A certain salesman's yearly income is determined by a base salary plus

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

Dear Bunuel,

I'm not sure if you need to consider two cases here based on the question's second statement.
It is like stating " if the difference between A and B is 4, I would consider A-B = 4 and not |A-B| =4.

The similar question, which you used to merge the topic clearly specifies that the absolute difference between the base salary and the commission is..., there I can understand the two cases but not for the question above, where it does not state anything about the absolute difference.

Please correct if I'm wrong.

Hi santorasantu,

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. THAT is why Bunuel addressed it.

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

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

Hi stopchange,

The specific question that is asked refers to a base salary and a commission LAST YEAR, so we're dealing with 2 unknowns, NOT 2 variables. This means that the two numbers are constants, but we do NOT know what they are (and thus, we don't know which one is bigger).

Fact 1 uses a 'hypothetical' that points out that increasing JUST the commission (by 30%) would have led to an increase in income (of 10%). By extension, this assumes that the other pieces (in this case, the base salary) stay the same.

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

I am not still satisfied with the explanation given above.How can we assume 2 cases when it is mentioned in statement (2) that difference between the amount of salesman's base salary and the the amount of commission was equal to 50 percent of the salesman's base salary last year.

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 base salary larger than his commission 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 B greater than C?

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, B is greater than C
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 B is NOT greater than C
Case b: C - B = -0.5B. When we solve this for C, we get C = 0.5B, which means B IS greater than C
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

RELATED VIDEO

In Option A

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

1.1({salary} + {commission}) = {salary} + 1.3{commission};

1.1{salary} + 1.1{commission} = {salary} + 1.3{commission};

0.1{salary} = 0.2{commission};

{salary}=2{commission}.

Hope it's clear.

Approximation using critical reasoning here

1. Question Stem is having "base salary account for more than half of the salesman's yearly income last year".
so i need prove the same, in order to solve this question.

statement 1. it is understood that after increasing 30% commission overall salary increased by 10% - meant base salary is larger than commission.

Sufficient

Statement 2. this statement is talking about difference of both is 50%..... blah blah. and clearly stated indirectly that it is not sufficient.

hence answer is A.

trust it make sense GMATPrepNow?

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.

____________________________________________________

from the question, we know base + commission = total
Base = b
commision = c
total = t

from the statement 1,
1.3c + b = 1.1c + 1.1b
--> 0.2c = 0.1b
--> 2c = b
clearly, b > c.
sufficient

from the statement 2,
b-c = 0.5b
--> 0.5b = c
--> b = 2c
therefore b > c.
sufficient

the answer is D

Hi h31337u,

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 earlier in the sentence in Fact 2. 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.

Algebraically, this means that there are TWO possibilities:

B - C = 0.5B

OR

C - B = 0.5B

These two equations will lead to different results (and different answers to the question that is asked), so Fact 2 is INSUFFICIENT.

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

Manhattans OE:

Let s be the salesman's base salary, and let c be his total commission. From the question stem we can phrase the question as:

Is c > s?

(1) SUFFICIENT: The salesman's total income is defined as s + c. This allows us to construct the following equation:

1.1( s + c) = s + 1.3 c

This gives us:
1.1 s + 1.1 c = s + 1.3 c

0.1 s = 0.2 c

Therefore c is one half the size of the salesman's base salary — and both numbers must be non-negative. This implies that the salary must account for two-thirds of the income. Thus we can answer definitively that the commission was not larger than his salary — indeed the opposite is true.

(2) INSUFFICIENT: Either s – c = .5 s or c – s = .5 s. We can say that one of the two is larger but we don't know which.

The correct answer is A.

Should'nt the second statement say the absolute difference between base and commision for us to employ modulus?
I want to know if on gmat the question reads that ..... the difference between a and b is bla bla should i equate a-b = bla bla or should i use |a-b|=bla bla or should i look out for something to tell the difference

Hi Deeptanshu02,

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 earlier in the sentence in Fact 2. The word "difference" implies that one of them IS bigger, but we don't know which one.

If you find that you are not sure about the exact meaning of a phrase in a Quant question, then it can sometimes help to create a simple example to define whether a pattern exists or not. For example:

The difference between Tom's net worth and Mark Zuckerberg's net worth is approximately 85 billion dollars....

So who has a higher net worth? Tom or Mark Zuckerberg?

Tom appears first in the sentence, but Mark Zuckerberg is the one who has the higher net worth. In simple terms, the modulus is 'implied' (and it does not matter who is first in the sentence).

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

"The difference between Tom's net worth and Mark Zuckerberg's net worth is approximately 85 billion dollars....
" Well the statement implies its T-M=85billion dollar if we dont know whose net worth is bigger shouldnt we say that the absolute difference between Tom's net worth and Mark Zuckerberg's net worth is approximately 85 billion dollars.... or if we know whose bigger it should be difference between mark and toms net worth either way my opinion does'nt matter on GMAT What matter is how GMAC thinks so does GMAC Cosnider the sentence construction in red and in green the same?