Problem Solving

JJMforthegold wrote:Experts-

I can see the calculation way of solving this, but are there any other ways to get the answer?

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 the 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
b

Hi JJMforthegold,

Yes, we can figure out the correct answer without doing much calculation; however, the analysis would take more or less the same time as it would take if you do the complete calculation.

I see that it does not involve very ugly numbers.

10% of 35.50 = ~3.5.., thus minimum bill > 35.50 + 3.5 > 39.

Since 10% of 35.50 = ~3.5, we have 5% of 35.50 = ~1.75, thus maximum bill > 39 + 1.75 > 40.75.

Range of bill: 39+ - 40.75+

The correct answer can be A or B. Option A must be incorrect as the minimum bill would be marginally greater than 39, and it cannot go beyond 40, similarly, the maximum bill would be marginally greater than 40.75, and it cannot go beyond 42.

The correct answer: B

Hope this helps!

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JJMforthegold wrote:Experts-

I can see the calculation way of solving this, but are there any other ways to get the answer?

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 the 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
b

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

JJMforthegold wrote:Experts-

I can see the calculation way of solving this, but are there any other ways to get the answer?

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 the 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

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