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

Question

A certain salesman's yearly income is determined by a base salary plus a commission on the sales he makes during the year. Was the salesman's commission larger than his base salary last year?

(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.

(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.

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hr1212 · Answer

Let income be I, base salary be BS and commission be C then, I = BS + C
Was C > BS?

Statement 1 - 1.1I = BS + 1.3C

Multiplying first equation by 1.1 and equating both the equations,

1.1BS + 1.1C = BS + 1.3C
0.1BS = 0.2C
BS = 2C

C > BS => No

Hence, this statement is sufficient.

Statement 2 - |BS - C| = BS/2

BS/2 = C
BS = 2C

or

3BS/2 = C
BS = 2C/3

C > BS => Maybe

Hence, this statement is insufficient.

Answer: A

*Edited explanation

iamchinu97 · Answer

No answers should be A

statement 2 is talking about absolute difference and not the normal difference

so |BS-C| = BS/2

case 1: BS-C = BS/2
C= BS/2
C<BS

case 2: C-BS = BS/2 
C= 3BS/2
C=1.5BS
C>BS

So statement 2 is Insuffiecient.

bb  please update the answer.

hr1212 · Answer

Right! Thanks for pointing out. Missed the absolute difference, edited the explanation.

Usernamevisible · Answer

Let:

* Base salary = S
* Commission = C

We need to know:

C > S ?

---

Statement (1)

“If the commission had been 30% higher, the total income would have been 10% higher.”

Translate carefully.

Original income:

S + C

New commission:

1.3C

New total income:

S + 1.3C

This new total is 10% higher than original:

S + 1.3C = 1.1(S + C)

Simplify:

S + 1.3C = 1.1S + 1.1C

1.3C − 1.1C = 1.1S − S

0.2C = 0.1S

2C = S

C = S/2

So commission is LESS than salary.

Question: was commission larger than salary?

Answer: NO.

Statement (1) is sufficient.

---

Statement (2)

“The absolute difference between salary and commission was 50% of salary.”

Translate:

|S − C| = 0.5S

Now split cases.

Case 1: S > C

S − C = 0.5S

C = 0.5S

Commission smaller.

---

Case 2: C > S

C − S = 0.5S

C = 1.5S

Commission larger.

---

Both are possible.

Statement (2) is NOT sufficient.

---

Final Answer

A

Statement (1) alone is sufficient, but statement (2) alone is not sufficient.

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

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GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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My Rewards