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27 May 2020, 04:26
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
48% (01:46) correct
52%
(03:11)
wrong
based on 23
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For all positive numbers a and b, the function {a, b} = k, where k is the multiple of b nearest to a. If x and y are positive integers such that x/y= 15.25 and {xy, y} = 16, what is the value of y?
(1) {x/y, y} = {x/y, 2y}
(2) {x/y, y} = {x/y, y^2}
Are You Up For the Challenge: 700 Level Questions
(1) {x/y, y} = {x/y, 2y}
(2) {x/y, y} = {x/y, y^2}
Are You Up For the Challenge: 700 Level Questions
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27 May 2020, 05:49
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Bunuel
Solution
Step 1: Analyse Question Stem
- • For all positive numbers a and b, {a , b} =k, where k is multiple of b nearest to a.
- o This means, k/b = Integer.
• \(\frac{x}{y} =15.25 =\frac{61}{4 }⟹ x = \frac{61}{4}*y\)
- o Since, x is an integer, y must be a multiple of 4.
- o This means, 16/y = integer
- So, Possible values of y = 4, 8 16
y cannot be 1 because in that case x won’t be an integer.
- o Or we need to determine out of 4, 8, and 16 which one is the exact value of y.
Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE
Statement 1: {x/y, y} = {x/y, 2y}
- • According to this statement: {15.25, y}= {15.25, 2y}
• Now, let’s check all three values of y.
- o If y = 4
- Then, {15.25, y}= {15.25, 4} = 16 and {15.25, 2y}= {15.25, 8}=16
Thus, y can be 4
- Then, {15.25, y}= {15.25, 8} = 16 and {15.25, 2y}= {15.25, 16}=16
Thus, y can be 8
Statement 2: {x/y, y} = {x/y, y^2}
- • According to this statement: {15.25, y}= {15.25, \(y^2\)}
• Now, let’s check all three values of y.
- o If y = 4
- Then, {15.25, y}= {15.25, 4} = 16 and {15.25, \(y^2\)}= {15.25, 16}=16
Thus, y can be 4
- Then, {15.25, y}= {15.25, 8} = 16 and {15.25, \(y^2\)}= {15.25, 64}= 0
Thus, y cannot be 8
- Then, {15.25, y}= {15.25, 16} = 16 and {15.25, \(y^2\)}= {15.25, 256}= 0
Thus, y cannot be 16.
Thus, the correct answer is Option B.
27 May 2020, 09:52
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Bunuel
There are many issues with the question itself. The question defines a function "for all positive numbers", but the function makes no sense when b is not an integer. Nor is the function well-defined. What is the value of {3, 2}, for example? It could equal 2 or 4. A function, by definition, needs to produce a single well-defined value for any valid input, and this function does not. And the GMAT would never use mathematical notation, in this case set notation, that is already used for a well-defined purpose and repurpose it to define a function. If you do that, it then becomes unclear what {x, y} means - is that a set, or are we applying a function to x and y?
So as written I don't think the question is even worth attempting. If the issues with it were resolved, I imagine the intended answer is B; if {xy, y} is 16, then from the definition of the function, 16 needs to be a multiple of y, so y can only be 1, 2, 4, 8 or 16. Since x/y = 15.25, y cannot be 1 or 2, since we'd never get a decimal ending in .25 if we divide an integer by 1 or 2. Now that we know what x/y is, and have three cases for y, we can see which cases remain valid when considering each Statement, and Statement 2 only admits one value of y (4 only), while Statement 1 admits two different values (4 or 8).
