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01 Mar 2014, 07:44
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E
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Difficulty:
25%
(medium)
Question Stats:
78% (01:49) correct
22%
(02:02)
wrong
based on 673
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The value of x is one quarter of z. The sum of x, y, and z is equal to 26. If the value of y is twice the value of z, what is the largest factor of the sum of y and z?
A. 2
B. 3
C. 8
D. 12
E. 24
A. 2
B. 3
C. 8
D. 12
E. 24
01 Mar 2014, 07:45
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In this problem, we are given the information to set up the following three equations with three unknowns:
x = z/4
x + y + z = 26
y = 2z
Using the method of substitution, we can now solve for each of the three unknowns.
Since the first equation, x = z/4, is an equation for x in terms of z, and the third equation, y = 2z, is an equation for y in terms of z, we can replace x and y in the second equation by their equivalent expressions as follows:
x + y + z = (z/4) + (2z) + z = 26
We are left with an equation with just one unknown z. We can now solve for z:
(z/4) + (2z) + z = 26
z/4 + 8z/4 + 4z/4 = 13z/4 = 26
z/4 = 2
z = 8
Now that we know z, we can easily solve for y, then compute y + z (note: we can also solve for x, but since we are not interested in the value of x there is no need to do so):
y = 2z = 2(8) = 16
y + z = 16 + 8 = 24
Since the largest factor of any number is the number itself, the largest factor of the sum of y and z is 24.
The correct answer is E.
x = z/4
x + y + z = 26
y = 2z
Using the method of substitution, we can now solve for each of the three unknowns.
Since the first equation, x = z/4, is an equation for x in terms of z, and the third equation, y = 2z, is an equation for y in terms of z, we can replace x and y in the second equation by their equivalent expressions as follows:
x + y + z = (z/4) + (2z) + z = 26
We are left with an equation with just one unknown z. We can now solve for z:
(z/4) + (2z) + z = 26
z/4 + 8z/4 + 4z/4 = 13z/4 = 26
z/4 = 2
z = 8
Now that we know z, we can easily solve for y, then compute y + z (note: we can also solve for x, but since we are not interested in the value of x there is no need to do so):
y = 2z = 2(8) = 16
y + z = 16 + 8 = 24
Since the largest factor of any number is the number itself, the largest factor of the sum of y and z is 24.
The correct answer is E.
24 Aug 2015, 19:51
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Hi All,
While most Test Takers would treat this as a 'system' algebra question and solve it that way, there are some interesting Number Property patterns in this prompt that will actually allow you to use the answer choices (and some pattern-matching) to get to the solution.
To start, I'm going to deal with the last piece of information first:
Y is twice Z
The prompt asks for the BIGGEST factor of the SUM of Y and Z. Since Y = 2Z, the sum of Y and Z is (2Z) + Z = 3Z. This means that the BIGGEST factor is a MULTIPLE OF 3 (and likely one of the larger multiples of 3 in the answer choices).
The second piece of information tells us...
X+Y+Z = 26
By extension...
X+(Y+Z) = 26
X+(larger multiple of 3) = 26
From the answer choices, there are really only 2 options that make any sense: Answers D and E....
With Answer D:
IF....Y+Z = 12, then X= 14, but....
The first piece of information tells us that X = 1/4 of Z, so X has to be relatively small....In this example, it's LARGER than Z, so D is NOT the answer. At this point, the answer would have to be E, but here's the proof...
IF...Y+Z = 24 and Y= 2Z....
Y = 16
Z = 8
X is 1/4 of Z, so X = (1/4)(8) = 2
X+Y+Z=26
2+16+8=26
All of the numbers 'fit' what we were told, so this MUST be the answer.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
While most Test Takers would treat this as a 'system' algebra question and solve it that way, there are some interesting Number Property patterns in this prompt that will actually allow you to use the answer choices (and some pattern-matching) to get to the solution.
To start, I'm going to deal with the last piece of information first:
Y is twice Z
The prompt asks for the BIGGEST factor of the SUM of Y and Z. Since Y = 2Z, the sum of Y and Z is (2Z) + Z = 3Z. This means that the BIGGEST factor is a MULTIPLE OF 3 (and likely one of the larger multiples of 3 in the answer choices).
The second piece of information tells us...
X+Y+Z = 26
By extension...
X+(Y+Z) = 26
X+(larger multiple of 3) = 26
From the answer choices, there are really only 2 options that make any sense: Answers D and E....
With Answer D:
IF....Y+Z = 12, then X= 14, but....
The first piece of information tells us that X = 1/4 of Z, so X has to be relatively small....In this example, it's LARGER than Z, so D is NOT the answer. At this point, the answer would have to be E, but here's the proof...
IF...Y+Z = 24 and Y= 2Z....
Y = 16
Z = 8
X is 1/4 of Z, so X = (1/4)(8) = 2
X+Y+Z=26
2+16+8=26
All of the numbers 'fit' what we were told, so this MUST be the answer.
Final Answer:
GMAT assassins aren't born, they're made,
Rich
