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11 Jul 2025, 10:26
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Column A: The number of individuals who did not agree with both statements
= Total number of respondents M − Number of respondents who agreed with both M/10
M - (1/10)M = (9/10)M
Column B: The number of individuals who did not disagree with both statements
= Total number of respondents M − Number of respondents who disagreed with both M/5
M - (1/5)M = (4/5)M
Attachment:
GMAT-Club-Forum-6hweyrxm.png [ 10.25 KiB | Viewed 226 times ]
11 Jul 2025, 11:49
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Ans: A = 9M/10 and B = 4M/5
Let's say M = 60 total employees ( LCM of 5, 4, and 3). There are 2 must-choose options (Either Agree or Disagree)
find out A = number of employees who did not answer "agree" to both proposals
and B = number of employees who did not answer "disagree" to both proposals
Now, Out of 60 --> 2/5 agreed with P1A = 24
of these 24 --> 1/4 agree with P2A = 6
These 6 are the ones who agree with both P1 and P2
so those who did not answer agree to both = A = 60-6 = 54 that is (9M/10)
From above, we know that 24 agreed with proposal 1 (P1A)--> which means 60-24 = 36 disagreed with P1 (P1D)
Of these 2/3rd agreed with P2 = 24, which means remaining 36-24 = 12 disagreed with both P1 and P2.
So B = 60- 12 = 48 that is (4M/5)
Let's say M = 60 total employees ( LCM of 5, 4, and 3). There are 2 must-choose options (Either Agree or Disagree)
find out A = number of employees who did not answer "agree" to both proposals
and B = number of employees who did not answer "disagree" to both proposals
Now, Out of 60 --> 2/5 agreed with P1A = 24
of these 24 --> 1/4 agree with P2A = 6
These 6 are the ones who agree with both P1 and P2
so those who did not answer agree to both = A = 60-6 = 54 that is (9M/10)
From above, we know that 24 agreed with proposal 1 (P1A)--> which means 60-24 = 36 disagreed with P1 (P1D)
Of these 2/3rd agreed with P2 = 24, which means remaining 36-24 = 12 disagreed with both P1 and P2.
So B = 60- 12 = 48 that is (4M/5)
11 Jul 2025, 11:51
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Ok lets solve this using table method let M = 100
Number of employees who agreed with P1 = (2/5)*100=40, So who don't agree they are 60
[color=#0f0f0f]of those 1/4 also agreed with Proposal 2 = (1/4)*40 =10 so remaining 30 disagree P2[/color]
Of those who disagreed with Proposal 1 2/3 agreed with Proposal 2 = (2/3)*60 = 40 that means remaining who Disagree with P2 are 20
Now final table will look like this
Column A: number of employees who did not answer "agree" to both proposals = All - (who agree on Both)
100 - 10 = 90 so this is 9M/10 as our M =100
Column B: number of employees who did not answer "disagree" to both proposals. = All - (who disagree on Both)
100 - 20 = 80 so this is 4M/5 as our M =100
Number of employees who agreed with P1 = (2/5)*100=40, So who don't agree they are 60
[color=#0f0f0f]of those 1/4 also agreed with Proposal 2 = (1/4)*40 =10 so remaining 30 disagree P2[/color]
Of those who disagreed with Proposal 1 2/3 agreed with Proposal 2 = (2/3)*60 = 40 that means remaining who Disagree with P2 are 20
Now final table will look like this
| Agree P2 | Disagree P2 | Total | |
| Agree P1 | 10 | 30 | 40 |
| Disagree P1 | 40 | 20 | 60 |
| Total | 50 | 50 | 100 |
Column A: number of employees who did not answer "agree" to both proposals = All - (who agree on Both)
100 - 10 = 90 so this is 9M/10 as our M =100
Column B: number of employees who did not answer "disagree" to both proposals. = All - (who disagree on Both)
100 - 20 = 80 so this is 4M/5 as our M =100
