Last year the range of the annual salaries of the 100 employ

BTGmoderatorDC wrote:Last year the range of the annual salaries of the 100 employees at Company X was $30,000. If the annual salary of each of the 100 employees this year is 10 percent greater than it was last year, what is the range of the annual salaries of the 100 employees this year?

(A) $27,000
(B) $30,000
(C) $33,000
(D) $36,000
(E) $63,000

OA C

Source: GMAT Prep

Hey BTGmoderatorDC,
You posted this question 2 months ago: https://www.beatthegmat.com/last-year-t ... 06593.html

Cheers,
Brent

BTGmoderatorDC wrote:Last year the range of the annual salaries of the 100 employees at Company X was $30,000. If the annual salary of each of the 100 employees this year is 10 percent greater than it was last year, what is the range of the annual salaries of the 100 employees this year?

(A) $27,000
(B) $30,000
(C) $33,000
(D) $36,000
(E) $63,000

OA C

Source: GMAT Prep

A quick solution is to assign some values to the highest paid and lowest paid workers

Let $10,000 = the lowest salary LAST YEAR
Let $40,000 = the highest salary LAST YEAR
This satisfies the condition that the range LAST YEAR = $30,000

If the annual salary of each of the 100 employees this year is 10 percent greater than it was last year, . . .
(1.1)($10,000) =$11,000, so the lowest salary is NOW $11,000
(1.1)($40,000) =$44,000, so the lowest salary is NOW $44,000

. . . what is the range of the annual salaries of the 100 employees this year?
Range = $44,000 - $11,000 = $33,000

Answer: C

A faster solution is to recognize that if EACH PERSON gets a 10% increase, then the range will increase by 10%
So, the $30,000 range increases by 10% to $33,000

Cheers,
Brent

BTGmoderatorDC wrote:Last year the range of the annual salaries of the 100 employees at Company X was $30,000. If the annual salary of each of the 100 employees this year is 10 percent greater than it was last year, what is the range of the annual salaries of the 100 employees this year?

(A) $27,000
(B) $30,000
(C) $33,000
(D) $36,000
(E) $63,000

OA C

Source: GMAT Prep

We can let the lowest salary from last year = 10,000 and the highest = 40,000. (Note that we could use any two values, as long as their difference is $30,000.)

Thus, the new low salary is 1.1 x 10,000 = 11,000 and the new high salary is 40,000 x 1.1 = 44,000.

So the new range is 44,000 - 11,000 = 33,000.

Alternate Solution:

We can let x = the lowest salary last year and thus x + 30,000 = the highest salary last year. Since each of the employees’ salaries increased by 10% this year from last year, the lowest salary this year is 1.1x and the highest salary this year is 1.1(x + 30,000) = 1.1x + 33,000. Therefore, the range of salaries this year is:

1.1x + 33,000 - 1.1x = 33,000.

Answer: C