If 0

Question

If 0 < a < b and k = (2a + 7b)/b , which of the following must be true? A. k < 2 B. k < 7 C. k < 9 D. k > 9 E. k > 11

BrentGMATPrepNow · Accepted Answer

Here's another approach:

k = (2a + 7b)/b
= 2a/b + 7b/b
= 2(a/b) + 7
Since 0 < a < b, we know that a/b is less than 1, which means that 2(a/b) is some number less than 2. 
So, we get k = (some number less than 2) + 7
From here, we can see that k must be less than 9
Answer: C

Cheers,
Brent

ENGRTOMBA2018 · Answer

Please follow posting guidelines (link in my signature) especially writing the correct topic title. Also do mention the source of the question if you select the tag: "Source-Other Please Specify".

As for your question, it is very simple and straightforward with number plug in.

Assume a=1 and b=2 as a<b, you get k = (2+14)/2 = 8. This eliminates all but option C , making it the correct answer.

kanusha · Answer

Assume , a = 1 , b = 2
 K = \frac{2+14}{2} 
 \frac{16}{2} 
K = 8
K<9
C

DadhichD · Answer

Who said that 'a' and 'b' are full integers ? So we have to assume that always ?

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RaguramanS · Answer

k= \frac{2a+7b}{b} k =2( \frac{a}{b}) +7 given a>0;b>0 --> \frac{a}{b} = proper fraction \frac{a}{b} <1 k<2(1)+7 k<9

Bunuel · Answer

No, you should not assume that a variable is necessarily an integer if you are not explicitly told so. Having said that, solutions above do not assume that a and b are integers. For example check solution here: https://gmatclub.com/forum/if-0-a-b-and ... l#p1591061

sashiim20 · Answer

Let a = 1, b = 2.

k = \frac{(2a + 7b)}{b}

k = \frac{2a}{b} + \frac{7b}{b}

k = \frac{2*1}{2} + 7

k = 1+ 7 = 8

k < 9 . Answer (C)..

ScottTargetTestPrep · Answer

We can simplify the given equation:
 
k = (2a + 7b)/b
 
k = 2a/b + 7b/b
 
k = 2a/b + 7
 
Since 0 < a < b, a/b must be less than 1, so 2a/b must be less than 2; thus, k < 2 + 7 or k < 9.
 
Answer: C

ydmuley · Answer

k = \frac{(2a + 7b)}{b}

k = 2\frac{a}{b} + 7

As we know that  0 < a < b  we know that value if  2\frac{a}{b}  should be <= 2

k < 2 + 7

k < 9

Hence, Answer is C

HWPO · Answer

Simply choose numbers:

a = 2 , b =4

k = (4+28)/4 = > 32/4 = 8.

Answer: C

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If 0<a<b and k= (2a+7b)/b , which of the following must be true?

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