Official Solution:
Statement 1: This statement yields three possibilities for P, Q, and R, in some order: {1, 3, 5}, {3, 5, 7}, {5, 7, 9}; it makes no difference which of P, Q, and R is which digit, because they are all added together.
• If P, Q, and R are 1, 3, and 5 (in whatever order), then the digit T must be 1. This means the digits aren't distinct, so it is impossible.
• If P, Q, and R are 3, 5, and 7 (in whatever order), then T= I. That means S is one of the leftover digits O, 2, 4 6, 8, 9. If these values are plugged into S one at a time, the only one that yields all distinct digits is S -4 (34 + 54+74=162).
• If P, Q, and R are 5, 7, and 9 (in whatever order), then T = 2. That means S is one of the leftover digits O, 1, 3, 4, 6, 8. If these values are plugged into S one at a time, the only one that yields all distinct digits is S = 8 (58 + 78 + 98 = 234).
• Therefore, there are only two possible values of TUV: 162 and 234. In both cases, the sum of T, U, and V is 9,
so
(I) is sufficient. Statement 2:
If T = 2, then trial and error will yield a number of working sets of digits yielding different values for TUV. Examples: 58 + 68 + 78 = 204 (T+ U + V = 6); 41 + 71 + 91 203 ( T+ U + V = 5); 49+69 +89 207 (T+ U + V = 9); and several others.
Therefore,
(2) is insufficient.
Answer Agmatbusters
Weekly Quant Quiz Question -10
If the given addition is correct, what is the sum of T, U and V?
P, Q, R, S, T, U and V are distinct digits. Attachment:
Gmatbusters Quiz -2.jpeg
a) P, Q and R are consecutive odd integers.
b) T = 2ONLY THE TEXT SOLUTIONS ARE ALLOWED