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2/5 of them agreed with Proposal 1, and of those, 1/4 also agreed with Proposal 2.
Of those who disagreed with Proposal 1, 2/3 agreed with Proposal 2.
Let's create a table for this, P1 - agree with P1, P1 Not, disagree with p1
P1P1 Not
P2(1/4)*2/5(3/5)*2/3
P2 not1/3(3/5)
2/53/5M

who did not answer "agree" to both proposals, p1 Not and P2 Not = (1/3)(3/5)*M = M/5
who did not answer "disagree" to both proposals, Mean agree with both proposals = (1/4)*2/5 = M/10
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In a company survey, M employees evaluated both Proposal 1 and Proposal 2, selecting either 'agree' (A) or 'disagree' (D) for each.

Condition 1 -2/5 of them agreed with Proposal 1, and of those, 1/4 also agreed with Proposal 2.
=> P1 + A= M*2/5 , then P1+D=M*3/5
Also if if 1/4th of P1 i.e, M/10 agreed with both P1 and P2...... Answer for column 1

Of those who disagreed with Proposal 1, 2/3 agreed with Proposal 2.
=>M*2/3 * 3/5 = P2+A,
=> M*1/3 *3/5 = M/5 = P1,P2 +D disagreed with both proposal .... Answer for column 2

Therefore employees who disagreed with both proposal =
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In a company survey, M employees evaluated both Proposal 1 and Proposal 2, selecting either 'agree' or 'disagree' for each.

  • 2/5 of them agreed with Proposal 1, and of those, 1/4 also agreed with Proposal 2.
  • Of those who disagreed with Proposal 1, 2/3 agreed with Proposal 2.

Select for Column A the expression that represents the number of employees who did not answer "agree" to both proposals, and select for Column B the expression that represents the number of employees who did not answer "disagree" to both proposals. Make only two selections, one in each column.

P1 Agree = 2M/5
P1 Disagree = 3M/5

P1 Agree and P2 Agree = 1/4 * 2/5 = M/10

Only P2 Agree = 2/3 * 3/5 = 2M/5

The number of employees who did not answer "agree" to both proposals,
= M - M/10 = 9M/10

Column A = 9M/10


The number of employees who did not answer "disagree" to both proposals
Disagree with 1 = 3/5
1/3 from this disagreed with both => 1/3 * 3/5 = 1/5
> Required value = M - M/5 = 4M/5

Column B = 4M/5
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P1Not P1
P2M/102M/5
Not P23M/10M/5
2M/53M/5

Column A the expression that represents the number of employees who did not answer "agree" to both proposals = M - M/10 = 9M/10
Column B the expression that represents the number of employees who did not answer "disagree" to both proposals = M - M/5 = 4M/5
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This question was provided by GMAT Club
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In a company survey, M employees evaluated both Proposal 1 and Proposal 2, selecting either 'agree' or 'disagree' for each.

  • 2/5 of them agreed with Proposal 1, and of those, 1/4 also agreed with Proposal 2.
  • Of those who disagreed with Proposal 1, 2/3 agreed with Proposal 2.

Select for Column A the expression that represents the number of employees who did not answer "agree" to both proposals, and select for Column B the expression that represents the number of employees who did not answer "disagree" to both proposals. Make only two selections, one in each column.
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Given fraction are \(\frac{2}{5},\)\(\frac{1}{4}\),\(\frac{2}{3}\)
Calculating LCM of denominator = 60
Let the total number of employees be M=60( for easy calculation and representation)
Now using two way table:
P2 AgreeP2 Disagree Row Total
P1 Agree61824
P1 Disagree241236
Column Total303060

Given(2/5) of them agreed with proposal1, and of those (1/4) also agreed with proposal 2.
==>P1 Agree= Proposal1 agreed=\(\frac{2}{5}\)*60 =24
Both Agreed = P1 Agree and P2 Agree cell= \(\frac{1}{4}\)*24 = 6
P1Agree and P2Disagree cell = 24-6= 18
P1 Disagree total = 60-24= 36

