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29 Jul 2021, 05:30
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
100% (01:09) correct
0%
(00:00)
wrong
based on 49
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Two numbers are such that the ratio between them is 3:5; but if each is increased by 10, the ratio between them becomes 5:7. What are these numbers ?
(A) 3, 5
(B) 7, 9
(C) 13, 22
(D) 15, 25
(E) 30, 50
(A) 3, 5
(B) 7, 9
(C) 13, 22
(D) 15, 25
(E) 30, 50
29 Jul 2021, 06:40
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Bunuel
We can solve this question algebraically or testing the answer choices.
On test day, I'd probably test the other choices since that's the fastest.
APPROACH #1: Test the answers
Since we're told the two numbers have a ratio of 3 : 5, let's see which answer choices have the same ratio.
(A) 3, 5 = 3 : 5 ratio. Keep.
(B) 7, 9 does NOT equal a 3 : 5 ratio. ELIMINATE.
(C) 13, 22 does NOT equal a 3 : 5 ratio. ELIMINATE.
(D) 15, 25 = 3 : 5 ratio. Keep.
(E) 30, 50 = 3 : 5 ratio. Keep.
When we add 10 to each value, the new ratio becomes 5 : 7
(A) 3, 5
Add 10 to each value to get: 13 : 15. Since this ratio does not equal 5:7, we can eliminate A
(D) 15, 25
Add 10 to each value to get: 25 : 35. Since this ratio simplifies to equal 5:7, the correct answer is D
APPROACH #2: Algebra
Let x and y be the two values
Two numbers are such that the ratio between them is 3:5
We can write: x/y = 3/5
Cross multiply to get 5x = 3y
Rearrange to get: 5x - 3y = 0
If each number is increased by 10, the ratio between them becomes 5:7
We get: (x + 10)/(y + 10) = 5/7
Cross multiply: 7(x + 10)= 5(y + 10)
Expand: 7x + 70 = 5y + 50
Rearrange: 7x - 5y = -20
We now have the following system of equations:
5x - 3y = 0
7x - 5y = -20
Multiply both sides of the top equation by 7, and multiply both sides of the bottom equation by 5 to get:
35x - 21y = 0
35x - 25y = -100
Subtract the bottom equation from the top equation to get: 4y = 100
Solve: y = 25
Since only one of the answer choices has 25 as a possible value, the correct answer must be D
29 Jul 2021, 07:13
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Bunuel
Let the two numbers be 3x and 5x respectively.
\(\frac{3x + 10}{5x + 10} = \frac{5}{7}\)
\(21x + 70 = 25x + 50\)
\(4x = 20\)
x = 5
So, the two numbers are 3x = 15 and 5x = 25. (D), IMO!
