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.

please explain why salary - commission is in absoulute value sign?

Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE


_________________

hi,

the above highlited part is wrong.
in that you are assuming salary = comission = 100
if both are equal how can you compare which one is bigger.

let say salary = \(s\)
comission =\(c\)

\(1.1(s + c) = s + 1.3 c\)
\(1.1s + 1.1c = s + 1.3 c\)
taking s items one side and c item one side
\(0.1s = 0.2c\)
ok now multiply both sides with 10
\(s = 2c\)

hope its clear now
_________________

My 2 cents
from question stem: commission + base = 1

for statement 1,
-> 1.3base + commission = 1.1
plus 1base + commission = 1
-> 0.3 base = 0.1
-> base = 33%
-> sufficient

for statement 2,
-> base - commission = 0.5base
or
-> commission - base = 0.5base
-> base is equal 50% or 33%
-> not greater than 50%
-> not suffificent

-> Correct Answer is A

JMO, please correct me if there is any logical flaw. Thanks very much!

For statement 1, why can we assume that the base salary stays the same? i.e no percent change associated with base salary. If only the commission had been 30% higher, then the answer would be A, but what if the base salary could be, for example, 20% lower? Wouldn't the answer then be E?

Thanks

Can we also solve this problem via average weight logic?

Income increased by %10 when the commission is increased by %30. If commission and base salary were equal, then income would increase by %15 since base salary has %0 increase and the commision has %30 increase. (0+30)/2 = 15.

Since it is increased by %10, base salary (which has %0 increase) pulls it, meaning weight of S > C

Hi GouthamNandu,

The prompt never stated whether the base salary was larger than the commission or the commission was larger than the base salary, so we CANNOT assume that the base salary is bigger just because it was mentioned first in the sentence. The word "difference" implies that one of them IS bigger, but we don't know which one. Bunuel addresses this point in one of his posts.

GMAT assassins aren't born, they're made,
Rich
_________________

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?

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:

RELATED VIDEO

_________________

In Option A

How did u get {salary}=2{commission}. Please help