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# A student spent 60% of her money on books and spent 1/3 of the remaind

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Manager
Joined: 21 Jun 2019
Posts: 99
Concentration: Finance, Accounting
GMAT 1: 670 Q48 V34
GPA: 3.78
A student spent 60% of her money on books and spent 1/3 of the remaind  [#permalink]

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12 Jul 2019, 08:12
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Difficulty:

15% (low)

Question Stats:

80% (01:51) correct 20% (01:58) wrong based on 50 sessions

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A student spent 60% of her money on books and spent 1/3 of the remainder on notebooks. She had \$30 left. How much money did the student have at first?

A)225
B)167.5
C) 68.2
D) 245
E) 112.5
Intern
Joined: 10 Feb 2019
Posts: 11
Location: Ukraine
Concentration: General Management, Entrepreneurship
GPA: 3.23
A student spent 60% of her money on books and spent 1/3 of the remaind  [#permalink]

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12 Jul 2019, 23:54
1
GeorgeKo111 wrote:
A student spent 60% of her money on books and spent 1/3 of the remainder on notebooks. She had \$30 left. How much money did the student have at first?

A)225
B)167.5
C) 68.2
D) 245
E) 112.5

Let's look at the question stem:
2. 0.6x spent on books => 0.4x left
3. 0.4x * 1/3 spent on notebooks => 0.4x*2/3 left which is 30\$
4. Let's then get back => x=30 / 0.4 / (2/3) = 112.5\$

Please give KUDDOOOOOSSSS if the explanation helped you
Manager
Status: Not Applying
Joined: 27 Apr 2009
Posts: 152
Location: India
Schools: HBS '14 (A)
GMAT 1: 730 Q51 V36
Re: A student spent 60% of her money on books and spent 1/3 of the remaind  [#permalink]

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13 Jul 2019, 00:46
Let's assume the student had \$x at the start.
She spent 60% on books
=> Remainder = x - 0.6x = 0.4x

She spent 1/3 of this on notebooks
=> Remainder = 0.4x - (1/3)(0.4x) = 0.8x/3

Given then 0.8x/3 = 30
=> x = (30*3)/0.8 = 112.5

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Intern
Joined: 12 Feb 2018
Posts: 18
Re: A student spent 60% of her money on books and spent 1/3 of the remaind  [#permalink]

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08 Aug 2019, 10:20
1
Let's assume the student had 100\$ initially.
60\$-spent on books; Remaining 40\$;
1/3(40\$)-spent on notebooks;2/3(40\$)-left amount;
for 100\$, 2/3(40\$)is left. So, if 30\$ is left then initial amount can be calculated

100=>2/3(40\$)
x=>30\$left; cross multiply(30*100)/(80/3)=9000/80=112.5\$
option E
Intern
Joined: 13 Mar 2019
Posts: 27
Re: A student spent 60% of her money on books and spent 1/3 of the remaind  [#permalink]

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08 Aug 2019, 19:20
1
Out of the initial x dollars.
40% is left.
Out of that 40 %, 1/3 is spent on notebooks, 2/3 is the remainder which is given as 30 \$.
So, 2/3* 40%*x = 30.
x = 112.5
Re: A student spent 60% of her money on books and spent 1/3 of the remaind   [#permalink] 08 Aug 2019, 19:20