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

Question

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

Kudos for a correct solution.

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

Kudos for a correct  solution .

Psiva00734 · Answer

bret left with N dollars.

He spent 1/4 in hardware store. He has 3/4N
He spent 7$ in dry cleaners then 3/4N-7
After that half of is left in grocery stone 3/4N-7/2
=3N-28/8. Finally he left home with 10$

3N-28/8=10

3N-28=80=>3N=108=>3N=36.
Option A sufficient

EMPOWERgmatRichC · Answer

Hi All,

Since this question asks us for the amount of money that Bert started with, the answers are numbers and the "steps" in the prompt are basic math calculations based on the money Bert has, we can TEST THE ANSWERS.

Among the 5 choices, Answer D looks easiest, so we'll start there...

IF....N = 60
Bert spends 1/4 at the hardware store: 60 - (1/4)(60) = 45
Bert spends $7 at the dry cleaners: 45 - 7 = 38
Bert spends half of what's left at the grocery: 38 - 19 = 19
Bert is left with $10.....
Not in this example; he has $19
This answer is TOO BIG. We need a smaller starting number....

Let's TEST Answer B next....

IF....N = 44
Bert spends 1/4 at the hardware store: 44 - (1/4)(44) = 33
Bert spends $7 at the dry cleaners: 33 - 7 = 26
Bert spends half of what's left at the grocery: 26 - 13 = 13
Bert is left with $10.....
Not in this example; he has $13
This answer is TOO BIG. We need a smaller starting number....

There's only one answer left....

Final Answer:  A

GMAT assassins aren't born, they're made,
Rich

mvictor · Answer

started to test answer B
if he had 44, then he spent 11 at hardware store
now he was left with 33$
he spent 7 dollars on cleaning, thus he remained with 26$
he then spent 1/2 of 26, or 13, and was left with 13. but we know that he returned home with 10 dollars
hence, the only option that can be right is A.

it is a nice technique to plug in numbers from answer choices.

we can start with either B, or C.

in case we start with B: if after we plug in, and get an answer that is too big, then the right answer must be A (which is a smaller number than B). If B is too small, test answer choice D. If D is too big, then answer choice C must be right. If D is not enough, answer E is the right one.

In case we start with C: if it is too small, then answ. A & B & C are not correct, and we can check now either D or E. If one of them is not the right answer, then the other one must be!

Another method is simply spotting that 1/2(3N/4 -7) = 10$. We can conclude that 3N/4 - 7 = 20$
3N/4 = 27
N = (27*4)/3
N = 36

chetan2u · Answer

pure algebric way...
started with N... spent N/4 at hardware store... left with 3N/4, out of which 7 spent at the dry cleaners...
1/2 of remaining(3N/4) at grocery store.. left with 10 in end...
so 1/2(3N/4-7) =10...
3N/4=27.... N =36...ans A...

Artmetalist · Answer

Backsolve can be easily apply here..

1) He had $10 left in his pocket when he got home.

2) He paid half of what was left at grocery store. He must have 2x $10 = $20 before he went into the geocery

3) He paid $7 at the dry cleaners. So, now he must have $20 + $7 = $27

4) He spent 1/4 of $N at the hardware store, which means 3/4 of N = $27

Then, N = (27 x 4)/3 = $36

Hope this helps.

bumpbot · Answer

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

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