Word Problem

Roland2rule wrote:A restaurant meal cost $35.50 and there was no tax. If the tip was more than 10 percent but less than 15 percent of the cost of the meal, then total amount paid must have been between:

A. $40 and $42
B. $39 and $41
C. $38 and 40
D. $37 and $39
E. $36 and $37

Let's first see what happens when the tip is 10%
10% of $35.50 = $3.55
So, the total cost (WITH a 10% tip) = $35.50 + $3.55 = $39.05
So, the total cost must be GREATER THAN $39.05
This means the TOTAL cost could be $39.06
Check the answer choices....
A, D and E do not allow for the total cost to be $39.06, so we can ELIMINATE them.

Looks like we need to consider the 15% option as well.
If 10% of $35.50 = $3.55, then 5% of $35.50 = a little more than $1.75
So, a 15% tip ≈ $3.55 + $1.75 ≈ $5.30
So, the total cost (WITH a 15% tip) = $35.50 + $5.30 ≈ $40.80
So, the total cost must be LESS THAN $40.80
This means the TOTAL cost could be $40.20
Check the answer choices....
C does not allow for the total cost to be $40.20, so we can ELIMINATE C.

Answer: B

ASIDE: Here's an article about calculating percentages in your head: https://www.gmatprepnow.com/articles/me ... -percent-y

Cheers,
Brent

BTGmoderatorRO wrote:A restaurant meal cost $35.50 and there was no tax. If the tip was more than 10 percent but less than 15 percent of the cost of the meal, then total amount paid must have been between:

A. $40 and $42
B. $39 and $41
C. $38 and 40
D. $37 and $39
E. $36 and $37

OA is B
Can someone gimme the mathematical approach to this question? I would really appreciate the work of an expert.

To solve, we can set up two expressions, one for a tip of 10% and another for a tip of 15%. Remember, the quickest way to determine the total cost with tip is to use "percent greater." Thus, when the tip is 10% we can multiply 35.50 by 1.10 and when the tip is 15% we can multiply by 1.15.

For 10%: $35.5 x 1.10 = $39.05

For 15%: $35.5 x 1.15 ≈ $40.83

These two values fall between $39 and $41.

Answer: B