Given:Of those who disagreed with proposal 1 , (2/3) agreed with proposal 2.
==>P1 Disagree and P2 agree cell = \(\frac{2}{3}\)*36 = 24
P1 disagree and P2 disagree = 36-24=12

Column A:
Employees who did not answer agree to both proposals = Total -(both agreed)= 60- 6= 54
But we assumed M=60
==> 54=\(\frac{9}{10}\)(60)= \(\frac{9}{10}\)M

Column B:
Employees who didn't answer disagree to both proposals= Total -(P1 disagree and P2 disagree cell)= 60-12= 48
But we assumed M=60
==>48= \(\frac{4}{5}\)(60)= \(\frac{4}{5}\)M
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M employees evaluated both Proposal 1 and Proposal 2, selecting either 'agree' or 'disagree' for each

2/5 of them agreed with Proposal 1, and of those, 1/4 also agreed with Proposal 2.
Of those who disagreed with Proposal 1, 2/3 agreed with Proposal 2.

So we know that the possible choices are
Agree–Agree
Agree–Disagree
Disagree–Agree
Disagree–Disagree

Now in that lets go through them 1 by 1,
Proposal 1 Agree = 2M/5
Proposal 1 Disagree = 3M/5

Proposal 1 Agree Proposal 2 Agree (Agree–Agree)= 0.25 * 2M/5 = M/10
=> Proposal 1 Agree Proposal 2 Disagree (Agree–Disagree) = 2M/5 - M/10 = 3M/10

Proposal 1 Disagree Proposal 2 Agree (Disagree –Agree)= 2/3* 3M/5 = 2M/5
=> Proposal 1 Disagree Proposal 2 Disagree (Disagree –Disagree) = 3M/5 - 2M/5 = M/5

Number of employees who did not agree to both proposals = M - (Agree - Agree) = M - M/10 = 9M/10
Number of employees who did not disagree to both proposals = M - (Disagree –Disagree) = M - M/5 = 4M/5

Column A = 9M/10
Colum B = 4M/5
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Bunuel
 


This question was provided by GMAT Club
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In a company survey, M employees evaluated both Proposal 1 and Proposal 2, selecting either 'agree' or 'disagree' for each.

  • 2/5 of them agreed with Proposal 1, and of those, 1/4 also agreed with Proposal 2.
  • Of those who disagreed with Proposal 1, 2/3 agreed with Proposal 2.

Select for Column A the expression that represents the number of employees who did not answer "agree" to both proposals, and select for Column B the expression that represents the number of employees who did not answer "disagree" to both proposals. Make only two selections, one in each column.
As given M emps.

#emps agreed to P1(Proposal 1) = 2M/5.

#emps agreed to both P1 & P2 = 1/4 * 2M/5 => M/10.

M/10 agreed with both proposals.

Hence to get number of employees who did not answer "agree" to both proposals, We need to remove the above ones

Column A = M - M/10=> 9M/10.

Similarly, #emps disagreed to P1 = 3M/5. Of them 2/3 agreed. Means 1/3 disagreed. => 1/3 * 3M/5 =M/5.

M/5 disagreed with both proposals.

Hence to get the number of employees who did not answer "disagree" to both proposals
Column B = M - M/5 => 4M/5.

Hence IMO A : 9M/10, B : 4M/5
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In a company survey, M employees evaluated both Proposal 1 and Proposal 2, selecting either 'agree' or 'disagree' for each.

  • 2/5 of them agreed with Proposal 1, and of those, 1/4 also agreed with Proposal 2.
  • Of those who disagreed with Proposal 1, 2/3 agreed with Proposal 2.

Select for Column A the expression that represents the number of employees who did not answer "agree" to both proposals, and select for Column B the expression that represents the number of employees who did not answer "disagree" to both proposals. Make only two selections, one in each column.

