ktrout2020 wrote:A certain salesman's yearly income is determined by a base salary plus a commission on the sales he makes during the year. Did the salesman's base salary account for more than half of the salesman's yearly income last year?
(1) If the amount of the commission had been 30 percent higher, the salesman's income would have been 10 percent higher last year.
(2) The difference between the amount of the salesman's base salary and the amount of the commission was equal to 50 percent of the salesman's base salary last year.
Source: Manhattan Prep
Target question: Was the salesman's commission larger than his base salary last year?
This is a good candidate for
rephrasing the target question.
Let B = base salary last year
Let C = commission last year
So, B+C = TOTAL income last year
REPHRASED target question: Is C greater than B?
Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
Statement 1: If the amount of the commission had been 30 percent higher, the salesman's total income (salary plus commission) would have been 10 percent higher last year.
If we increase the commission by 30% the NEW commission = 1.3C, which means the TOTAL income = 1.3C + B
This NEW income is 10%
greater than the actual TOTAL income (B+C)
We can write: 1.3C + B = 1.1(B + C)
Expand: 1.3C + B = 1.1B + 1.1C
Rearrange to get: 0.2C = 0.1B
Make "prettier" by multiplying both sides by 10 to get: 2C = 1B
Since C and B are both POSITIVE, we can see that B must be greater than C (since B is equal to C+C)
Another way say this is,
C is NOT greater than B
Since we can answer the
REPHRASED target question with certainty, statement 1 is SUFFICIENT
Statement 2: The absolute difference between the amount of the salesman's base salary and the amount of the commission was equal to 50 percent of the salesman's base salary last year.
We can write: |C - B| = 0.5B
This gives us two possible cases:
Case a: C - B = 0.5B. When we solve this for C, we get C = 1.5B, which means
C is greater than B
Case b: C - B = -0.5B. When we solve this for C, we get C = 0.5B, which means
C is NOT greater than B
Since we cannot answer the
REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
