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-2 ≤ x ≤ -1 and 1 ≤ y ≤ 2. What is the greatest poss

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-2 ≤ x ≤ -1 and 1 ≤ y ≤ 2. What is the greatest poss

by Max@Math Revolution » Tue Jun 25, 2019 11:53 pm

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[GMAT math practice question]

-2 ≤ x ≤ -1 and 1 ≤ y ≤ 2. What is the greatest possible value of ( x + y ) / x?

A. -1
B. -1/2
C. 0
D. 1/2
E. 1
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by GMATGuruNY » Wed Jun 26, 2019 2:12 am
Max@Math Revolution wrote:[GMAT math practice question]

-2 ≤ x ≤ -1 and 1 ≤ y ≤ 2. What is the greatest possible value of ( x + y ) / x?

A. -1
B. -1/2
C. 0
D. 1/2
E. 1
(x+y)/x = 1 only if y=0.
Since the range for y does not include 0, eliminate E.

If x=-2 and y=1, then (x+y)/y = (-2+1)/-2 = 1/2.
Since 1/2 is the greatest of the remaining answer choices, the correct answer is D.
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by Max@Math Revolution » Fri Jun 28, 2019 12:33 am
=>

(x+y)/x = x/x + y/x = 1 + y/x
Since -2 ≤ x ≤ -1 and 1 ≤ y ≤ 2, we have -2 ≤ y/x ≤ -1/2 and -1 ≤ 1 + y/x ≤ 1/2.
Thus, the greatest possible value of (x+y)/x is ½.

Therefore, the answer is D.
Answer: D
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