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Is the range of the integers 6, 3, y, 4, 5, and x greater

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Is the range of the integers 6, 3, y, 4, 5, and x greater [#permalink] New post 25 Jun 2012, 02:03
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Re: Is the range of the integers 6, 3, y, 4, 5, and x greater [#permalink] New post 25 Jun 2012, 02:04
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Is the range of the integers 6, 3, y, 4, 5, and x greater than 9?

Given integers are: {3, 4, 5, 6, x, y}

(1) y > 3x. If x=1 and y=4 then the range=6-1=5<9 but if x=100 then the range>9. Not sufficient.

(2) y > x > 3. If x=4 and y=5 then the range=6-3=3<9 but if x=100 then the range>9. Not sufficient.

(1)+(2) From x > 3 we have that the least value of x is 4, and from y > 3x=12 we have that the least value of y is 13, hence the least value of the range is 13-3=10>9. Sufficient.

Answer: C.
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Re: Is the range of the integers 6, 3, y, 4, 5, and x greater [#permalink] New post 25 Jun 2012, 07:41
Hi,

Range = Largest value - smallest value.

6, 3, y, 4, 5, and x, where x & y are integers

Using (1),
y>3x, if x=1, then y = 4, 5,..100....
in each case range can be 5, 6,....So, range is greater than 5. Insufficient.

Using (2),
y>x>3.
Minimum value of x = 4,
y=5,6,7... We can't say whether range is greater than 9.

Combining both statements;
x_{min} = 4
& since, y > 3x, y_{min}=13,
thus, 3, 4, 4, 5, 6, & 13 has range (13-3)=10, which is greater than 9
and on increasing x, range will also increase.

Thus, answer is (C),

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Re: Is the range of the integers 6, 3, y, 4, 5, and x greater [#permalink] New post 29 Jun 2012, 03:36
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SOLUTION

Is the range of the integers 6, 3, y, 4, 5, and x greater than 9?

Given integers are: {3, 4, 5, 6, x, y}

(1) y > 3x. If x=1 and y=4 then the range=6-1=5<9 but if x=100 then the range>9. Not sufficient.

(2) y > x > 3. If x=4 and y=5 then the range=6-3=3<9 but if x=100 then the range>9. Not sufficient.

(1)+(2) From x > 3 we have that the least value of x is 4, and from y > 3x=12 we have that the least value of y is 13, hence the least value of the range is 13-3=10>9. Sufficient.

Answer: C.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Is the range of the integers 6, 3, y, 4, 5, and x greater [#permalink] New post 02 May 2014, 12:38
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Re: Is the range of the integers 6, 3, y, 4, 5, and x greater   [#permalink] 02 May 2014, 12:38
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