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08 Feb 2024, 05:16
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Both A and B: 37
Rejected: 45
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
30% (03:34) correct
70%
(03:34)
wrong
based on 540
sessions
History
Date
Time
Result
Not Attempted Yet
A candidate applying for a research program must undergo up to three interview cycles. The first interview is conducted by A, followed by B, and, if necessary, by C. A candidate is selected as soon as exactly two interviewers provide a recommendation. For example, if both A and B recommend a candidate, the candidate is selected and does not proceed to an interview with C. C interviews only those candidates recommended by exactly one of A or B.
A total of 132 candidates applied for the research program, of which C interviewed 82. The number of candidates recommended by A, B, and C were 70, 86, and 50, respectively.
Based on the information provided, select for Both A and B the number of candidates recommended by both A and B, and select for Rejected the total number of candidates out of 132 who were not selected for the research program.
A total of 132 candidates applied for the research program, of which C interviewed 82. The number of candidates recommended by A, B, and C were 70, 86, and 50, respectively.
Based on the information provided, select for Both A and B the number of candidates recommended by both A and B, and select for Rejected the total number of candidates out of 132 who were not selected for the research program.
| Both A and B | Rejected | |
| 13 | ||
| 37 | ||
| 44 | ||
| 45 | ||
| 50 | ||
| 82 |
ShowHide Answer
Official Answer
Both A and B: 37
Rejected: 45
A candidate applying for a research program must undergo up to three interview cycles. The first interview is conducted by A, followed by B, and, if necessary, by C. A candidate is selected as soon as exactly two interviewers provide a recommendation. For example, if both A and B recommend a candidate, the candidate is selected and does not proceed to an interview with C. C interviews only those candidates recommended by exactly one of A or B.
A total of 132 candidates applied for the research program, of which C interviewed 82. The number of candidates recommended by A, B, and C were 70, 86, and 50, respectively.
Based on the information provided, select for Both A and B the number of candidates recommended by both A and B, and select for Rejected the total number of candidates out of 132 who were not selected for the research program.
Official Solution:
Denoting the candidates recommended by both A and B as "Both," the number of candidates recommended by only A is 70 - Both, and the number of candidates recommended by only B is 86 - Both. Since C interviewed 82 candidates, and C only interviews those recommended by exactly one of A or B, we have (70 - Both) + (86 - Both) = 82, which gives Both = 37.
Therefore, both A and B recommended 37 candidates, and since C (together with A or B) recommended 50 candidates, the total number of candidates selected for the program is 37 + 50 = 87. Thus, the number of candidates not selected for the program is 132 - 87 = 45.
Correct answer:
Both A and B "37"
Rejected "45"
GMAT-Club-Forum-o7floj9i.png [ 10.11 KiB | Viewed 2876 times ]
A total of 132 candidates applied for the research program, of which C interviewed 82. The number of candidates recommended by A, B, and C were 70, 86, and 50, respectively.
Based on the information provided, select for Both A and B the number of candidates recommended by both A and B, and select for Rejected the total number of candidates out of 132 who were not selected for the research program.
Official Solution:
Denoting the candidates recommended by both A and B as "Both," the number of candidates recommended by only A is 70 - Both, and the number of candidates recommended by only B is 86 - Both. Since C interviewed 82 candidates, and C only interviews those recommended by exactly one of A or B, we have (70 - Both) + (86 - Both) = 82, which gives Both = 37.
Therefore, both A and B recommended 37 candidates, and since C (together with A or B) recommended 50 candidates, the total number of candidates selected for the program is 37 + 50 = 87. Thus, the number of candidates not selected for the program is 132 - 87 = 45.
Correct answer:
Both A and B "37"
Rejected "45"
Attachment:
GMAT-Club-Forum-o7floj9i.png [ 10.11 KiB | Viewed 2876 times ]
General Discussion
02 Jan 2025, 11:13
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1. There are 6 different scenarios or groups for each person:
- Group 1: were not recommended by both A and B, therefore not even going to C.
- Group 2: were recommended by A, not by B, therefore going to C and not getting recommended.
- Group 3: were recommended by A, not by B, therefore going to C and getting recommended.
