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If 3 < x < 7 and 5 > y > 2, which of the following must be true?

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If 3 < x < 7 and 5 > y > 2, which of the following must be true? [#permalink] New post   20 Jan 2019, 02:20
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If 3 < x < 7 and 5 > y > 2, which of the following must be true?

A. x + y > 8
B. x - y > 0
C. x - 2y < 2
D. 2x - y > 1
E. x + y > 5

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Re: If 3 < x < 7 and 5 > y > 2, which of the following must be true? [#permalink] New post   20 Jan 2019, 02:39
selim wrote:
If 3<x<7 and 5>y>2, which of the following must be true?

A. x+y>8
B.x-y>0
C.x-2y<2
D.2x-y>1
E. x + y>5


Consider x=4 & y=3

A. x+y>8 --> NO
B.x-y>0 --> Yes, If x=4& y=4 then NO
C.x-2y<2 -->NO
D.2x-y>1 --> Yes If 8-6>1 and x=3.1 & 4.9 Yes
E. x + y>5 Yes

selim Bunuel Am'I missing something here?
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Re: If 3 < x < 7 and 5 > y > 2, which of the following must be true? [#permalink] New post   20 Jan 2019, 03:27
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NandishSS wrote:
selim wrote:
If 3 < x < 7 and 5 > y > 2, which of the following must be true?

A. x + y > 8
B. x - y > 0
C. x - 2y < 2
D. 2x - y > 1
E. x + y > 5


Consider x=4 & y=3

A. x+y>8 --> NO
B.x-y>0 --> Yes, If x=4& y=4 then NO
C.x-2y<2 -->NO
D.2x-y>1 --> Yes If 8-6>1 and x=3.1 & 4.9 Yes
E. x + y>5 Yes

selim Bunuel Am'I missing something here?


Notice that the question asks: which of the following must be true?

Given 3 < x < 7 and 2 < y < 5.

Add those two: 5 < x + y < 12. So, E MUST be true.

A. x + y > 8. Not necessarily true. Consider x = 4 and y = 3.

B. x - y > 0. Not necessarily true. Consider x = 3.5 and y = 4.

C. x - 2y < 2. Not necessarily true. Consider x = 6.9 and y = 2.1.

D. 2x - y > 1. From the stem: 6 < 2x and 5 > y. Subtract the second one from the first: 1 < 2x - y. So, D is also always true.

Two correct answers. The question is flawed.
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Re: If 3 < x < 7 and 5 > y > 2, which of the following must be true? [#permalink] New post   19 Jan 2021, 23:58
Bunuel wrote:
NandishSS wrote:
selim wrote:
If 3 < x < 7 and 5 > y > 2, which of the following must be true?

A. x + y > 8
B. x - y > 0
C. x - 2y < 2
D. 2x - y > 1
E. x + y > 5


Consider x=4 & y=3

A. x+y>8 --> NO
B.x-y>0 --> Yes, If x=4& y=4 then NO
C.x-2y<2 -->NO
D.2x-y>1 --> Yes If 8-6>1 and x=3.1 & 4.9 Yes
E. x + y>5 Yes

selim Bunuel Am'I missing something here?


Notice that the question asks: which of the following must be true?

Given 3 < x < 7 and 2 < y < 5.

Add those two: 5 < x + y < 12. So, E MUST be true.

A. x + y > 8. Not necessarily true. Consider x = 4 and y = 3.

B. x - y > 0. Not necessarily true. Consider x = 3.5 and y = 4.

C. x - 2y < 2. Not necessarily true. Consider x = 6.9 and y = 2.1.

D. 2x - y > 1. From the stem: 6 < 2x and 5 > y. Subtract the second one from the first: 1 < 2x - y. So, D is also always true.

Two correct answers. The question is flawed.



How did you calculate option D?

I get this:

7>x>3 means x>3 or x<7.
Here, x>3
2x>6

Now, 2x>6
y>2
-------
(Subtract) 2x-y>4 , if it is the right process, then how option D is also right ans?

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Re: If 3 < x < 7 and 5 > y > 2, which of the following must be true? [#permalink]
19 Jan 2021, 23:58
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