If p^2, a perfect square number, is divisible by 5, and q, an integer,

Question

If  p^2 , a perfect square number, is divisible by 5, and q, an integer, is not divisible by 5, which of the following must be divisible by 10?

(A)  pq + 5

(B)  p + q

(C)  2(p + 5q)

(D)  2(5p + q)

(E)  p^2 + 5q

CrackverbalGMAT · Answer

p can either be a multiple of 5 or10 so that  p^2  is divisible by 5 and q has to be an even or odd number (if odd it should not be a multiple of 5)

What we can try to do is see if we can prove that a certain Option is Not true (Not divisible by 10) for any of the combinations of p and q

Option 1:   pq + 5. If p = 5 and q = 2, then pq + 5 = 15. Not True.

Option 2:   p + q. If p = 5 and q = 2, then p + q = 7. Not True.

Option 3:   2(p + 5q)

p = 5, q = 2 then 2(5 + 10) = 30. True

p = 5, q = 3 then 2(5 + 15) = 40. True

p = 10, q = 2 then 2(10 + 10) = 40. True

p = 10, q = 3 then 2(10 + 15) = 50. True

We can prove that the other 2 options are not true as we have done for Options 1 and 2, but it is not necessary.

Option C

Arun Kumar

IanStewart · Answer

We have no information at all about whether p and q are even or odd, but we're looking for an answer divisible by 10, so an answer that is certainly even. The only candidates are C and D.

The answer must also be divisible by 5. We know p is divisible by 5, since p^2 is. q is not divisible by 5, but 5q clearly is, and p + 5q is the sum of two multiples of 5, so must also be a multiple of 5. So 2(p + 5q) will be a multiple of 10, and C is the answer.

rocky620 · Answer

Stem 1:  p^2 is a divisible by 5 means p is either a multiple of 5 or 10.
 Stem 2:  q is not divisible by 5 means it any be any number not ending with 5 or 0.

Answer choice analysis:

(A) pq+5 - can never be true as the number will never end in a zero

(B) p+q - can never be true, as q is not a multiple of 5

(C) 2(p+5q) - this will always be true, as 2p will always end with a zero (as p is a multiple of 5 or 10) and 10q will definitely end in zero. so their sum will always be divisible by 10.

(D) 2(5p+q) - can never be true because of q

(E) p^2+5q - can be true in only some cases (when p is a multiple of 10 and q is an even number)

Hence C is the answer

Harsh9676 · Answer

IMO C

P^2 = a perfect square and a multiple of 5

P^2 = 25, 125 , 625, ........... (P = 5, 15, 25........)

q = an integer not a multiple of 5

Multiples of 10 - The units digit = 0

A. pq + 5 >>>> 5 (4) + 5 = 25 >> not a multiple of 10
B. P + q >>>>> 5 + 1 = 6 >> not a multiple of 10
C. 2(p+5q) >>> 10 p + 10 q >> Always a multiple of 10

(D) 2(5p+q) >> 10 P + q >>> q can be 1, 2, 3, >> need not be a multiple of 10

(E) p^2+5q >>> 125 + 5 (2) = 135 >> not a multiple of 10

If p^2, a perfect square number, is divisible by 5, and q, an integer,

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If p^2, a perfect square number, is divisible by 5, and q, an integer,

Prep Toolkit

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