BTGModeratorVI wrote: ↑Thu Nov 26, 2020 1:14 pm
If a certain positive two-digit number has tens' digit w and units' digit x, what is the value of w + x ?
(1) 20w + 4x = 44
(2) The product of w and x is 2.
Answer:
B
Source: GMAT prep
Given: The positive two-digit number has tens' digit w and units' digit x
Since 2-digit numbers do not have 0 in the tens position, we know that w can equal 1, 2, 3, 4, 5, 6, 7, 8 or 9
On the other hand, x can be any of the digits from 0 to 9
Target question: What is the value of w + x ?
Statement 1: 20w + 4x = 44
The first thing we should recognize is that w cannot be greater than 2, since 20w will be greater than 44 for values of w greater than 2.
This means EITHER w = 1 OR w = 2
Let's check each case...
Case a: w = 1.
We get: 20(1) + 4x = 44.
Solve to get: x = 6
So, it could be the case that w = 1 and x = 6, in which case the answer to the target question is
w + x = 1 + 6 = 7
Case b: w = 2.
We get: 20(2) + 4x = 44.
Solve to get: x = 1
So, it could be the case that w = 2 and x = 1, in which case the answer to the target question is
w + x = 2 + 1 = 3
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The product of w and x is 2
Since w and x are INTEGERS, there are exactly two possible solutions (w = 1 & x = 2 OR w = 2 & x = 1)
Let's examine each possible case:
Case a: w = 1 and x = 2. In this case, the answer to the target question is
w + x = 1 + 2 = 3
Case b: w = 2 and x = 1. In this case, the answer to the target question is
w + x = 2 + 1 = 3
Since those are the only possible cases, it MUST be the case that
w + x = 3
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
