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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. ### Request Expert Reply # Quentin's income is 60% less than Rex's income, and Sam's income is 25

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Math Expert V
Joined: 02 Sep 2009
Posts: 53768
Quentin's income is 60% less than Rex's income, and Sam's income is 25  [#permalink]

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2
9 00:00

Difficulty:   15% (low)

Question Stats: 84% (02:06) correct 16% (02:34) wrong based on 198 sessions

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Quentin's income is 60% less than Rex's income, and Sam's income is 25% less than Quentin's income. If Rex gave 60% of his income to Sam and 40% of his income to Quentin, Quentin's new income would be what fraction of Sam's new income?

A. 8/9
B. 11/12
C. 8/13
D. 11/13
E. 12/13

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Director  G
Joined: 20 Feb 2015
Posts: 795
Concentration: Strategy, General Management
Re: Quentin's income is 60% less than Rex's income, and Sam's income is 25  [#permalink]

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1
let Rex's , quentin's and sam's income be R , Q and S
as per the question !!

Q = 0.40R (Quentin's income is 60% less than Rex's)
S = 0.30R (Sam's income is 25% less than Quentin's)

after the transaction ,

S = 0.30R + 0.60R ( Rex gave 60% of his income to Sam)
Q = 0.40R + 0.40R (Rex gave 40% of his income to quentin)

Ratio Q/S = 80R/90R =8/9
Intern  B
Joined: 30 Jul 2014
Posts: 40
Quentin's income is 60% less than Rex's income, and Sam's income is 25  [#permalink]

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My approach :

We can take some easy numbers and make calculations simpler.
Let R ( Rex's income) = 100
Q (Quentin's income) = 40%R = 40
S (Sam's income) = 75% Q = (3/4)*40 = 30

Now, if Rex gives 40% to Quentin --> Q = 40 + 40 = 80
60% given to Sam --> S = 30+60 = 90

The ratio is : Q/S = 80/90 = 8/9
Manager  S
Joined: 18 Oct 2016
Posts: 139
Location: India
WE: Engineering (Energy and Utilities)
Re: Quentin's income is 60% less than Rex's income, and Sam's income is 25  [#permalink]

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Option A

Q = 0.4R
S = 0.75Q = 0.75*0.4R = 0.3R
New Income:
Q = 0.4R + 0.4R = 0.8R
S = 0.3R + 0.6R = 0.9R

Q/S =8/9
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Intern  B
Joined: 12 Jul 2016
Posts: 17
Re: Quentin's income is 60% less than Rex's income, and Sam's income is 25  [#permalink]

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Let Rex's income be 100, so the first statement would be :
Rex : 100
Quentin : 40
Sam : 30
Then, Rex gave 60% of his income to Sam and 40% of his income to Quentin. So the new incomes are :
Rex : 0
Quentin: 80
Sam :90
So
The ratio is : Q/S = 80/90 = 8/9
Director  V
Joined: 04 Dec 2015
Posts: 750
Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
Re: Quentin's income is 60% less than Rex's income, and Sam's income is 25  [#permalink]

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Quentin's income is 60% less than Rex's income, and Sam's income is 25% less than Quentin's income. If Rex gave 60% of his income to Sam and 40% of his income to Quentin, Quentin's new income would be what fraction of Sam's new income?

A. 8/9
B. 11/12
C. 8/13
D. 11/13
E. 12/13

Let Rex's income be = 100
Quentin's income = 60% less than Rex's income = 40% of 100 = 40
Sam's income = 25% less than Quentin's income = 75% of 40 = $$\frac{75}{100}$$ x 40 = 30

Rex gave 60% of his income to Sam = 60% of 100 = $$\frac{60}{100}$$ x 100 = 60
Sam's new income = 30 + 60 = 90

Rex gave 40% of his income to Quentin = 40% of 100 = $$\frac{40}{100}$$ x 100 = 40
Quentin's new income = 40 + 40 = 80

Required fraction = Quentin's new income / Sam's new income = $$\frac{80}{90}$$ = $$\frac{8}{9}$$

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Joined: 12 Nov 2016
Posts: 724
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37 GRE 1: Q157 V158 GPA: 2.66
Re: Quentin's income is 60% less than Rex's income, and Sam's income is 25  [#permalink]

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Bunuel wrote:
Quentin's income is 60% less than Rex's income, and Sam's income is 25% less than Quentin's income. If Rex gave 60% of his income to Sam and 40% of his income to Quentin, Quentin's new income would be what fraction of Sam's new income?

A. 8/9
B. 11/12
C. 8/13
D. 11/13
E. 12/13

Is this really a 500 level question? Definitely seems a bit trickier- but anyways

Q= r(2/5) + r(2/5)
S = (3/4)Q + r(3/5)

Let R be 100

Q= 100(2/5) + 100(2/5)=

40 + 40 = 80

S = (3/4) 40 + 100(3/5)

30 + 60 = 90

80/90 = 8/9
Board of Directors P
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Re: Quentin's income is 60% less than Rex's income, and Sam's income is 25  [#permalink]

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Bunuel wrote:
Quentin's income is 60% less than Rex's income, and Sam's income is 25% less than Quentin's income. If Rex gave 60% of his income to Sam and 40% of his income to Quentin, Quentin's new income would be what fraction of Sam's new income?

A. 8/9
B. 11/12
C. 8/13
D. 11/13
E. 12/13

Let Rex's income be 100

So, Quentin's income is 40

Tus, Sam's income is 3/4*40 = 30

Quote:
If Rex gave 60% of his income to Sam and 40% of his income to Quentin, Quentin's new income would be what fraction of Sam's new income?

Sam's new income = 30 + 60 = 90
Quentin's new income = 40 + 40 = 80

Thus, the new fraction is 80/90 = 8/9, Answer must be (A)
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Re: Quentin's income is 60% less than Rex's income, and Sam's income is 25  [#permalink]

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Bunuel wrote:
Quentin's income is 60% less than Rex's income, and Sam's income is 25% less than Quentin's income. If Rex gave 60% of his income to Sam and 40% of his income to Quentin, Quentin's new income would be what fraction of Sam's new income?

A. 8/9
B. 11/12
C. 8/13
D. 11/13
E. 12/13

If we let Rex’s income be $10, then Quentin’s income is$4 and Sam’s income is $3. If Rex gives$6 to Sam and $4 to Quentin, then Quentin’s new income is$8 and Sam’s is \$9. Therefore, Quentin’s new income is 8/9 of Sam’s new income.

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# Scott Woodbury-Stewart

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See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews Re: Quentin's income is 60% less than Rex's income, and Sam's income is 25   [#permalink] 28 Oct 2018, 18:26
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# Quentin's income is 60% less than Rex's income, and Sam's income is 25

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