If a + b 0 and b – c

Question

If a + b > 0 and b – c < 0, which of the following statements must be true?

I. a + c > 0
II. c > a
III. b > 0

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

KSBGC · Answer

Given,

a + b > 0

b – c < 0

Multiply the 2nd one by -1

c - b >0

now add both of them

a + b + c - b >0

a + c >0.

A is the correct answer.

shobhitraj · Answer

Can you please elaborate how can we multiply by -1 here ?

Luca1111111111111 · Answer

You only multiply by -1 to switch the signs, so that the equation is positioned in the same way as the first equation. This allows you to sum them up

ScottTargetTestPrep · Answer

We see that c > b. However, we can’t tell whether c > a or a > c, so II is not necessarily true. Also, we can’t tell whether b > 0, so III is not necessarily true, either. Indeed, if we take a = 2, b = -1, and c = 1, we can verify that neither c > a nor b > 0 need be true.

Since we know that neither II nor III is necessarily true, the only answer is A. However, we show that statement I is true by the following:

Multiplying the second inequality by -1, we have:

c - b > 0

Adding the two inequalities together, we have:

a + c > 0

We see that I is true.

Answer: A

nilsruge · Answer

Another approach would be:

If

a + b > 0 > b - c

then

a + b > b - c
a + c > b - b
a + c > 0 (I.)

c > -a (not II.)

-> A

bumpbot · Answer

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If a + b > 0 and b – c < 0, which of the following statements must be

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