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Updated on: 28 May 2024, 14:48
Originally posted by EgmatQuantExpert on 07 Dec 2018, 02:30.
Last edited by Bunuel on 28 May 2024, 14:48, edited 2 times in total.
Last edited by Bunuel on 28 May 2024, 14:48, edited 2 times in total.
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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:
55%
(hard)
Question Stats:
71% (03:00) correct
29%
(02:52)
wrong
based on 364
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The total number of students that cleared an exam in the year 2016 and 2017 was at least 60% and 50% respectively. The total number of students that appeared in 2017 was 40% more than that of 2016 and the sum of students that cleared the exam in these two year is not less than 65. Which of the following cannot be the sum of students that appeared in these two years, if none of the students appeared in both the years?
A. 119
B. 120
C. 121
D. 122
E. 123
A. 119
B. 120
C. 121
D. 122
E. 123
Question of the Week- 26 (The total number of students that clear...)
e-GMAT Question of the Week #26
e-GMAT Question of the Week #26
07 Dec 2018, 04:23
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Let the number of students appeared in 2016 be x
so the number of students appeared in 2017 is 1.4x
The number of students cleared in 2016 >=.6x
The number of students cleared in 2017 >=.5 of 1.4x =0.7x
The total sum of students cleared in both year =1.3x
1.3x>=65
Therefore x>=50
and 1.4 x>=70
Hence total students cleared in both year is >=120
Hence Ans is A
so the number of students appeared in 2017 is 1.4x
The number of students cleared in 2016 >=.6x
The number of students cleared in 2017 >=.5 of 1.4x =0.7x
The total sum of students cleared in both year =1.3x
1.3x>=65
Therefore x>=50
and 1.4 x>=70
Hence total students cleared in both year is >=120
Hence Ans is A
General Discussion
11 Dec 2018, 05:23
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Solution
Given:
- • Minimum number of students that cleared an exam in 2016: 60%
• Minimum number of students that cleared the same exam in 2017: 50%
• Number of students appeared in 2017 was 40% more than that of 2016
• Total number of students cleared the exam in the two years combined is not less than 65
• None of the students appeared in the exam in both the years
To find:
- • Among the given options, which one cannot be the total number of students that appeared in the exam in the two years combined.
Approach and Working:
If we assume that number of students that appeared in the exam in 2016 was n, then
- • Number of students appeared in the exam in 2017 = 1.4n
Now, the least number of students cleared the exam in 2016 = n x 0.6 = 0.6n
Similarly, minimum number of students cleared the exam in 2017 = 1.4n x 0.5 = 0.7n
Given that, the total number of students cleared the exam in the 2 years combined is not less than 65.
Hence, we can write that,
- • 0.6n + 0.7n ≥ 65
Or, 1.3n ≥ 65
Or, n ≥ 50
Therefore, the minimum number of students that appeared in the exam = (n + 1.4n) = 2.4n = 2.4 x 50 = 120
As the number of total students cannot be less than 120, we can say that 119 cannot be the total number of students appeared in the exam.
Hence, the correct answer is option A.
Answer: A
