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# If 8x > 4 + 6x, what is the value of the integer x? (1) 6

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Director
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If 8x > 4 + 6x, what is the value of the integer x? (1) 6 [#permalink]  14 Oct 2007, 13:41
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If 8x > 4 + 6x, what is the value of the integer x?

(1) 6 – 5x > -13

(2) 3 – 2x < -x + 4 < 7.2 – 2x

have fun!
VP
Joined: 09 Jul 2007
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Re: inequality DS [#permalink]  14 Oct 2007, 14:20
beckee529 wrote:
If 8x > 4 + 6x, what is the value of the integer x?

(1) 6 – 5x > -13

(2) 3 – 2x < -x + 4 < 7.2 – 2x

have fun!

hmm tricky,
I got D
x=3 as it says x is an integer
VP
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8x > 4 + 6x

2x > 4

x > 2

statement 1

6 – 5x > -13

5x < 19

x < 19/5

x < ~4

since x is an integer then x must be 3.

sufficient

statement 2

3 – 2x < -x + 4 < 7.2 – 2x

-2x < -x+1 < 4.2 - 2x

2x > x-1 > -4.2 + 2x

0 > -x-1 > -4.2

0 < x+1 < 4.2

-1 < x < 3.2

x can be only 3 since the stem states that integer x > 2 .

sufficient

Intern
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OK, we know that 8x > 4 + 6x gives us x>2
statement 1 tells us that x<3.8
statement 2 tells us that -1<x<3.2
the only sufficient integer in the range is 3, but... maby I'm missing smth, but I always thought that to make statement sufficient in DS you have to get one an only answer, lets say x=3, but not 2<x<3.2, or 2<x<3.8. Yes, we are asked to find integer x, but none of the statements (or both taken together) give us the exact answer, just a range, so I'd go with E.
Pls, pls, pls correct me if I'm wrong, because it's not the first time I'm comming up with smth like this...
CEO
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Re: inequality DS [#permalink]  14 Oct 2007, 21:43
beckee529 wrote:
If 8x > 4 + 6x, what is the value of the integer x?

(1) 6 – 5x > -13

(2) 3 – 2x < -x + 4 < 7.2 – 2x

have fun!

Clear D.

rephrase stem: x>2.

S1: x<19/5 ---> x<less than 4 ---> 2<x<less than 4

Since X is an integer only 3 would suffice for x.

Suff.

S2:

3-2x< -x +4 < 7.2 -2x first add 2x.

3<x+4<7.2 Then subtract 4

-1<x<3.2 Discard the -1 and replace w/ 2

2<x<3.2. So again x can only be 3.

Suff.
Director
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good job guys.. answer is D. the only possible integer value for x is 3
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