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Bunuel
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The ratio of x to y is 3 : 4, and the ratio of x + 7 to y + 7 is 4 : 5 Updated on: 24 Jul 2019, 05:10
Originally posted by Bunuel on 24 Jul 2019, 00:49.
Last edited by Sajjad1994 on 24 Jul 2019, 05:10, edited 1 time in total.
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C
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82% (02:13) correct 18% (02:27) wrong based on 166 sessions

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The ratio of x to y is 3 : 4, and the ratio of x + 7 to y + 7 is 4 : 5. What is the ratio of x + 14 to y + 14?

(A) 3 : 4
(B) 4 : 5
(C) 5 : 6
(D) 5 : 7
(E) 6 : 7

Source: Nova GMAT
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C
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The ratio of x to y is 3 : 4, and the ratio of x + 7 to y + 7 is 4 : 5 24 Jul 2019, 00:57
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Bunuel
The ratio of x to y is 3 : 4, and the ratio of x + 7 to y + 7 is 4 : 5. What is the ratio of x + 14 to y + 14?

(A) 3 : 4
(B) 4 : 5
(C) 5 : 6
(D) 5 : 7
(E) 6 : 7
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Given: The ratio of x to y is 3 : 4, and the ratio of x + 7 to y + 7 is 4 : 5.
Asked: What is the ratio of x + 14 to y + 14?

\(\frac{x}{y} = \frac{3}{4}\)
x=3k & y=4k
\(\frac{x+7}{y+7} = \frac{3k+7}{4k+7} = \frac{4}{5}\)
k = 7
x=21 & y=28
\(\frac{x + 14}{y + 14}= \frac{21+14}{28+14} = \frac{35}{42} = \frac{5}{6}\)

IMO C
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The ratio of x to y is 3 : 4, and the ratio of x + 7 to y + 7 is 4 : 5 24 Jul 2019, 01:01
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Bunuel
The ratio of x to y is 3 : 4, and the ratio of x + 7 to y + 7 is 4 : 5. What is the ratio of x + 14 to y + 14?

(A) 3 : 4
(B) 4 : 5
(C) 5 : 6
(D) 5 : 7
(E) 6 : 7
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given
x:y=3/4
and x+y/y+7 = 4:5
solve for x & y ; x= 21 and y=28
so x+14 / y+14 ; 5:6
IMO C
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The ratio of x to y is 3 : 4, and the ratio of x + 7 to y + 7 is 4 : 5 24 Jul 2019, 01:16
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It is given

X/Y = 3/4 & X+7/ Y+7 = 4/5

If we observe there is addition of 7 in numerator and denominator and the ratio increases by 1 in the numerator and denominator.

Hence if we add 14 to numerator and denominator there will be addition of 2 in the output ratio which will become
X+14/Y+14 = 3+2/4+2
X+14/Y+14= 5/6

Hence the answer is (C)
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The ratio of x to y is 3 : 4, and the ratio of x + 7 to y + 7 is 4 : 5 24 Jul 2019, 01:57
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Bunuel
The ratio of x to y is 3 : 4, and the ratio of x + 7 to y + 7 is 4 : 5. What is the ratio of x + 14 to y + 14?

(A) 3 : 4
(B) 4 : 5
(C) 5 : 6
(D) 5 : 7
(E) 6 : 7
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Follow the pattern :


\(\frac{x}{y}\) = 3/4

\(\frac{x + 7}{y + 7}\) = 4/5

\(\frac{x + 14}{y + 14}\) = 5 / 6
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The ratio of x to y is 3 : 4, and the ratio of x + 7 to y + 7 is 4 : 5 25 Jul 2019, 04:49
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Solution


Given:
    • The ratio of x to y is 3 : 4
    • The ratio of x + 7 to y + 7 is 4 : 5

To find:
    • The ratio of x + 14 to y + 14

Approach and Working Out:
    • \(\frac{x}{y} = \frac{3}{4}\)
      o Implies, \(x = \frac{3y}{4}\)

    • \(\frac{(x + 7)}{(y + 7)} = \frac{4}{5}\)
      o Implies, \(\frac{(3y + 28)}{(4y + 28)} = \frac{4}{5}\)
      o Thus, 15y + 140 = 16y + 112
      o y = 28

    • Thus, \(x = 3 * \frac{28}{4} = 21\)

Therefore, \(\frac{(x + 14)}{(y + 14)} = \frac{35}{42} = \frac{5}{6}\)

Answer: C

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The ratio of x to y is 3 : 4, and the ratio of x + 7 to y + 7 is 4 : 5 26 Jul 2019, 12:21
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Bunuel
The ratio of x to y is 3 : 4, and the ratio of x + 7 to y + 7 is 4 : 5. What is the ratio of x + 14 to y + 14?

(A) 3 : 4
(B) 4 : 5
(C) 5 : 6
(D) 5 : 7
(E) 6 : 7

Source: Nova GMAT
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We have the following:

x/y = 3/4

4x = 3y

x = 3y/4

and

(x + 7)/(y + 7) = 4/5

5x + 35 = 4y + 28

5x + 7 = 4y

Substituting 3y/4 for x, we have:

5(3y/4)+ 7 = 4y

Multiplying the equation by 4, we have:

15y + 28 = 16y

28 = y

Therefore, x = 3(28)/4 = 21.

Since x + 14 = 21 + 14 = 35 and y = 28 + 14 = 42,

(x + 14)/(y + 14) = 35/42 = 5/6.

Answer: C
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The ratio of x to y is 3 : 4, and the ratio of x + 7 to y + 7 is 4 : 5 10 Feb 2021, 08:52
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