- Group 4: were recommended by A and B, therefore going to C.
- Group 5: were not recommended by A, recommended by B, therefore going to C and not getting recommended.
- Group 6: were not recommended by A, recommended by B, therefore going to C and getting recommended.
2. Let each group have a number of people G1, G2, G3,.... Then, we can build the following table:
3. Based on the given information, the following two equations can be said:
- (1): G1 + G2 + G3 + G4 + G5 + G6 = 132
- (2): G2 + G3 + G5 + G6 = 82
4. The question asks us to find G4 and the sum G1 + G2 + G5.
5. From the table, we can add the two equations: G2 + G3 + G4 = 70, G4 + G5 + G6 = 86 \(\rightarrow\) G2 + G3 + G4 + G5 + G6 + G4 = 156 = G1 + G2 + G3 + G4 + G5 + G6 - G1 + G4 = 132 - G1 + G4 \(\rightarrow\) G4 - G1 = 24.
6. Using (2) and (1), 82 = G2 + G3 + G5 + G6 = (G1 + G2 + G3 + G4 + G5 + G6) - (G1 + G4) = 132 - (G1 + G4) \(\rightarrow\) G1 + G4 = 132 - 82 = 50.
7. Let's add the two resulting equations: (G4 - G1) + (G1 + G4) = (24) + (50) \(\rightarrow 2 *\)G4 = 74 \(\rightarrow\) G4 = 37. Also, G1 = 37 - 24 = 13.
8. Using equation (2) and that G3 + G6 = 50, it can be said that: 82 = G2 + G3 + G5 + G6 = 50 + G2 + G5 \(\rightarrow\) G2 + G5 = 32.
9. That means G1 + G2 + G5 = 13 + 32 = 45.
10. Our answer will be: Both A and B - 37 and Rejected - 45.
- Group 1: were not recommended by both A and B, therefore not even going to C.
- Group 2: were recommended by A, not by B, therefore going to C and not getting recommended.
- Group 3: were recommended by A, not by B, therefore going to C and getting recommended.
- Group 4: were recommended by A and B, therefore going to C.
- Group 5: were not recommended by A, recommended by B, therefore going to C and not getting recommended.
- Group 6: were not recommended by A, recommended by B, therefore going to C and getting recommended.
2. Let each group have a number of people G1, G2, G3,.... Then, we can build the following table:
| Groups | A | B | C |
| 1 | 0 | 0 | Not interviewed (0) |
| 2 | G2 | 0 | 0 |
| 3 | G3 | 0 | G3 |
| 4 | G4 | G4 | Not interviewed (0) |
| 5 | 0 | G5 | 0 |
| 6 | 0 | G6 | G6 |
| # of recommended | 70 | 86 | 50 |
3. Based on the given information, the following two equations can be said:
- (1): G1 + G2 + G3 + G4 + G5 + G6 = 132
- (2): G2 + G3 + G5 + G6 = 82
4. The question asks us to find G4 and the sum G1 + G2 + G5.
5. From the table, we can add the two equations: G2 + G3 + G4 = 70, G4 + G5 + G6 = 86 \(\rightarrow\) G2 + G3 + G4 + G5 + G6 + G4 = 156 = G1 + G2 + G3 + G4 + G5 + G6 - G1 + G4 = 132 - G1 + G4 \(\rightarrow\) G4 - G1 = 24.
6. Using (2) and (1), 82 = G2 + G3 + G5 + G6 = (G1 + G2 + G3 + G4 + G5 + G6) - (G1 + G4) = 132 - (G1 + G4) \(\rightarrow\) G1 + G4 = 132 - 82 = 50.
7. Let's add the two resulting equations: (G4 - G1) + (G1 + G4) = (24) + (50) \(\rightarrow 2 *\)G4 = 74 \(\rightarrow\) G4 = 37. Also, G1 = 37 - 24 = 13.
8. Using equation (2) and that G3 + G6 = 50, it can be said that: 82 = G2 + G3 + G5 + G6 = 50 + G2 + G5 \(\rightarrow\) G2 + G5 = 32.
9. That means G1 + G2 + G5 = 13 + 32 = 45.
10. Our answer will be: Both A and B - 37 and Rejected - 45.
