p, q, and r are positive integers. If p, q, and r are assembled into

Question

p, q, and r are positive integers. If p, q, and r are assembled into the six-digit number pqrpqr, which one of the following must be a factor of pqrpqr?

(A) 23
(B) 19
(C) 17
(D) 7
(E) none of the above

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IanStewart · Accepted Answer

The six-digit number PQRPQR, where P, Q and R are the digits of the number, is equal to PQR*1000 + PQR = PQR(1000 + 1) = 1001*PQR. So the number must be divisible by 1001, which has no obvious divisors, but if you notice 1001 = 980 + 21 = 7(140 + 3) = 7*11*13, you can see that 7, 11 and 13 will all need to be divisors of PQRPQR, and 7 is the only divisor among the answer choices.

desertEagle · Answer

pqrpqr = 1001 x pqr

1001 = 7x11x13

pqrpqr is a factor of 7, 11, 13, 77, 91, 143, 1001

So answer is D

chetan2u · Answer

pqrpqr = pqr*1001 = pqr*7*11*13

7 is in the choices.

D

Similar question
 https://gmatclub.com/forum/a-b-and-c-are-positive-integers-if-a-b-and-c-are-assembled-into-t-187529.html

Crytiocanalyst · Answer

pqrpqr = pqr*(1001)

= pqr*7*11*13

THerefore IMO D

KashishGandhi · Answer

I assumed p=q=r=1. Then the number becomes 111,111. I started with the simplest divisor 7 and 111,111 is a multiple of 7. None of the other options are divisors of 111,111.
Therefore (D)

p, q, and r are positive integers. If p, q, and r are assembled into

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p, q, and r are positive integers. If p, q, and r are assembled into

Prep Toolkit

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

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