If ab, is ac? 1) a/b c/b 2) 5ab 6bc

Question

If a>b, is a>c?

1) a/b > c/b
2) 5ab > 6bc

For each piece of additional information, I have used a plug-in numbers approach to provide affirmative and negative answers to the question. However, it took me more time than desired.

Could someone please explain to me an approach that can help me to solve this question in a quicker way?

Thank you so much.

chetan2u · Answer

You don't require to get into the plugging in... solve the equations.. 1) a/b > c/b \frac{a}{b}-\frac{c}{b}>0................\frac{a-c}{b}>0 ............. a) if b>0, a-c>0... or... a>c... b) If b<0,a-c<0... or... a 6bc 5ab-6bc>0..............b(5a-6c)>0... again two cases.. a) if b>0, 5a-6c>0... or.... 5a>6c... b) If b<0, 5a-6c<0.... or... 5a<6c... so the answer depends on whether b is positive or negative.. Insuff combined.. still the cases remain same and depend on whether b<0 and b>0.. Insuff E

Bunuel · Answer

Please post DS questions in DS forum. Thank you.

HKD1710 · Answer

i plugged no number in this question. relation between a and b is given and asked between a and c.

statement-1 says a/b > c/b. it would depend on the sign of b whether a>c or not. here is why:
a/b - b/c > 0 
(1/b)*(a-c) > 0
it means either a-c and b both are positive or both are negative.
insufficient.

statement-2 does not give any clue about the sign of a, b or c. insuff.

if we combine stmt-1 and stmt-2, we are left with no information about signs of a,b,c.
hence answer should be E.

mvictor · Answer

I spent slightly more than 2 minutes on this question... the trick here is to consider all possible values, including negative and fractions. 1. suppose a=-2, b=-3 a/b = 2/3 suppose c=1 and b=-3 c/b = -1/3 but c>a test with positive numbers...and get vice versa. A and D are eliminated. 2. 5ab > 6bc suppose a=2, b=1, and c=1. a>c. suppose a=-1, b=-2, c=1 5ab > 6bc but ac or c

If a>b, is a>c? 1) a/b > c/b 2) 5ab > 6bc

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