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# If a > 12 and b < 7, which of the following must be true?

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Math Expert
Joined: 02 Sep 2009
Posts: 53864
If a > 12 and b < 7, which of the following must be true?  [#permalink]

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19 Feb 2019, 22:09
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25% (medium)

Question Stats:

73% (01:05) correct 27% (01:47) wrong based on 52 sessions

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If a > 12 and b < 7, which of the following must be true?

I. a + b > 12
II. a – b > 5
III. a + b < 19

A. I only
B. II only
C. III only
D. I and II only
E. I and III only

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Re: If a > 12 and b < 7, which of the following must be true?  [#permalink]

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19 Feb 2019, 22:44
Bunuel wrote:
If a > 12 and b < 7, which of the following must be true?

I. a + b > 12
II. a – b > 5
III. a + b < 19

A. I only
B. II only
C. III only
D. I and II only
E. I and III only

If a > 12 and b < 7

Consider a=13 & b=-13

Hence a + b > 12 not true

Consider a=20 & b= 6 --> a + b < 19 Not true

Consider a least value be 13 & for b be 6

a – b > 5 True

Hence B
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Re: If a > 12 and b < 7, which of the following must be true?  [#permalink]

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19 Feb 2019, 22:49
A) If b is negative then a+b is not always greater than 12.
C) If a is big number then a+b is not always less than 19.
B) As a> 12 & b <7 so minimum difference will be 5 even if b is negative, difference wont be below 5.

So, Answer should be B ONLY.
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Re: If a > 12 and b < 7, which of the following must be true?  [#permalink]

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20 Feb 2019, 00:32
Bunuel wrote:
If a > 12 and b < 7, which of the following must be true?

I. a + b > 12
II. a – b > 5
III. a + b < 19

A. I only
B. II only
C. III only
D. I and II only
E. I and III only

consider a = 13 and b =6 and -ve values
we can test the cases and find that only a-b>5 is possible
IMO B
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Re: If a > 12 and b < 7, which of the following must be true?  [#permalink]

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22 Feb 2019, 07:04
Here,in the question, answer is must be..but answer B is not must be.B can be answer not must be that wanted in the question .

Posted from my mobile device
Math Expert
Joined: 02 Sep 2009
Posts: 53864
Re: If a > 12 and b < 7, which of the following must be true?  [#permalink]

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22 Feb 2019, 07:12
Talha95 wrote:
If a > 12 and b < 7, which of the following must be true?

I. a + b > 12
II. a – b > 5
III. a + b < 19

A. I only
B. II only
C. III only
D. I and II only
E. I and III only

Here,in the question, answer is must be..but answer B is not must be.B can be answer not must be that wanted in the question .

Posted from my mobile device

The second option is always true, so it must be true.

Recall that we can subtract inequalities when their signs are in the opposite directions:

If $$a>b$$ and $$c<d$$ (signs in opposite direction: $$>$$ and $$<$$) --> $$a-c>b-d$$ (take the sign of the inequality you subtract from).
Example: $$3<4$$ and $$5>1$$ --> $$3-5<4-1$$.

So, if we subtract b < 7 from a > 12, we get a - b > 5, which is the second

Hope it's clear.

For more check Manipulating Inequalities.
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Re: If a > 12 and b < 7, which of the following must be true?  [#permalink]

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22 Feb 2019, 15:24
A different (and equivalent) way to look at the algebra here, if you don't know rules about subtracting inequalities: you can add two inequalities that face in the same direction. So if you just rewrite the second inequality so it is a "greater than", we have:

a > 12
7 > b

and we can now add these:

a + 7 > b + 12
a - b > 5

So II must be true.
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If a > 12 and b < 7, which of the following must be true?  [#permalink]

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22 Feb 2019, 18:32
Talha95 wrote:
Here,in the question, answer is must be..but answer B is not must be.B can be answer not must be that wanted in the question .

Posted from my mobile device

b<7
Multiply by( -1 )
-b>-7
Now add this with first one.
a>12
-b>-7
So, a-b>5
So the correct answer must be B.
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If a > 12 and b < 7, which of the following must be true?   [#permalink] 22 Feb 2019, 18:32
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