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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Wed Feb 25, 2009 5:38 am

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If -2 < a < 11 and 3 < b < 12, then which of the following is NOT true?

A. 1 < a + b < 23
B. -14 < a - b < 8
C. -7 < b - a < 14
D. 1 < b + a < 23
E. -24 < a b < 132

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Source: Beat The GMAT — Problem Solving | Wed Feb 25, 2009 5:38 am

sureshbala: Master | Next Rank: 500 Posts; Posts: 319; Joined: Wed Feb 04, 2009 10:32 amFollowed by: 9 members; Location: Delhi; Thanked: 84 times

Re: NOT true

by sureshbala » Wed Feb 25, 2009 6:41 am

sanju09 wrote:If -2 < a < 11 and 3 < b < 12, then which of the following is NOT true?

A. 1 < a + b < 23
B. -14 < a - b < 8
C. -7 < b - a < 14
D. 1 < b + a < 23
E. -24 < a b < 132

Given -2<a<11
and 3<b<12

So, 1<a+b<23. Hence A and D are true.

Now minimum value of a-b = -2-12=-14(for a-b to be minimum, a must be minimum and b must be maximum)
and maximum value of a-b = 11-3 = 8 (for a-b to be maximum, a must be maximum and b must be minimum)

Hence -14<a-b<8.
Choice C is also true.

Multiplying the above inequality by -1, we get
-8<b-a<14

Also minimum value of ab is -24 and maximum value of ab is 132.
Hence, -24<ab<132.
So choice E is also true.

I don't think D can be the answer because if -8<b-a<14 then obviously -7<b-a<14 is also TRUE.

Any take on this folks?

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mygmat.2009: Senior | Next Rank: 100 Posts; Posts: 42; Joined: Thu Feb 19, 2009 10:26 am; Thanked: 3 times; GMAT Score:720

by mygmat.2009 » Wed Feb 25, 2009 6:32 pm

If b= 3.1 and a = 10.9

b - a = 3.1 - 10.9 = -7.8

-7 < b-a is false

==> Choice C

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Sam

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8137; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Fri Apr 27, 2018 9:27 am

sanju09 wrote:If -2 < a < 11 and 3 < b < 12, then which of the following is NOT true?

A. 1 < a + b < 23
B. -14 < a - b < 8
C. -7 < b - a < 14
D. 1 < b + a < 23
E. -24 < a b < 132

If we add the two inequalities together, we have:

1 < a + b < 23

Thus, A is true and since a + b = b + a, D is also true.

Multiplying the second inequality by -1, we have 3 > -b > -12 or -12 < -b < 3. Now, adding the latter to the first inequality, we have:

-14 < a - b < 8

So B is true.

Similarly, multiplying the first inequality by -1, we have 2 > -a > -11 or -11 < -a < 2. Now. adding the latter to the second inequality, we have:

-8 < b - a < 14

So C is NOT true since (b - a) could be -7.5, which does not fall into -7 < b - a < 14.

Answer: C

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

inequalities

by GMATGuruNY » Fri Apr 27, 2018 10:44 am

sanju09 wrote:If -2 < a < 11 and 3 < b < 12, then which of the following is NOT true?

A. 1 < a + b < 23
B. -14 < a - b < 8
C. -7 < b - a < 14
D. 1 < b + a < 23
E. -24 < a b < 132

If -14 < a-b < 8 (option B) is multiplied by -1, we get:
14 > -a+b > -8
14 > b-a > -8
-8 < b-a < 14.
Implication:
If B is true, then C is NOT true, since C indicates that -7 < b-a < 14.
In other words:
B and C cannot both be true.

Test whether B or C is true.
If we multiply 3 < b < 12 by -1, we get:
-3 > -b > -12
-12 < -b < -3

Adding together -2 < a < 11 and -12 < -b < -3, we get:
-2 + (-12) < a-b < 11 + (-3)
-14 < a-b < 8.
Since B is true, we know that C is NOT true.

The correct answer is C.

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