has 3 as the tens digit. Sufficient.
(2) x divided by 110 has a remainder of 30. We have that : 30, 140, 250, 360, ... so, there are more than 1 value of the tens digit possible. Not sufficient.
Answer: A. Discuss this question HERE.
Example #4 (easy)
What is the remainder when the positive integer n is divided by 6?
(1) n is multiple of 5
(2) n is a multiple of 12
(1) n is multiple of 5. If n=5, then n yields the remainder of 5 when divided by 6 but if n=10, then n yields the remainder of 4 when divided by 6. We already have two different answers, which means that this statement is not sufficient.
(2) n is a multiple of 12. Every multiple of 12 is also a multiple of 6, thus n divided by 6 yields the remainder of 0. Sufficient.
Answer: B. Discuss this question HERE.
Example #5 (medium)
If s and t are positive integers such that s/t = 64.12, which of the following could be the remainder when s is divided by t ?
A. 2
B. 4
C. 8
D. 20
E. 45
divided by yields the remainder of can always be expressed as: (which is the same as ), where is the quotient and is the remainder.
Given that , so according to the above , which means that must be a multiple of 3. Only option E offers answer which is a multiple of 3
Answer. E. Discuss this question HERE.
Step-by-step explanation:
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