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be divisible by 4, which will make
divisible by 2*4=8 (basically
if then will be divisible by 8*3=24).
(1) When 3x is divided by 2, there is a remainder. This implies that , which means that .
Therefore
is divisible by 8. Sufficient.
(2) x = 4y + 1, where y is an integer. We have that , thus is
divisible by 8. Sufficient.
Answer: D. Discuss this question HERE.
Example #8 (medium)
If x^3 ‐ x = n and x is a positive integer greater than 1, is n divisible by 8?
(1) When 3x is divided by 2, there is a remainder.
(2) x = 4y + 1, where y is an integer.
, notice that we have the product of three consecutive integers.
Now, notice that if , then and are consecutive even integers, thus one of them will also
be divisible by 4, which will make
divisible by 2*4=8 (basically
if then will be divisible by 8*3=24).
(1) When 3x is divided by 2, there is a remainder. This implies that , which means that .
Therefore
is divisible by 8. Sufficient.
(2) x = 4y + 1, where y is an integer. We have that , thus is
divisible by 8. Sufficient.
Answer: D. Discuss this question HERE.
Example #9 (hard)
When 51^25 is divided by 13, the remainder obtained is:
A. 12
B. 10
C. 2
D. 1
E. 0
, now if we expand this expression all terms but the last one will have in
them, thus will leave no remainder upon division by 13, the last term will be
. Thus the question
becomes: what is the remainder upon division ‐1 by 13? The answer to this question is 12: .
Answer: A. Discuss this question HERE.
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GMAT Club Math Book
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