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GMAT695
Joined: 12 Jul 2023
Last visit: 15 Aug 2025
Posts: 546
Given Kudos: 243
Location: India
Concentration: Entrepreneurship, Finance
Schools: Stern '27 Fuqua '27 Columbia '27
GMAT Focus 1: 535 Q77 V78 DI74 
GMAT Focus 2: 575 Q83 V74 DI78
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GMAT 1: 420 Q31 V17
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WE:Business Development (Finance)
28 Jun 2024, 06:36
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x: 19
y: 7
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:
53% (03:09) correct
47%
(03:20)
wrong
based on 448
sessions
History
Date
Time
Result
Not Attempted Yet
The chair of the board of directors for a certain company is planning to call a meeting of the board to vote on a measure. Passing a measure requires at least 75% of the members of the board to vote for the measure. The chair has taken an informal poll of the board members, and exactly x members (including the chair) said they would vote for the measure, while the remaining y members said they would vote against it. The chair correctly determined that the measure would not pass if all members voted as they said they would, but the measure would pass if the chair could convince just one member who said she would vote against the measure to instead vote for the measure,
assuming all other members vote as they said they would.
Select a value for x and a value for y that are jointly consistent with the information provided. Make only two selections, one in each column.
assuming all other members vote as they said they would.
Select a value for x and a value for y that are jointly consistent with the information provided. Make only two selections, one in each column.
| x | y | |
| 4 | ||
| 7 | ||
| 12 | ||
| 15 | ||
| 19 |
ShowHide Answer
Official Answer
x: 19
y: 7
Updated on: 03 Apr 2025, 20:20
Originally posted by HarshavardhanR on 29 Jun 2024, 23:00.
Last edited by HarshavardhanR on 03 Apr 2025, 20:20, edited 1 time in total.
Last edited by HarshavardhanR on 03 Apr 2025, 20:20, edited 1 time in total.
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"The chair correctly determined that the measure would not pass if all members voted as they said they would"
x < (3/4)*(x + y)
4x < 3x + 3y
x < 3y ..............(1)
"but the measure would pass if the chair could convince just one member who said she would vote against the measure to instead vote for the measure"
x + 1 >= (3/4)*(x + y)
4x + 4 >= 3x + 3y
x + 4 >= 3y .................(2)
From (1) and (2),
x < 3y < x + 4
For 3 times y to still be less than x + 4, y should be small. For instance, if y = 19, 3 x 19 = 57. No value of x from the choices will give an x + 4 that is greater than 3y.
So,
for y, consider the smaller values and see what happens.
(1) y = 4
Then 3y = 12
x<3y => x can only be 4 or 7. But in both these cases, x + 4 will be < 3y (8, 11 are both < 12). We need x+4 to be greater than 3y.
Hence y= 4 can be rejected.
(2) y = 7.
Then 3y = 21.
All the choices here will work for x (all are < 21). But there is exactly one case where x + 4 is > 21. x = 19.
When x = 19 and y = 7,
x < 3y < x + 4 (19 < 21 < 23).
This must be the answer (multiple answers satisfying the given conditions are not possible here!).
x = 19; y = 7.
___
Harsha
x < (3/4)*(x + y)
4x < 3x + 3y
x < 3y ..............(1)
"but the measure would pass if the chair could convince just one member who said she would vote against the measure to instead vote for the measure"
x + 1 >= (3/4)*(x + y)
4x + 4 >= 3x + 3y
x + 4 >= 3y .................(2)
From (1) and (2),
x < 3y < x + 4
For 3 times y to still be less than x + 4, y should be small. For instance, if y = 19, 3 x 19 = 57. No value of x from the choices will give an x + 4 that is greater than 3y.
So,
for y, consider the smaller values and see what happens.
(1) y = 4
Then 3y = 12
x<3y => x can only be 4 or 7. But in both these cases, x + 4 will be < 3y (8, 11 are both < 12). We need x+4 to be greater than 3y.
Hence y= 4 can be rejected.
(2) y = 7.
Then 3y = 21.
All the choices here will work for x (all are < 21). But there is exactly one case where x + 4 is > 21. x = 19.
When x = 19 and y = 7,
x < 3y < x + 4 (19 < 21 < 23).
This must be the answer (multiple answers satisfying the given conditions are not possible here!).
x = 19; y = 7.
___
Harsha
General Discussion
29 Jun 2024, 22:12
Kudos
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\(\frac{x}{x+y}\) < 75% = \(\frac{3}{4}\)
4x < 3x + 3y
x < 3y
\(\frac{x+1}{x+y} >= \frac{3}{4}\)
\(4x + 4 >= 3x + 3y\)
\(x + 4 >= 3y\)
x < 3y <= x + 4
Then x must be among big numbers: 12, 15, 19
y be among small number: 4, 7
+) y = 4 => ey = 12 => There is no answer for x < 12 except 7 but then x+4 = 11 < 12
+) y = 7 => 3y = 21 => Try x = 19 < 21; x + 4 = 23 > 21
Then x = 19; y = 7
4x < 3x + 3y
x < 3y
\(\frac{x+1}{x+y} >= \frac{3}{4}\)
\(4x + 4 >= 3x + 3y\)
\(x + 4 >= 3y\)
x < 3y <= x + 4
Then x must be among big numbers: 12, 15, 19
y be among small number: 4, 7
+) y = 4 => ey = 12 => There is no answer for x < 12 except 7 but then x+4 = 11 < 12
+) y = 7 => 3y = 21 => Try x = 19 < 21; x + 4 = 23 > 21
Then x = 19; y = 7
