If positive integer y is equal to the sum of all the unique factors of the positive integer x, is |x-y| > 1?
x is not prime
x≠1
x is not prime
x≠1
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is |x-y| > 1?
Source: Beat The GMAT — Data Sufficiency |
Y = sum of unique factors of x
is |x-y| > 1?
St1: x <> Prime
if x = 1, y = 1 and |x-y|= 0 (NOT GREATER THAN 1)
if x = 4, y = 7 and |x-y|= 3 (GREATER THAN 1)
Not sufficient
St2: x <> 1
if x = 2, y = 3 and |x-y|= 1 (NOT GREATER THAN 1)
if x = 4, y = 7 and |x-y|= 3 (GREATER THAN 1)
Not sufficient
ST1 + ST2 together:
x = 4, y = 7 and |x-y|= 3 (GREATER THAN 1)
x = 6, y = 12 and |x-y|= 6 (GREATER THAN 1)
x = 8, y = 15 and |x-y|= 7 (GREATER THAN 1)
as x increases, y will increase at a faster rate such that |x-y| will always be greater than 1
hence C. Both statements are sufficient
is |x-y| > 1?
St1: x <> Prime
if x = 1, y = 1 and |x-y|= 0 (NOT GREATER THAN 1)
if x = 4, y = 7 and |x-y|= 3 (GREATER THAN 1)
Not sufficient
St2: x <> 1
if x = 2, y = 3 and |x-y|= 1 (NOT GREATER THAN 1)
if x = 4, y = 7 and |x-y|= 3 (GREATER THAN 1)
Not sufficient
ST1 + ST2 together:
x = 4, y = 7 and |x-y|= 3 (GREATER THAN 1)
x = 6, y = 12 and |x-y|= 6 (GREATER THAN 1)
x = 8, y = 15 and |x-y|= 7 (GREATER THAN 1)
as x increases, y will increase at a faster rate such that |x-y| will always be greater than 1
hence C. Both statements are sufficient
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Brent@GMATPrepNow
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Target question: Is |x-y| > 1?himu wrote:If positive integer y is equal to the sum of all the unique factors of the positive integer x, is |x-y| > 1?
x is not prime
x≠1
Given: positive integer y is equal to the sum of all the unique factors of the positive integer x
There are 3 cases to consider here.
case a: x = 1
This means y = 1
In this case, |x-y| = 0
case b: x is prime
Here, the only factors of x are: 1 and x, which means y = x+1
In this case, |x-y| = |x-(x+1)| = |-1| = 1
case c: x is composite
Here, the factors of x are: 1, x, and at least one extra number, which means y = x+1+(at least one extra number)
In this case, |x-y| > 1
Statement 1: x is not prime
This rules out case b, which leave us with case a or case c
In case a: |x-y| = 0
In case c: |x-y| > 1
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x≠1
This rules out case a, which leave us with case b or case c
In case b: |x-y| = 1
In case c: |x-y| > 1
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined:
Statement 1 rules out case b
Statement 2 rules out case a
This leaves us with case c, which means |x-y| > 1
Since we can now answer the target question with certainty, the combined statements are SUFFICIENT
Answer = C
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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GMATGuruNY
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Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
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