If a 12 and b

Question

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

NandishSS · Answer

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

999neil · Answer

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.

Archit3110 · Answer

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

Talha95 · Answer

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

Bunuel · Answer

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 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 .

IanStewart · Answer

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.

a > 12
7 > b

and we can now add these:

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

So II must be true.

TheUltimateWinner · Answer

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.

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

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