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Re: 12 Days of Christmas GMAT Competition - Day 8: ‘PQ’ represents a two-
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21 Dec 2021, 07:12
Given: ‘PQ’ represents a two-digit number.
Asked: What is the remainder when PQ is divided by 3?
(1) P*Q = 18.
If P=2; Q=9; 'PQ' = 29; the remainder when PQ is divided by 3 = 1
If P=3; Q=6; 'PQ' = 36; the remainder when PQ is divided by 3 = 0
If P=6; Q=3; 'PQ' = 63; the remainder when PQ is divided by 3 = 0
If P=9; Q=2; 'PQ' = 92; the remainder when PQ is divided by 3 = 2
NOT SUFFICIENT
(2) P + 2 leaves remainder 1 when divided by 3 and Q + 1 leaves remainder 2 when divided by 3.
P + 2 leaves remainder 1 when divided by 3
P + 2 = 3k + 1; where k is an integer
P = 3k - 1 = 2, 5 or 8
Q + 1 leaves remainder 2 when divided by 3
Q + 1 = 3m + 2; where m is an integer
Q = 3m + 1 = 1, 4 or 7
If P = 2; Q = 1; 'PQ' = 21; the remainder when PQ is divided by 3 = 0
If P = 5; Q = 1; 'PQ' = 51; the remainder when PQ is divided by 3 = 0
If P = 8; Q = 1; 'PQ' = 81; the remainder when PQ is divided by 3 = 0
If P = 2; Q = 4; 'PQ' = 24; the remainder when PQ is divided by 3 = 0
If P = 5; Q = 4; 'PQ' = 54; the remainder when PQ is divided by 3 = 0
If P = 8; Q = 4; 'PQ' = 84; the remainder when PQ is divided by 3 = 0
If P = 2; Q = 7; 'PQ' = 27; the remainder when PQ is divided by 3 = 0
If P = 5; Q = 7; 'PQ' = 57; the remainder when PQ is divided by 3 = 0
If P = 8; Q = 7; 'PQ' = 87; the remainder when PQ is divided by 3 = 0
If all possible cases, the remainder when PQ is divided by 3 = 0
SUFFICIENT
IMO B