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## Integers

This topic has 2 expert replies and 1 member reply
irock Senior | Next Rank: 100 Posts
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#### Integers

Fri Jun 03, 2011 1:06 am
Is the range of the integers 6, 3, y, 4, 5, and x greater
than 9 ?

(1) y > 3x
(2) y > x > 3

OA C

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### GMAT/MBA Expert

ceilidh.erickson GMAT Instructor
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Fri Feb 23, 2018 11:22 am
irock wrote:
Is the range of the integers 6, 3, y, 4, 5, and x greater than 9 ?

(1) y > 3x
(2) y > x > 3

OA C
Before looking at the statements, REPHRASE the question stem.

First, put the known values in order: 3, 4, 5, 6. The range of the values that we know is 6 - 3 = 3. We would know that we had a range greater than 9 if one of our variables was less than -3 (6 - -3 = 9) or greater than 12 (12 - 3 = 9).

Target question: is either x or y less than -3 or greater than 12?

(1) y > 3x
Test small values:
x = 0
y = 1

Test a large value:
x = 0
y = 100
Insufficient.

(n.b. when testing cases with 2 variables, it's often helpful to keep 1 variable constant, and only change the other one).

(2) y > x > 3
Test small values:
x = 4
y = 5

Test a large value:
x = 4
y = 100
Insufficient.

(1) & (2) together: y > 3x and y > x > 3
Test small values:
x = 4 (smallest possible value of x)
y = 13 (smallest possible integer greater than 3x)

Test a large value... we don't have to. The larger x gets, the larger y gets, and we'll definitely have a value greater than 12. Sufficient.

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### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
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Mon Feb 19, 2018 2:25 pm
Hi All,

We're given a set of 6 INTEGERS: 3, 4, 5, 6, X and Y. We're asked if the range is GREATER than 9. This is a YES/NO question. We can solve it by TESTing VALUES.

1) Y > 3X

IF.....
X=1 and Y=4, then the range = 6-1 = 5 and the answer to the question is NO
X=4 and Y=13, then the range = 13 - 3 - 10 and the answer to the question is YES
Fact 1 is INSUFFICIENT

2) Y > X > 3
X=4 and Y=5, then the range = 6-3 = 3 and the answer to the question is NO
X=4 and Y=13, then the range = 13 - 3 - 10 and the answer to the question is YES
Fact 2 is INSUFFICIENT

Combined, we know:
Y > 3X
Y > X > 3

Since both X and Y are INTEGERS and X>3, we know that X is AT LEAST 4... and since Y > 3X, this means that Y is AT LEAST 13. As X gets bigger, Y would also get bigger. Since the lowest value in the group is 3, the range of the group will ALWAYS be AT LEAST 13-3 = 10. Thus, the answer to the question is ALWAYS YES.

GMAT assassins aren't born, they're made,
Rich

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cans Legendary Member
Joined
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Fri Jun 03, 2011 1:13 am
integers are 3,4,5,6,x,y
range = largest-smallest
a)y>3x. if x=1, y>3 let it be 4. Range = 6-1 = 5<9
if x=1, y>3 let it be 100 range = 100-1 = 99>9
insufficient
b)y>x>3
x=4,y=5 => range = 6-3 = 3 <9
x=10,y=13 =>range = 13-3=10> 9
Insufficient
a&b together) y>3x and x>3
it means x is atleast 4 and thus y>12 or y is atleast 13
range=y-3 = as min y is 13, y-3 is minimum 10 thus range >9
Sufficient
IMO C

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