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
Integers
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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
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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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.
Final Answer: C
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Rich
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.
Final Answer: C
GMAT assassins aren't born, they're made,
Rich
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Before looking at the statements, REPHRASE the question stem.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
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
Answer to target question: no.
Test a large value:
x = 0
y = 100
Answer to target question: yes.
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
Answer to target question: no.
Test a large value:
x = 4
y = 100
Answer to target question: yes.
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)
Answer to target question: yes.
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.
The answer is C.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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Statement One Alone: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
y > 3x
Statement one is not sufficient to answer the question. For example, if x = 0, y could be 1 and the range is 6 - 0 = 6, which is less than 9. However, if x = 10, y could be 31 and the range is 31 - 3 = 28, which is greater than 9.
Statement Two Alone:
y > x > 3
Statement two is not sufficient to answer the question. For example, if x = 4, y could be 5 and the range is 6 - 0 = 6, which is less than 9. However, if x = 14, y could be 15 and the range is 15 - 3 = 12, which is greater than 9.
Statements One and Two Together:
From the two statements, we know that x > 3 and y > 3x. So the smallest integer x can be is 4 and the smallest integer y can be is 3(4) + 1 = 13. Thus the smallest range of the integers is 13 - 3 = 10, which is greater 9. Since 10 is the smallest range, any other range of the integers will be greater than 10 and hence greater than 9.
Answer: C
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