In the correctly worked addition problem shown, P, Q, R, and S are digits.
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(A) 3
(B) 2
(C) 1
(D) 1
(E) 2
OA A
Source: Official Guide
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For this question, it's best to use number sense.BTGmoderatorDC wrote: ↑Fri Nov 18, 2022 4:35 am#gmatclub.jpg
In the correctly worked addition problem shown, P, Q, R, and S are digits. If Q = 2P, which of the following could be the value of S ?
(A) 3
(B) 2
(C) 1
(D) 1
(E) 2
OA A
Source: Official Guide
However, we can also solve this question algebraically
Key property: The VALUE of the 3digit integer abc can be written as follows: abc = 100a + 10b + c
For example: 625 = 100(6) + 10(2) + 5
Likewise: 3P5 = 100(3) + 10(P) + 5, 4QR = 100(4) + 10(Q) + R, and 8S4 = 100(8) + 10(S) + 4
So the addition, 3P5 + 4QR = 8S4 can be written algebraically as: (300 + 10P + 5) + (400 + 10Q + R) = 800 + 10S + 4
Simplify: 705 + 10P + 10Q + R = 804 + 10S
Subtract 705 from both sides to get: 10P + 10Q + R = 99 + 10S
Subtract 10S from both sides: 10P + 10Q  10S + R = 99
Subtract R from both sides: 10P + 10Q  10S = 99  R
Factor the left side: 10(P + Q  S) = 99  R
Finally, since we're told that Q = 2P, we can substitute to get: 10(P + 2P  S) = 99  R
Simplify: 10(3P  S) = 99  R
Since 10(3P  S) is a multiple of 10, and since R is a digit, we know that R must equal 9
We get: 10(3P  S) = 99  9 = 90
Now take: 10(3P  S) = 90
Divide both sides by 10 to get: 3P  S = 9
Rearrange to get: S = 3P  9
Factor to get: S = 3(P  3)
This means S is a multiple of 3
Check the answer choices..... answer choice A (3) is the only multiple of 3
Answer: A
Cheers,
Brent