Proposal 1 :

Agree = 2/5M
Disagree = 3/5 M

Proposal 2 :

Agree (from Proposal 1 agree) = 1/4 * 2/5M = 1/10M
Agree (from Proposal 1 disagree) = 2/3 * 3/5 M = 2/5 M
Total Agree = M/2

Agree Both = M - 1/10 M = 9/10 M

Proposal 2 :
Disagree(from Proposal 1 disagree) = 1/3*3/5 M = 1/5M

Both disagree = M - 1/5M = 4/5M

Answers:

Column A: (9/10) * M
Column B: (4/5) * M
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2/5m agree with P1 Meaning 1-2/5 = 3/5m disagree with P1
1/4X2/5 = 1/10 agree with P2
Meaning 1-1/10 = 9/10 did not agree with P2
Column A 9/10
Of those that disagree with P1 2/3 agree with P2
So 2/3x3/5= 2/5 agree with P2
Agree with P1 =2/5 among these 1/4 agree with P2 meaning 3/4 disagree with P2
Disagree with both 1/3x3/5 =1/5
So did not disagree with both = 1-1/5 = 4/5
Column B 4/5
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In a company survey, M employees evaluated both Proposal 1 and Proposal 2, selecting either 'agree' or 'disagree' for each.

  • 2/5 of them agreed with Proposal 1, and of those, 1/4 also agreed with Proposal 2.
  • Of those who disagreed with Proposal 1, 2/3 agreed with Proposal 2.

Select for Column A the expression that represents the number of employees who did not answer "agree" to both proposals, and select for Column B the expression that represents the number of employees who did not answer "disagree" to both proposals. Make only two selections, one in each column.
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Given,
In a company survey, M employees evaluated both Proposal 1 and Proposal 2, selecting either 'agree' or 'disagree' for each.



  • 2/5 of them agreed with Proposal 1, and of those, 1/4 also agreed with Proposal 2.
  • Of those who disagreed with Proposal 1, 2/3 agreed with Proposal 2.


To find:
Column A: the expression that represents the number of employees who did not answer "agree" to both proposals
Column B: the expression that represents the number of employees who did not answer "disagree" to both proposals.

Solution:
Agree with Proposal 1, P1A = 2M/5
Of those, also agreed with Proposal 2, P1A2 = (1/ 4)* 2M/5 = M/10

Disagree with Proposal 1, P1D = 3M/5
Of those, agreed with Proposal 2, P1D2 = (2/3)*3M/5 = 2M/5
Remaining, who are disagreeing with both = 3M/5 – 2M/5 = M/5
So,
Number of persons who didn’t Ans “ agree to noth proposal “ = M – who agree to both proposal = M – M/10
= 9M/10
Number of persons who didn’t Ans “ Disagree tp both proposal” = M – who disagree t both proposal
= M – M/5
= 4M/5

Ans:
Column A = 9M/10
Column B = 4M/5


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In a company survey, M employees evaluated both Proposal 1 and Proposal 2, selecting either 'agree' or 'disagree' for each.

  • 2/5 of them agreed with Proposal 1, and of those, 1/4 also agreed with Proposal 2.
  • Of those who disagreed with Proposal 1, 2/3 agreed with Proposal 2.

Select for Column A the expression that represents the number of employees who did not answer "agree" to both proposals, and select for Column B the expression that represents the number of employees who did not answer "disagree" to both proposals. Make only two selections, one in each column.
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Bunuel
 


This question was provided by GMAT Club
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In a company survey, M employees evaluated both Proposal 1 and Proposal 2, selecting either 'agree' or 'disagree' for each.

  • 2/5 of them agreed with Proposal 1, and of those, 1/4 also agreed with Proposal 2.
  • Of those who disagreed with Proposal 1, 2/3 agreed with Proposal 2.

Select for Column A the expression that represents the number of employees who did not answer "agree" to both proposals, and select for Column B the expression that represents the number of employees who did not answer "disagree" to both proposals. Make only two selections, one in each column.
M/5 and M/10
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This question was provided by GMAT Club
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In a company survey, M employees evaluated both Proposal 1 and Proposal 2, selecting either 'agree' or 'disagree' for each.

  • 2/5 of them agreed with Proposal 1, and of those, 1/4 also agreed with Proposal 2.
  • Of those who disagreed with Proposal 1, 2/3 agreed with Proposal 2.

Select for Column A the expression that represents the number of employees who did not answer "agree" to both proposals, and select for Column B the expression that represents the number of employees who did not answer "disagree" to both proposals. Make only two selections, one in each column.

