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David received his allowance on Sunday. He spends 1/4 of his allowance

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Bunuel
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David received his allowance on Sunday. He spends 1/4 of his allowance [#permalink] New post   25 Feb 2018, 11:15
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David received his allowance on Sunday. He spends 1/4 of his allowance on Monday and 2/3 of the remainder on Tuesday. What part of his allowance is left for the rest of the week?

(A) 1/3
(B) 1/12
(C) 1/4
(D) 1/2
(E) 4/7
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C
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Re: David received his allowance on Sunday. He spends 1/4 of his allowance [#permalink] New post   25 Feb 2018, 11:49
Bunuel wrote:
David received his allowance on Sunday. He spends 1/4 of his allowance on Monday and 2/3 of the remainder on Tuesday. What part of his allowance is left for the rest of the week?

(A) 1/3
(B) 1/12
(C) 1/4
(D) 1/2
(E) 4/7


let allowance = 40

he spends 1/4 on Monday = 40/40 = 10

remaining = 30

2/3 of remaining = 2/3 x 30 = 20

remaining = 10 i.e 1/4

(C) imo
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Re: David received his allowance on Sunday. He spends 1/4 of his allowance [#permalink] New post   26 Feb 2018, 00:56
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Let Total Allowance= x
Allowance spent on Monday= \(\frac{1}{4}\)x

Remaining= x-\(\frac{1}{4}\)x= \(\frac{3}{4}\)x

Allowance spent on Tuesday= \(\frac{3}{4}\)x*\(\frac{2}{3}\)= \(\frac{1}{2}\)x

Remaining= \(\frac{3}{4}\)x-\(\frac{1}{2}\)x=\(\frac{1}{4}\)x

Answer: C.
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David received his allowance on Sunday. He spends 1/4 of his allowance [#permalink] New post   26 Feb 2018, 01:03
Let \(x\) be the total allowance

After Monday: \(x*\frac{3}{4}\) is left

After Tuesday: \(x*\frac{3}{4}*\frac{1}{3} = x*\frac{3}{12} = x*\frac{1}{4}\)

Ans: C
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Re: David received his allowance on Sunday. He spends 1/4 of his allowance [#permalink] New post   28 Feb 2018, 11:13
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Bunuel wrote:
David received his allowance on Sunday. He spends 1/4 of his allowance on Monday and 2/3 of the remainder on Tuesday. What part of his allowance is left for the rest of the week?

(A) 1/3
(B) 1/12
(C) 1/4
(D) 1/2
(E) 4/7


We can let n = the total allowance, and create the following expression:

n - [(1/4)n + 2/3(3/4)n] = remainder for the week

n - [n/4 + n/2] = remainder for the week

n - [n/4 + 2n/4] = remainder for the week

n - 3n/4 = n/4 = (¼)n = remainder for the week

Answer: C
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Re: David received his allowance on Sunday. He spends 1/4 of his allowance [#permalink] New post   28 Feb 2018, 11:34
Picking Numbers:

Allowance (A) = 12

Allowance spent on Monday = 12* 1/4 = 3

Allowance spent on Tuesday = 9* 2/3 = 6

Allowance left for the rest of the week = 3/12 = 1/4th of the total

IMO C
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Re: David received his allowance on Sunday. He spends 1/4 of his allowance [#permalink] New post   20 Jun 2018, 08:23
+1 for option C. We are told that 1/4 of the allowance is spent on Monday. 2/3 of remaining is spent on Tuesday. 1/4+1/2 = 3/4 is spent in total. Then 1/4 remains for the rest of the week. Hence option C.
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Re: David received his allowance on Sunday. He spends 1/4 of his allowance [#permalink] New post   20 Jun 2018, 09:04
Easy to pick up some number, I chose 12 to satisfy denominatora of both fractions 4 adn 3.
on Monday he spent 1/4 of 12 or 3$
on Tuesday he spent 2/3 of remaining (12-3) 9, 6$
So he is left with 3$ only (12-3-6)
Or 3/12=1/4
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Re: David received his allowance on Sunday. He spends 1/4 of his allowance [#permalink] New post   13 Sep 2021, 22:29
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Re: David received his allowance on Sunday. He spends 1/4 of his allowance [#permalink]
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