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27 Oct 2021, 02:45
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
61% (02:34) correct
39%
(02:25)
wrong
based on 595
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10% of GMAT test takers take the exam more than once and have a high score of 650 or greater, and 20% of GMAT test takers who take the test only once have a score of 650 or greater. if 40% of GMAT test takers take the exam more than once, What percent of GMAT test takers have a high score of less than 650?
A. 10.5%
B. 22%
C. 30%
D. 70%
E. 78%
A. 10.5%
B. 22%
C. 30%
D. 70%
E. 78%
PyjamaScientist
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27 Oct 2021, 03:21
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Use a group grid to organize the information.
Let total = 100.
In the grids below:
-- All the numbers in the grid have to add up horizontally and vertically.
-- Values given by the problem are entered in blue.
-- Values calculated based upon information was given by the problem are entered in red.
40% take the exam more than once.
10% take the exam more than once and have a score of 700 or greater.
20% of GMAT test takers who take the test only once have a score of 700 or greater.
Total with a score less than 700 = 78%.
Let total = 100.
In the grids below:
-- All the numbers in the grid have to add up horizontally and vertically.
-- Values given by the problem are entered in blue.
-- Values calculated based upon information was given by the problem are entered in red.
40% take the exam more than once.
10% take the exam more than once and have a score of 700 or greater.
20% of GMAT test takers who take the test only once have a score of 700 or greater.
Total with a score less than 700 = 78%.
Attachments
Test-takers-Grid-1.png [ 19 KiB | Viewed 7292 times ]
Test-takers-Grid-2.png [ 20.36 KiB | Viewed 7277 times ]
12 Jun 2024, 20:13
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To solve this problem, let's break down the given information and use basic probability concepts.
The answer is: 84%
- Given Data:
- 40% of GMAT test takers take the exam more than once.
- 60% of GMAT test takers take the exam only once (since 100% - 40% = 60%).
- 10% of test takers who take the exam more than once have a high score of 650 or greater.
- 20% of test takers who take the exam only once have a score of 650 or greater.
- Definitions and Calculations:
- Let P(M)P(M)P(M) represent the probability of taking the exam more than once.
- Let P(O)P(O)P(O) represent the probability of taking the exam only once.
- Let P(≥650∣M)P(\text{≥650} | M)P(≥650∣M) represent the probability of scoring 650 or greater given the exam is taken more than once.
- Let P(≥650∣O)P(\text{≥650} | O)P(≥650∣O) represent the probability of scoring 650 or greater given the exam is taken only once.
P(M)=0.40,P(O)=0.60P(M) = 0.40, \quad P(O) = 0.60P(M)=0.40,P(O)=0.60 P(≥650∣M)=0.10,P(≥650∣O)=0.20P(\text{≥650} | M) = 0.10, \quad P(\text{≥650} | O) = 0.20P(≥650∣M)=0.10,P(≥650∣O)=0.20 - Total Probability of Scoring 650 or Greater: We use the law of total probability to find the overall probability of scoring 650 or greater:
P(≥650)=P(≥650∣M)⋅P(M)+P(≥650∣O)⋅P(O)P(\text{≥650}) = P(\text{≥650} | M) \cdot P(M) + P(\text{≥650} | O) \cdot P(O)P(≥650)=P(≥650∣M)⋅P(M)+P(≥650∣O)⋅P(O)Substituting the values:
P(≥650)=(0.10⋅0.40)+(0.20⋅0.60)P(\text{≥650}) = (0.10 \cdot 0.40) + (0.20 \cdot 0.60)P(≥650)=(0.10⋅0.40)+(0.20⋅0.60) P(≥650)=0.04+0.12=0.16P(\text{≥650}) = 0.04 + 0.12 = 0.16P(≥650)=0.04+0.12=0.16 - Probability of Scoring Less Than 650: The probability of scoring less than 650 is the complement of the probability of scoring 650 or greater:
P(<650)=1−P(≥650)P(\text{<650}) = 1 - P(\text{≥650})P(<650)=1−P(≥650) P(<650)=1−0.16=0.84P(\text{<650}) = 1 - 0.16 = 0.84P(<650)=1−0.16=0.84
The answer is: 84%
