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

[Guest]

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.

My Question: Answer is given as A. I understand why 1 is sufficient. However, I would like to clarify why 2 is not sufficient. My thinking is if s-c=.5s, then c=.5s; and answering the rephrased question (is c>s?), you can answer yes.

MGMAT Solution for statement 2:
S=Salary, C= Comission, I=total income

"(2) INSUFFICIENT: Either s - c = .5s or c - s = .5s. Coupled with our knowledge that s and c must add to 100% of the salesman's income, we can say that one of the two is worth 75% of the income and the other is worth 25%. However, we don't know which is the bigger number: s or c."

[StaceyKoprince]

First, a clarification: the rephrased question should be "is s>c?" not, as typed above, c>s. (It is worded correctly in our posted solution in the CAT exams.)

My thinking is if s-c=.5s, then c=.5s

This is only one of the two possibilities though - it could also be that c-s = .5s
If s-c=.5s, then c=.5s, then you answer the question "is s>c?" with a yes.
But if c-s = .5s, then c = 1.5s, and you would have to answer the question no.

If you get both a yes and a no from the same statement, then that statement is insufficient to solve the problem.

[shaji]

[b]The difference between A & B =A-B and the diference between B & A=B-A. This is the maths logic.

Perhaps this will help clear the confusion.


[/b]

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.

My Question: Answer is given as A. I understand why 1 is sufficient. However, I would like to clarify why 2 is not sufficient. My thinking is if s-c=.5s, then c=.5s; and answering the rephrased question (is c>s?), you can answer yes.

MGMAT Solution for statement 2:
S=Salary, C= Comission, I=total income

"(2) INSUFFICIENT: Either s - c = .5s or c - s = .5s. Coupled with our knowledge that s and c must add to 100% of the salesman's income, we can say that one of the two is worth 75% of the income and the other is worth 25%. However, we don't know which is the bigger number: s or c."

[Guest]

[quote="shaji"][b]The difference between A & B =A-B and the diference between B & A=B-A. This is the maths logic.

Perhaps this will help clear the confusion.

So does statement 2 translate to s-c = 0.5c OR it could also mean c-s = 0.5c in the above problem. If you consider s-c = 0.5c it is sufficient to answer the question.


Please explain.

[unique]

[quote="shaji"][b]The difference between A & B =A-B and the diference between B & A=B-A. This is the maths logic.

Perhaps this will help clear the confusion.

So does statement 2 translate to s-c = 0.5c OR it could also mean c-s = 0.5c in the above problem. If you consider s-c = 0.5c it is sufficient to answer the question.


Please explain.

[shaji]

Yes! indeed. This is how it should be, but GMAT, as you may be aware tricks ,you with GMAT logic.

Getting into the mind of the GMAT test setteris indeed key to answering questions 'correct' the GMAT way.

[b]The difference between A & B =A-B and the diference between B & A=B-A. This is the maths logic.

Perhaps this will help clear the confusion.

So does statement 2 translate to s-c = 0.5c OR it could also mean c-s = 0.5c in the above problem. If you consider s-c = 0.5c it is sufficient to answer the question.


Please explain.

[rkafc81]

[b]The difference between A & B =A-B and the diference between B & A=B-A. This is the maths logic.

Perhaps this will help clear the confusion.

this is not exactly true, if my understanding is correct. the difference is the absolute value of B - A or A -B , not B - A or A -B.

HOWEVER, if know B was larger than A, then you could write B - A as the difference between B and A. Same goes for A and B.

I also got fooled on the question by this math rule!

So I did some research on the net. And found this (which is THE key takeaway from this problem):

"In real life, the difference between a and b is |a-b| (or |b-a|, which is the same); differences are always positive.
"

this is the same idea as distance on a number line being positive always.

see more here:
http://mathforum.org/library/drmath/view/63137.html

[tim]

thanks!

[asharma8080]

I came across this one recently and had a question.

I understand the formula is C + S = I, Now, I got A as well but I went this path and I am trying to figure out WHY this is the wrong path:

I did this:
C+S = I,
Or, S = I -C
And, given:
1.3C + S = 1.1 (I)
Or, S = 1.1I - 1.3C

Therefore,
I - C = 1.1I-1.3C
Solving for C,
We get C = (1/3) I , therefore S=(2/3) I

However, the explanation find C = (1/2) S

What am I doing wrong here? Is it wrong to assume that 1.3C + S = 1.1 I?

Edit: I actually figured it out, I am doing it right but I am comparing I and C instead of C and S. Once I have C = 1/3 I and S = 2/3 I , I know that S is two times C.

[karizmaticafroz]

Hi I just happened to come across this question. And i see that both the statements are insufficient alone and together.

1) If the amount of the commission had been 30 percent higher, the salesman's income would have
been 10 percent higher last year.

Now the typical equation we would frame for this is

1.1(Base+comm)=base+1.3comm.

But we are missing one important point here...only the base is common..the commission amount is variable and so it should be

1.1(base+comm1)=base+1.3comm2

Hence Insufficient.

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.

|base-comm|=0.5base

Notice this is only the difference or absolute value. If we can consider do different things here

base-comm=0.5base
comm-base=0.5base

Both give a different answer. Hence Insufficient again.

1+2 (Combination)

Answer cannot be determined even after combining as it will still give lot of unknown varaibles.

So my answer is E .
Please let me know if my approach is wrong.

[RonPurewal]

Hi I just happened to come across this question. And i see that both the statements are insufficient alone and together.

1) If the amount of the commission had been 30 percent higher, the salesman's income would have
been 10 percent higher last year.

Now the typical equation we would frame for this is

1.1(Base+comm)=base+1.3comm.

that's the correct equation.

But we are missing one important point here...only the base is common..the commission amount is variable and so it should be

1.1(base+comm1)=base+1.3comm2

no.
we're not talking about two different commissions. we're talking about (i) last year's actual commission vs. (ii) whatever would be 30% greater than last year's actual commission.
so your first equation is correct.

analogy:
I scored N points in yesterday's game. If I had scored just 20% more points, we would have won.
--> I'm talking about scoring 1.2N points here, not 1.2 times some random new number.