Susan spent one-third of her money on books and half of the remaining

Question

Susan spent one-third of her money on books and half of the remaining money on clothing. She then spent three-fourths of what she had left on food. She had $5 left over. How much money did she start with?

A. $60
B. $80
C. $120
D. $160
E. $180

A. $60
B. $80 
C. $120 
D. $160 
E. $180

Abhishek009 · Answer

Let the amount of money she had be 12x

Amount spent on books = 4x
Amount spent on clothing = 4x
Amount spent on food = 3x
Amount left = x = $5

So, the total amount of money she had is $ 60, Answer must be (A)

EgmatQuantExpert · Answer

Solution 
  Given:  
 • Susan spent
 o  \frac{1}{3}^{rd}  of her money on books,
o  \frac{1}{3}^{rd} on clothing
o  \frac{1}{4}^{th}  on food

• She had $5 left over

To find:  
 • The total money she had at the beginning

Approach and Working:   
 • Let the initial amount be $X
• Left over money =  (1 - \frac{1}{3} - \frac{1}{3} - \frac{1}{4}) * $X = $5 
 o Implies, X = $5 * 12 = $60

Hence, the correct answer is Option A

Answer: A

https://e-gmat.com/blogs/wp-content/uploads/2018/08/Ability-Quiz-WP-e1533292133520.png

ScottTargetTestPrep · Answer

We can let the total amount of money Susan had = n.

So she spent n/3 on books, (1/2)(n - n/3) = (1/2)(2n/3) = n/3 on clothing and (3/4)(n - n/3 - n/3) = (3/4)(n/3) = n/4 on food. We can create the equation:

n/3 + n/3 + n/4 + 5 = n

Multiplying the equation by 12, we have:

4n + 4n + 3n + 60 = 12n

11n + 60 = 12n

60 = n

So she had $60 before she spent it on books, clothing and food.

Answer: A

Epistle · Answer

Please how did your get your 60, 
from your calculations there is really no way x=$5
will turn to 60 
what am i missing

please assist

MBAHOUSE · Answer

Fractions and equations are current subject at the gmat test.

ThatDudeKnows · Answer

We need something that's divisible by 3. B and D are out.
Let's just try C. If we need something smaller, it's A; if we need something larger, it's E.

She starts with $120.
She spends $40 on books and has $80 remaining. 
She spends $40 on clothing and has $40 remaining. 
She spends $30 on food and has $10 remaining. We want her to have $5 remaining, so $10 is too much. We need something smaller.

Answer choice A.

Susan spent one-third of her money on books and half of the remaining

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Susan spent one-third of her money on books and half of the remaining

Prep Toolkit

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