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06 Aug 2024, 19:00
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
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Question Stats:
56% (02:25) correct
44%
(02:32)
wrong
based on 289
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The ratio of two positive integers, \(m\) and \(n\), is 4 to 3. If the values of \(m\) and \(n\) are increased in a ratio of 1 to 1, which of the following cannot be the resulting integers?
I. 8 and 5
II. 25 and 21
III. 13 and 11
A. I only
B. II only
C. III only
D. I and II only
E. I and III only
I. 8 and 5
II. 25 and 21
III. 13 and 11
A. I only
B. II only
C. III only
D. I and II only
E. I and III only
11 Aug 2024, 02:00
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Bunuel
Official Solution:
The ratio of two positive integers, \(m\) and \(n\), is 4 to 3. If the values of \(m\) and \(n\) are increased in a ratio of 1 to 1, which of the following cannot be the resulting integers?
I. 8 and 5
II. 25 and 21
III. 13 and 11
A. I only
B. II only
C. III only
D. I and II only
E. I and III only
When two numbers are increased in a ratio of 1:1, it implies that the same positive number was added to both of them.
If a fraction is between 0 and 1, adding the same positive number to both the numerator and denominator increases the value of the fraction. For instance, if we add 2 to the numerator and denominator of \(\frac{1}{3}\), we get \(\frac{1 + 2}{3 + 2} = \frac{3}{5}\), which is greater than the initial fraction of \(\frac{1}{3}\).
If a fraction is more than 1, adding the same positive number to both the numerator and denominator decreases the value of the fraction. For instance, if we add 2 to the numerator and denominator of \(\frac{3}{2}\), we get \(\frac{3 + 2}{2 + 2} = \frac{5}{4} = 1.25\), which is less than the initial fraction of \(\frac{3}{2} = 1.5\).
For the question at hand, the original ratio was 4:3, which is more than 1 (≈1.3), thus adding the same positive number to both the numerator and the denominator will decrease the value of the new ratio, bringing it closer to, but still above 1. Therefore, both 25 and 21 (\(\frac{25}{21} \approx 1.2\)), and 13 and 11 (\(\frac{13}{11} \approx 1.2\)), are possible values for the resulting integers since their ratio is less than 1.3, while 8 to 5 cannot be the resulting integers, as their ratio is 1.6, which is greater than 1.3.
Answer: A
General Discussion
06 Aug 2024, 20:06
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m:n is 4:3 meaning m can be 4,8,12,16,20 etc and n can be 3,6,9,12,15 etc. So 4x : 3x
value increased by 1 to 1, means add the same value, say y, to both.
we are looking for options that are not in tandem with 4x+y : 3x+y
(I) clearly, 8:5 is not possible to achieve.
(II) 25:21, 4x:3x=16:12 (x=4) when y=9, 16+9:12+9 = 25:21. So, this option follows the given condition.
(III) Similarly, when x=2 and y=5, 13:11 is applicable
(A) is the answer
value increased by 1 to 1, means add the same value, say y, to both.
we are looking for options that are not in tandem with 4x+y : 3x+y
(I) clearly, 8:5 is not possible to achieve.
(II) 25:21, 4x:3x=16:12 (x=4) when y=9, 16+9:12+9 = 25:21. So, this option follows the given condition.
(III) Similarly, when x=2 and y=5, 13:11 is applicable
(A) is the answer
