If p and q are positive integers such that qp, what is the remainder

Question

If p and q are positive integers such that q > p, what is the remainder when q is divided by p?

(1) q = pm + 4, where m is a positive integer.
(2) p < 4

gmatophobia · Answer

Question  : What is the remainder when q is divided by p?

Statement 1

(1) q = pm + 4, where m is a positive integer.

Assume p = 5 and m = 4 ⇒ q = 24.
Remainder ( \frac{24}{5} ) = 4 
 Assume p = 4 and m = 4 ⇒ q = 20.
Remainder ( \frac{20}{4} ) = 0

Hence, the statement is not sufficient. We can eliminate A and D.

Statement 2

(2) p < 4

We don't have any information on q. Hence, the statement is not sufficient.

Eliminate B.

Combined

Assume p = 2 and m = 4 ⇒ q = 12.
Remainder ( \frac{12}{2} ) = 0 
 Assume p = 3 and m = 3 ⇒ q = 13.
Remainder ( \frac{13}{3} ) = 1

The statement combined is not sufficient.

Option E

Bunuel · Answer

Similar questions to practice: https://gmatclub.com/forum/if-x-and-y-a ... 97243.html https://gmatclub.com/forum/if-j-and-k-a ... 01663.html Hope it helps.

unraveled · Answer

If p and q are positive integers such that q > p, what is the remainder when q is divided by p?

(1) q = pm + 4, where m is a positive integer.
Two variables many possibilities.
1. q = 32, p = 7, m = 4, r = 4
2. q = 30, p = 2, m = 13, r = 0

INSUFFICIENT.

(2) p < 4
Nothing about q so two variables with infinite possibilities.

INSUFFICIENT.

Together 1 and 2
1. q = 30, p = 2, m = 13, r = 0 
2. q = 28, p = 3, m = 24, r = 1

INSUFFICIENT.

Answer E.

vatsal240102 · Answer

Why is statement 1 insuff. Isn't it of the form Dividend=Divisor(Quotient) + Remainder?

unraveled · Answer

You got it right when you say that. But don't you think that why would GMAT or any standardised test ask for a remainder by giving a simple "Dividend=Divisor(Quotient) + Remainder" form. If it's given in such a form and asks for a simple(as it looks in the first impression) remainder, then questions must be raised. Even after that if you don't understand then look clearly in the St. 1 and think of 4 which is remainder here as it looks like(more so when m too is an integer). Here, there are three variables q,p and m. Assuming two would give us the third. So, with two variables(p and m) having infinite possibilities, there is high chances of getting infinite number of remainder when the third variable is divided by one of the two - in our case when q is divided by p. But we need only two different values of remainder to make it insufficient. The statement in that form is just for trapping the over-smartness.

HTHs.

vatsal240102 · Answer

I get your point about it being too direct but according to Question stem & Statement 1, theoretically shouldn't it be true that the values of p,q & m will always be such that the remainder has to be 4? How do we disprove it to eliminate A

unraveled · Answer

m should not have been a variable here which you are missing i guess and instead focused on remainder being 4. If m's value is fixed then what you say is right. Otherwise, whenever there are variables to deal with be more cautious.

If p and q are positive integers such that q>p, what is the remainder

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

If p and q are positive integers such that q>p, what is the remainder

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards