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# The ratio of two numbers is 7/6. If the smaller of the two numbers is

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Math Expert
Joined: 02 Sep 2009
Posts: 44654
The ratio of two numbers is 7/6. If the smaller of the two numbers is [#permalink]

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25 Dec 2017, 01:09
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15% (low)

Question Stats:

85% (00:53) correct 15% (01:27) wrong based on 98 sessions

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The ratio of two numbers is 7/6. If the smaller of the two numbers is decreased by two the ratio is 7/5, what is the larger number?

A. 28
B. 21
C. 14
D. 12
E. 10
[Reveal] Spoiler: OA

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Joined: 07 Dec 2017
Posts: 303
Re: The ratio of two numbers is 7/6. If the smaller of the two numbers is [#permalink]

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25 Dec 2017, 01:49
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Expert's post
Bunuel wrote:
The ratio of two numbers is 7/6. If the smaller of the two numbers is decreased by two the ratio is 7/5, what is the larger number?

A. 28
B. 21
C. 14
D. 12
E. 10

Questions which change an old to a new ratio can often be tricky so we'll use the answers.
This is an Alternative approach.

If the larger number is 14 the smaller is 14* (6/7) = 12.
If this is decreased by 2 to 10 then the new ratio is 14/10 = 7/5.
Yes!

* Had (C) not been correct we would have gone up to (B) or down to (D) depending on if we needed to increase or decrease our answer.
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Joined: 22 May 2016
Posts: 1566
The ratio of two numbers is 7/6. If the smaller of the two numbers is [#permalink]

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25 Dec 2017, 12:01
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Bunuel wrote:
The ratio of two numbers is 7/6. If the smaller of the two numbers is decreased by two the ratio is 7/5, what is the larger number?

A. 28
B. 21
C. 14
D. 12
E. 10

1) Set up the original ratio with a multiplier, x
The ratio of two numbers is 7/6 : $$\frac{7x}{6x}$$

2) Set up the equation*
The smaller number is decreased by two (LHS):
$$\frac{7x}{6x-2}$$
The new ratio is $$\frac{7}{5}$$ (RHS), so
$$\frac{7x}{6x-2} = \frac{7}{5}$$

$$5(7x) = 7(6x - 2)$$
$$35x = 42x - 14$$
$$14 = 7x$$
$$x = 2$$

That multiplier, x, is only for original ratio, $$\frac{7x}{6x}$$

3) Larger number's value? x = 2
Larger number = 7x = (7)(2) = 14

*the number added to 6x and the numbers in the new ratio are just numbers, i.e., not accompanied by any multiplier x
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Joined: 07 Dec 2014
Posts: 965
The ratio of two numbers is 7/6. If the smaller of the two numbers is [#permalink]

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Updated on: 25 Dec 2017, 13:49
1
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Bunuel wrote:
The ratio of two numbers is 7/6. If the smaller of the two numbers is decreased by two the ratio is 7/5, what is the larger number?

A. 28
B. 21
C. 14
D. 12
E. 10

(7/5)/(7/6)=6/5
6/5=[x/(y-2)]/(x/y)➡
5xy=6xy-12x➡
y=12
x=14
C

Originally posted by gracie on 25 Dec 2017, 12:30.
Last edited by gracie on 25 Dec 2017, 13:49, edited 5 times in total.
Intern
Joined: 14 Jun 2017
Posts: 23
Location: United States
GMAT 1: 710 Q48 V38
GPA: 2.8
Re: The ratio of two numbers is 7/6. If the smaller of the two numbers is [#permalink]

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25 Dec 2017, 12:42
Let, small number = S, Big number= B. Given, B/S= 7/6 (big over small ratio has to be greater than 1)
Implies 6B=7S or 6B-7S=0.....(i)

Now, small number decreased by 2. B/(S-2)= 7/5 implies 5B-7S=-14....(ii)

Now you have 2 linear equations with 2 unknowns, B and S. Solve to get B=14, hence C.
Manager
Joined: 24 Nov 2016
Posts: 148
Re: The ratio of two numbers is 7/6. If the smaller of the two numbers is [#permalink]

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25 Dec 2017, 17:59
Bunuel wrote:
The ratio of two numbers is 7/6. If the smaller of the two numbers is decreased by two the ratio is 7/5, what is the larger number?

A. 28
B. 21
C. 14
D. 12
E. 10

Lets call the larger $$a$$ and the smaller $$b$$.

First equation: $$\frac{a}{b}=\frac{7}{6}$$, then $$a=\frac{7b}{6}$$.

Second equation: $$\frac{a}{b-2}=\frac{7}{5}$$, then $$5a=7b-14$$.

Solve for $$b$$ by substituting $$a$$ in the second equation: $$5a=7b-14$$, becomes $$5*\frac{7b}{6}=7b-14$$, $$35b=42b-84$$, $$-7b=-84$$, $$b=12$$

Solve for $$a$$ by substituting $$b$$ in the first equation: $$a=\frac{7b}{6}=\frac{7(12)}{6}=7*2=14$$

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Joined: 26 Mar 2013
Posts: 1614
The ratio of two numbers is 7/6. If the smaller of the two numbers is [#permalink]

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26 Dec 2017, 02:44
Bunuel wrote:
The ratio of two numbers is 7/6. If the smaller of the two numbers is decreased by two the ratio is 7/5, what is the larger number?

A. 28
B. 21
C. 14
D. 12
E. 10

Another approach

Let small number = S, large number= L

Old ratio: L/S= 7/6= 14/12 = 21/18 = 28/24

New ratio: L/S = 7/5 =14 /10 = 21/15 = 28/20

Compare the old and new such that the small number decreased by 2

The large number = 14

Intern
Joined: 26 Dec 2017
Posts: 1
Re: The ratio of two numbers is 7/6. If the smaller of the two numbers is [#permalink]

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26 Dec 2017, 22:56
As 14/12 = 7/6 ads after decreasing the smallest by 2 becomes 14/10= 7/5 so the largest number is
C which is 14

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Re: The ratio of two numbers is 7/6. If the smaller of the two numbers is   [#permalink] 26 Dec 2017, 22:56
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