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Solution



Given:
    • a ≥ 30 and b ≤ 15

To find:
    • From the given options, which one is always true

Approach and Working:
    • We can do subtraction of two inequality expression only when they possess opposite signs. Also, the resulting inequality expression will hold the sign of the first inequality
    • If we do the subtraction, we get
      o a – b ≥ 30 – 15 or, a – b ≥ 15

Hence, the correct answer is option C.

Answer: C
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Bunuel
If a ≥ 30 and b ≤ 15, then which of the following must also be true?

A. a − b ≤ 45
B. a − b ≤ 15
C. a − b ≥ 15
D. a + b ≤ 45
E. a + b ≥ 45


You can solve this question by using the concept of the number line. You know that "b" will always be less than 15 and "a" will always be more than 30. The minimum difference between these numbers is 15. We can't limit the summation as "b" can have any sign i.e. positive or negative. So options D & E are out.
Now if we change the values of both "a" and "b" then they will move farther from each other and the minimum possible distance between them is only 15. And this difference is written in an equation form in option C.

So, C is my answer.
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Bunuel
If a ≥ 30 and b ≤ 15, then which of the following must also be true?

A. a − b ≤ 45
B. a − b ≤ 15
C. a − b ≥ 15
D. a + b ≤ 45
E. a + b ≥ 45

In many of the answer choices, we have -b (subtract b)

So let's take: b ≤ 15
And multiply both sides by -1 to get: -b ≥ -15 [aside: Since I multiplied both sides of the inequality by a NEGATIVE number, I had to REVERSE the direction of the inequality symbol]

So we now have the following:
a ≥ 30
-b ≥ -15

If we ADD the two inequalities we get: a + (-b) ≥ 30 + (-15)
Simplify to get: a - b ≥ 15

Answer: C

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Hello from the GMAT Club BumpBot!

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