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GMAT Club 12 Days of Christmas is a 4th Annual GMAT Club Winter Competition based on solving questions. This is the Winter GMAT competition on GMAT Club with an amazing opportunity to win over $40,000 worth of prizes!
24 Feb 2022, 05:15
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
76% (01:32) correct
24%
(01:55)
wrong
based on 55
sessions
History
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Not Attempted Yet
If Ferdinand, Quentin, and Zamir have a total of $28, how much money does Ferdinand have?
(1) Ferdinand has $3 less than Quentin, who has more money than Zamir does.
(2) Quentin has $5 more than Zamir, who has less money than Ferdinand does.
Source: Total GMAT Math - Jeff Sackmann
(1) Ferdinand has $3 less than Quentin, who has more money than Zamir does.
(2) Quentin has $5 more than Zamir, who has less money than Ferdinand does.
Source: Total GMAT Math - Jeff Sackmann
Updated on: 24 Feb 2022, 09:12
Originally posted by BrentGMATPrepNow on 24 Feb 2022, 07:27.
Last edited by BrentGMATPrepNow on 24 Feb 2022, 09:12, edited 2 times in total.
Last edited by BrentGMATPrepNow on 24 Feb 2022, 09:12, edited 2 times in total.
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rahulp11
If Ferdinand, Quentin, and Zamir have a total of $28, how much money does Ferdinand have?
(1) Ferdinand has $3 less than Quentin, who has more money than Zamir does.
(2) Quentin has $5 more than Zamir, who has less money than Ferdinand does.
Source: Total GMAT Math - Jeff Sackmann
Given: Ferdinand, Quentin, and Zamir have a total of $28 (1) Ferdinand has $3 less than Quentin, who has more money than Zamir does.
(2) Quentin has $5 more than Zamir, who has less money than Ferdinand does.
Source: Total GMAT Math - Jeff Sackmann
Let F = the amount of money Quentin has
Let Q = the amount of money Ferdinand has
Let Z = the amount of money Zamir has
So we can write: F + Q + Z = 28
Target question: What is the value of Z
Statement 1: Ferdinand has $3 less than Quentin, who has more money than Zamir does.
So we can write: F = Q - 3 (we also know that Q > Z, but that doesn't help us solve the system below)
We now have the following system of equations:
F + Q + Z = 28
F = Q - 3
Take the top equation and replace F with Q - 3 to get: (Q - 3) + Q + Z = 28
Simplify to get: 2Q + Z = 31
At this point, we can see that there are many different solutions to this equation, which means there are many different possible values for Z
Since we can’t answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: Quentin has $5 more than Zamir, who has less money than Ferdinand does.
So we can write: Q = Z + 5 (we also know that Z > F, but that doesn't help us solve the system below)
We now have the following system of equations:
F + Q + Z = 28
Q = Z + 5
Take the top equation and replace Q with Z + 5 to get: F + (Z + 5) + Z = 28
Simplify: F + 2Z = 23
At this point, we can see that there are many different solutions to this equation, which means there are many different possible values for Z
Since we can’t answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that F = Q - 3
Statement 2 tells us that Q = Z + 5
When we combine this with the given information, we get the following system:
F + Q + Z = 28
F = Q - 3
Q = Z + 5
Since we have three different linear equations with three different variables, we know we can solve this system for F, Q and Z, which means we COULD answer the target question with certainty (although we'd never waste valuable time on tests they doing so)
The combined statements are SUFFICIENT
Answer: C
24 Feb 2022, 09:02
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rahulp11
If Ferdinand, Quentin, and Zamir have a total of $28, how much money does Ferdinand have?
(1) Ferdinand has $3 less than Quentin, who has more money than Zamir does.
(2) Quentin has $5 more than Zamir, who has less money than Ferdinand does.
Source: Total GMAT Math - Jeff Sackmann
(1) Ferdinand has $3 less than Quentin, who has more money than Zamir does.
(2) Quentin has $5 more than Zamir, who has less money than Ferdinand does.
Source: Total GMAT Math - Jeff Sackmann
Source Explanation:
The question sets up what could turn out to be a 3-variable system of equations. To solve one of those, you need three distinct equations.
The question itself gives you one:
f + q + z = 28
Statement (1) is insufficient. It gives you an equation:
f = q − 3
and an inequality:
q > z
The inequality isn’t very helpful, since we need exact relationships to determine
the value of any of the individual variables.
Statement (2) is similar and is also insufficient. First, there’s an equation:
q = z + 5
and also an inequality:
z < f
Again, we need one more equation to solve for any of the variables.
Taken together, we have all we need. The question provided one equation,
and each statement added another, giving us a total of 3 distinct equations with
the same three variables. No need to solve for f;
we can confidently select (C).