Proposal 1Proposal 2Proposal 1 & 2
Agree2M/5 2M/20
Disagree3M/5

3M/5 people disagreed with Proposal 1,
2/3 of 3M/5 agreed with Proposal 2 = 2M/5 OR (3M/5 -2M/5) also disagreed with Proposal 2
= M/5.

Column A the expression that represents the number of employees who did not answer "agree" to both proposals
= total number number of employees – number of employees who agreed to both proposals= M-M/10= 9M/10

Column B the expression that represents the number of employees who did not answer "disagree" to both proposals
= Total number of people – number of employees who disagreed to proposals = M- M/5 = 4M/5
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Bunuel
 


This question was provided by GMAT Club
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In a company survey, M employees evaluated both Proposal 1 and Proposal 2, selecting either 'agree' or 'disagree' for each.

  • 2/5 of them agreed with Proposal 1, and of those, 1/4 also agreed with Proposal 2.
  • Of those who disagreed with Proposal 1, 2/3 agreed with Proposal 2.

Select for Column A the expression that represents the number of employees who did not answer "agree" to both proposals, and select for Column B the expression that represents the number of employees who did not answer "disagree" to both proposals. Make only two selections, one in each column.



We can segregate the employee as shown above.

Column A: \(\frac{9M}{10}\)

Column B: \(\frac{4M}{5}\)
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Proposal1=2M/5
Proposal1 and Proposal2 = 1/4*2M/5 = M/10

The number of employees who did not answer agree to both proposals is M minus the number of employees who did answer agree to both proposals: M - M/10 = 9M/10

DisagreeProposal1=M-2M/5=3M/5
DisagreeProposal1 and Proposal2 = 2/3*3M/5 = 2M/5
DisagreeProposal1 and DisagreeProposal2 = 3M/5 - 2M/5 = M/5

The number of employees who did not answer disagree to both proposals is M minus the number of employees who did answer disagree to both proposals: M - M/5 = 4M/5

Column A = 9M/10
Column B = 4M/5
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p1+agreep1+disagreetotal
p2+agreeM/102M/5
p2+disagree3M/10M/5
total2M/53M/5M
for column A - from 4 catogories we need to add the remaining employee other than no. of employees who answer 'agree' to both proposals so,
(p1+agree) and (p2+disagree) + (p1+disagree) and (p2+disagree) + (p1+disagree) and ( p2+agree)
= (3M/10) + M/5 + (2M/5) = 9M/10
for column B -
add all except no. of employee disagree to both, so,
M/10 + 3M/10 + 2M/5 = 4M/5
Bunuel
 


This question was provided by GMAT Club
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In a company survey, M employees evaluated both Proposal 1 and Proposal 2, selecting either 'agree' or 'disagree' for each.

  • 2/5 of them agreed with Proposal 1, and of those, 1/4 also agreed with Proposal 2.
  • Of those who disagreed with Proposal 1, 2/3 agreed with Proposal 2.

Select for Column A the expression that represents the number of employees who did not answer "agree" to both proposals, and select for Column B the expression that represents the number of employees who did not answer "disagree" to both proposals. Make only two selections, one in each column.
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P1 (Agree)P1' (Disagree)
P2 (Agree)1/4*2/5M = M/102/3*3M/5=2M/5M/2
P2' (Disagree)3M/10M/5M/2
2M/5M-2M/5 =3M/5Total = M

Number of employees who did not answer "agree" to both proposals = M - M/10 = 9M/10
Number of employees who did not answer "disagree" to both proposals = M - M/5 = 4M/5
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This question was provided by GMAT Club
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In a company survey, M employees evaluated both Proposal 1 and Proposal 2, selecting either 'agree' or 'disagree' for each.

  • 2/5 of them agreed with Proposal 1, and of those, 1/4 also agreed with Proposal 2.
  • Of those who disagreed with Proposal 1, 2/3 agreed with Proposal 2.

Select for Column A the expression that represents the number of employees who did not answer "agree" to both proposals, and select for Column B the expression that represents the number of employees who did not answer "disagree" to both proposals. Make only two selections, one in each column.
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