Bert left the house with N dollars. He spent 1/4 of this...

[BTGmoderatorLU]

Bert left the house with N dollars. He spent 1/4 of this at the hardware store, then $7 at the dry cleaners, and then half of what was left at the grocery store. When he got home, he had $10 left in his pocket. What was the value of N?

A. $36
B. $44
C. $52
D. $60
E. $68

The OA is A.

I'm confused by this PS question. Experts, any suggestion about how can I solve it? Thanks in advance.

[GMATGuruNY]

Bert left the house with N dollars. He spent 1/4 of this at the hardware store, then $7 at the dry cleaners, and then half of what was left at the grocery store. When he got home, he had $10 left in his pocket. What was the value of N?

A. $36
B. $44
C. $52
D. $60
E. $68

We can PLUG IN THE ANSWERS, which represent the total amount of money.
When the correct answer is plugged in, the amount left in Bert's pocket = 10.

B: 44
Amount spent at the hardware store = (1/4)(44) = 11.
Amount spent at the dry cleaners = 7.
Remaining amount = 44-11-7 = 26.
Since 1/2 of the remaining amount is spent at the grocery store, 1/2 of the remaining amount is left in Bert's pocket:
(1/2)(26) = 13.
The amount left in Bert's pocket is TOO BIG.
Thus, the correct answer must be LESS THAN 44.

The correct answer is A.

A: 36
Amount spent at the hardware store = (1/4)(36) = 9.
Amount spent at the dry cleaners = 7.
Remaining amount = 36-9-7 = 20.
Since 1/2 of the remaining amount is spent at the grocery store, 1/2 of the remaining amount is left in Bert's pocket:
(1/2)(20) = 10.
Success!

[Scott@TargetTestPrep]

Bert left the house with N dollars. He spent 1/4 of this at the hardware store, then $7 at the dry cleaners, and then half of what was left at the grocery store. When he got home, he had $10 left in his pocket. What was the value of N?

A. $36
B. $44
C. $52
D. $60
E. $68

Since Bert spends 1/4 of his money at the hardware store, he has 3N/4 left.

Since he spends 7 dollars at the dry cleaners, he has 3N/4 - 7 left.

We are given that he spends half of his remaining money at the grocery store and after that, he has 10 dollars left. Thus, half of 3N/4 - 7 must equal 10; in other words:

1/2(3N/4 - 7) = 10

3N/4 - 7 = 20

3N/4 = 27

N/4 = 9

N = 36.

Answer: A

[DrMaths]

Try reversing the process:

(10 * 2 + 7) * 4./3 = 36

(Note 4/3 is the inverse of 3/4, whereby 1/4 has been removed from 1 whole)