If a and b are positive integers such that a/b = 2.86, which of the fo

Hi Bunuel.Why not D 26.Even it is divisible by 13.Confused b/w b and d?Where am i wrong?Sorry not clear

What if a = 143 and b = 50

a/b = 2.86..do you think 26 divides 143?
No. it does not .

We have to reduce the fraction to conclude must be true answers.

Golden TIP : suppose you are stuck between 13 and 26 , and the question is about the must be true condition.

If some integer is divisible by 26, then it is always divisible by 13 -> you can not have 2 correct answers, it has to be one of them

If some integer is divisible by 13, then it is not always divisible by 26 -> unique solution.

In such conditions always select the GCF of the numbers, or in simple terms the lowest factor.

The question is: "which of the following must be a divisor of \(a\)". We know that \(a\) must be divisible by both 11 and 13, but we don't know whether it's divisible by 2 (in order to be divisible by 2*13=26).

Or consider this: \(\frac{a}{b}=\frac{143}{50}\), so the lowest value of \(a\) is 143 and it's not divisible by any of the answer choices but B (13).

Hope it's clear.

I did it like this:

We know that a/b =2.86, which means the decimal part i.e. 0.86 = Remainder/Divisor
Simplifying the equation, we get Remainder/Divisor = 43/50. So the divisor should be a multiple of 50.Hence answer is E.

Where am I going wrong?

You did everything right except that 50 must be a factor of b, which is a divisor in our case, but we are asked about a not b.

2.86 = 286/100 = 143/50 = a/b

'a' must be a multiple of 143 (= 11*13) and b must be a multiple of 50.
So it 'a' must be divisible by 13.

Hi,

Sorry for bumping this old thread but i also faced the same question in one of my CATs.
My question is that we have been given a fraction and in the form of a/b..
we are asked to identify the divisor of 'a' , which in this case refers to 'b'
we have a = 2.86*b... Now, since a must be an integer, the only value that satisfies the equation is 50.

Is this question really ambiguous or is it just me not being able to differentiate between factors and divisors...

Thanks,
Gaurav

A factor and a divisor are the same thing (well, we can say that a factor is a positive divisor but this is not relevant here). We need to find which of the options could be a factor (divisor) of a, not the value of b, which would be impossible to find from a/b = 2.86.

Hi earnit,

The prompt gives us a couple of facts to work with:
1) A and B are positive INTEGERS
2) A/B = 2.86

We can use these facts to figure out POSSIBLE values of A and B. The prompt asks us for what MUST be a divisor of A. Since we're dealing with a fraction, A and B could be an infinite number of different integers, so we have to make both as SMALL as possible; in doing so, we'll be able to find the divisors that ALWAYS divide in (and eliminate the divisors that only SOMETIMES divide in).

The simplest place to start is with...
A = 286
B = 100
286/100 = 2.86

These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)...

A = 143
B = 50
143/50 = 2.86

There is no other way to reduce this fraction, so A must be a multiple of 143 and B must be an equivalent multiple of 50. At this point though, the value of B is irrelevant to the question. We're asked for what MUST divide into A....

Since A is a multiple of 143, we have to 'factor-down' 143. This gives us (11)(13). So BOTH of those integers MUST be factors of A. You'll find the match in the answer choices.

Final Answer:
GMAT assassins aren't born, they're made,
Rich

Right. I got this method.
But what is exactly wrong in the approach above: that states

\(Dividend/Divisor\) =\(Quotient\) + \(Remainder/Divisor\)

Ex: 5/2 = 2.5 = 2 + 0.5 => 2 + 1/2 (where 1 is the remainder and 2 is the divisor)

Hi earnit,

In real basic terms, you're doing math that has nothing to do with the question that is asked.

In this prompt, the ONLY reason that the "B" variable is there is to help you figure out what the minimum value of the "A" variable is.

Once we know that A is a multiple of 143, and the question asks what MUST be a factor of A, the value of B is no longer needed.

GMAT assassins aren't born, they're made,
Rich

Hi All,

The prompt gives us a couple of facts to work with:
1) A and B are positive INTEGERS
2) A/B = 2.86

We can use these facts to figure out POSSIBLE values of A and B. The prompt asks us for what MUST be a divisor of A. Since we're dealing with a fraction, A and B could be an infinite number of different integers, so we have to make both as SMALL as possible; in doing so, we'll be able to find the divisors that ALWAYS divide in (and eliminate the divisors that only SOMETIMES divide in).

The simplest place to start is with...
A = 286
B = 100
286/100 = 2.86

These values are NOT the smallest possible values though (since they're both even, we can divide both by 2)...

A = 143
B = 50
143/50 = 2.86

There is no other way to reduce this fraction, so A must be a multiple of 143 and B must be an equivalent multiple of 50. At this point though, the value of B is irrelevant to the question. We're asked for what MUST divide into A....

Since A is a multiple of 143, we have to 'factor-down' 143. This gives us (11)(13). So BOTH of those integers MUST be factors of A. You'll find the match in the answer choices.

Final Answer:
GMAT assassins aren't born, they're made,
Rich

a/b = 286/100 = 11*13*2/100=11*13/50. Since neither 11 nor 13 is a factor of 50 and since both 11 and 13 are prime, a is divisible by 11 and 13.

Answer choice B.

VeritasKarishma \(\frac{remainder}{divisor }\) =\(\frac{ 86}{100}\) i.e.\( \frac{43}{50}\)


cross multiply and i get 43d=50r so divisor must be multiple of 50 ? so i picked 50 whats wrong with my approach any idea why it doasnt work and whats difference between this problem and the one in the link below

i followed this approach https://gmatclub.com/forum/when-positiv ... l#p1930580


UPDATE: in the question below

https://gmatclub.com/forum/if-a-and-b-a ... 07422.html

If a and b are positive integers such that a/b = 82.024, which of the following can be the value of b?

(A) 100
(B) 150
(C) 200
(D) 250
(E) 550


24/100 is reduced to 3/125 which means 3 is remainder when divisor is 125

so 3B=125R so B (divisor must be multiple of 125) so its clear here that 250 is answer... but why this method doesnt work in that question dont get

\(\frac{a}{b} = 286/100 = 143/50\)

We need something that divides 143. Has to be odd.

Answer choice B.

We have a/b = 2.86 = 286/100 = 143/50. Since this fraction cannot be reduced further, a must be a multiple of 143 and b must be a multiple of 50. Since a is a multiple of 143 = 13 * 11, 13 must be a divisor of a.

Answer: B

a/b = 2.86

Can be written as a = b * 2.86
=> a = b*2 + b*0.86 = 2b + b * \(\frac{86}{100}\)
=> a = 2b + b * \(\frac{43}{50}\)

This means, a when divided by b gives 2 as quotient and b * \(\frac{43}{50}\) as remainder.
Now, remainder has to be integer. And for b * \(\frac{43}{50}\) to be an integer b has to be a multiple of 50.
=> b = 50k where k is an integer

=> a = 2*50k + 50k * \(\frac{43}{50}\) = 100k + 43k = 143k = 13 * 11k
=> a is a multiple of 13 or 13 is a divisor of a

So, Answer will be B
Hope it helps!

MASTER Remainders