GMAT Number Theory

Question

If n is a positive integer, then the remainder when n^7-n is divided by 7 is

Possible Answers

Selected	Possible Answer
	A. 3
	B. 0
	C. 5
	D. 4
	E. None

Question

If $n\in N$ then $n^{13} - n$ is always divisible by

Possible Answers

Selected	Possible Answer
	A. 13
	B. 16
	C. 15
	D. 14
	E. None

Question

If $n\in N$ then $n^{15} - 14n^3 + 26$ is always divisible by

Possible Answers

Selected	Possible Answer
	A. 19
	B. 13
	C. 15
	D. 17
	E. None

Question

If $n\in N$ then the remainder when n^8 - n^2+5 is divided by 7 is

Possible Answers

Selected	Possible Answer
	A. 5
	B. 0
	C. 3
	D. 4
	E. None

Question

Which of the following is a multiple of 5, $\forall n\in N$ ?

Possible Answers

Selected	Possible Answer
	A. $\quad n^6-n^2+10$
	B. $\quad n^{15}-n^{13}+25$
	C. $\quad n^5-n-25$
	D. $\quad n^{13}-n^{15}+35$
	E. None

Question

Which of the following is a multiple of 6, $\forall n\in N$ ?

Possible Answers

Selected	Possible Answer
	A.
	B.
	C.
	D.
	E. none

Question

$ab \equiv ac (mod-m) \Rightarrow b \equiv c (mod-m)$ is true only when

Possible Answers

Selected	Possible Answer
	A. and are co-prime
	B. and are relatively prime
	C. greatest common divisor of and is ‘1’
	D. Both (B) & (C)
	E. None

Question

The remainder when $n^{17}-18n+35$ is divided by 17 is

Possible Answers

Selected	Possible Answer
	A. 1
	B. 7
	C. 5
	D. 11
	E. None

Question

The remainder when $n^{12}-12n^2+132$ is divided by 11 is

Possible Answers

Selected	Possible Answer
	A. 11
	B. 7
	C. 0
	D. 9
	E. None

Question

If $n\in N$ then $(n^{10}-1)n$ is always a multiple of

Possible Answers

Selected	Possible Answer
	A. 9
	B. 7
	C. 11
	D. 10
	E. None

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GMAT Number Theory

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