If a 0 and 6a = 5b, which of the following must be true?

Question

If a > 0 and 6a = 5b, which of the following must be true?

(A) a = 6/5*b

(B) ab < 0

(C) a > b

(D) b = 5/6*a

(E) b > a

Source:   Nova GMAT  
Difficulty Level:   550

pushpitkc · Answer

Since
a > 0 and 6a = 5b, it is clear that both a and b are positive.
A set of values, which satisfies this equation is a=5,b=6

Now coming to the answer choices, 
Neither Is a = 6/5*6 nor Is b = 5/6*5
Similarly ab < 0 is also not true and a>b is also false.
Only option that remains is b>a(Option E)

GMATinsight · Answer

6a = 5b
i.e. a/b = 5/6

i.e. if a is 5 then b is 6

hence, a < b

Answer: Option E

amanvermagmat · Answer

6a = 5b means a/b = 5/6

Now we are given that a>0 and the ratio of a/b is also positive. So b also must be positive or b>0

Both positive numbers are in the ratio 5:6 so second number must be greater than the first number. Hence a<b

Option  E answer

AkshdeepS · Answer

As 6 > 5 and both are getting multiplied with a and b respectively, so "b "has to be greater than "a" to make both equal.

(E)

Abhishek009 · Answer

6a = 5b = 30 So, a = 5 & b = 6 Now check the options - (A) a = 6/5*b a = 6/5*6 =>1/5 ( Not True ) (B) ab < 0 ab = 30 > 0 ( Not True ) (C) a > b a = 5 & b = 6 So, a < b ( Not True ) (D) b = 5/6*a b = 5/6*5 => 1/6 ( Not True ) (E) b > a a = 5 & b = 6 So, we get b > a ( Correct Answer )

generis · Answer

I took just one extra explicit step to isolate one variable in terms of another. 6a = 5b means a = \frac{5}{6} b \frac{5}{6} of any non-zero number is less than that number ==> a < b (A) a is not greater than b. REJECT (B) is not possible because a>0, and for ab to be negative, b would have to be negative. Not possible. A positive number cannot be \frac{5}{6} of a negative number. REJECT (C) a is not greater than b. REJECT (D) b is not smaller than a. REJECT (E) b > a means a < b. CORRECT

ScottTargetTestPrep · Answer

If a is greater than zero and 6a = 5b, then b must be greater than a. Since a is positive and b > a, b must be positive. Let’s now analyze our answer choices.
 
A) a = 6/5*b = 6b/5
 
Since b must be greater than a, answer choice A is not possible.
 
B) ab < 0
 
Since a and b are both positive, answer choice B is not possible.
 
C) a > b
 
Since we have determined that b is greater than a, answer choice C is not possible.
 
D) b = 5a/6
 
Since b must be greater than a, answer choice D is not possible.
 
E) b > a
 
Since b is greater than a, answer choice E must be correct.
 
Answer: E

KSBGC · Answer

a>0.

6a = 5b

As a is positive 6a is positive thus 5b is also positive. How can we make them equal. it's lcm .

The might lcm of 5 and 6 is 30

a = 5

b= 6.

b>a.

The best answer is E.

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If a > 0 and 6a = 5b, which of the following must be true?

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If a > 0 and 6a = 5b, which of the following must be true?

Prep Toolkit

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