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If a and b are positive integers, is a/b = 5/8 ?

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If a and b are positive integers, is a/b = 5/8 ? [#permalink]

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Re: If a and b are positive integers, is a/b = 5/8 ? [#permalink]

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New post 30 Oct 2015, 07:01
Bunuel wrote:
If a and b are positive integers, is a/b = 5/8 ?

(1) 1/2 < a/b < 2/3

(2) b = 8


Kudos for a correct solution.


Solution:

Statement1 : Clearly insufficient.

Statement2 : We dont know about a. Insufficient.

Combined: 1/2 < a/b < 2/3 and b=8 ==> 4 < a < 5.3 ==> a=5. Sufficient.

Option C
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Re: If a and b are positive integers, is a/b = 5/8 ? [#permalink]

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New post 30 Oct 2015, 08:08
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Bunuel wrote:
If a and b are positive integers, is a/b = 5/8 ?
(1) 1/2 < a/b < 2/3
(2) b = 8
Kudos for a correct solution.


A really tricky question indeed. It requires solid concept on algebraic manipulation to crack.

The question asks whether \(\frac{a}{b}\) = \(\frac{5}{8}\)?

Statement 1 says \(\frac{1}{2}\) < \(\frac{a}{b}\) < \(\frac{2}{3}\) OR .5 <\(\frac{a}{b}\) <.66

Here the inequality satisfy multiple values for \(\frac{a}{b}\) between .5 & .66 as for example \(\frac{a}{b}\) = \(\frac{3}{5}\) , \(\frac{5}{9}\) etc. NOT sufficient.

Statement 2 says b=8. However there is no mention of a. Hence NOT sufficient.

Combining 1 & 2, we get \(\frac{1}{2}\) < \(\frac{a}{8}\) < \(\frac{2}{3}\)
Now trail out a with multiple values. a = 4 gives .5 , a = 5 gives .62 , a=6 gives .75.

Only a=5 satisfy the range. [0.5 to 0.66]

Thus Option (C) wins.
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Re: If a and b are positive integers, is a/b = 5/8 ? [#permalink]

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New post 30 Oct 2015, 08:21
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Bunuel wrote:
If a and b are positive integers, is a/b = 5/8 ?

(1) 1/2 < a/b < 2/3

(2) b = 8


Kudos for a correct solution.


Target question: Is a/b = 5/8

Given: a and b are positive integers

Statement 1: 1/2 < a/b < 2/3
In other words, 0.5 < a/b < 0.6666...
5/8 = 0.625, so 5/8 is between 1/2 and 2/3.
However, there are infinitely many other fractions between 1/2 and 2/3, so there's no way to say for certain that a/b = 5/8
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: b = 8
We have no idea what the value of a is, so there's no way to determine whether a/b = 5/8
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that 1/2 < a/b < 2/3
Statement 2 tells us that b = 8
Since a must be a POSITIVE INTEGER, we can test some values.
a cannot = 1, 2, 3 or 4, because these cases yield a fraction, a/b, that's not greater than 1/2
a cannot = 6, 7, 8 ...., because these cases yield a fraction, a/b, that's not less than 2/3
So, we can be certain that a EQUALS 5, which means a/b definitely EQUALS 5/8
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent
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Re: If a and b are positive integers, is a/b = 5/8 ? [#permalink]

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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If a and b are positive integers, is a/b = 5/8 ?

(1) 1/2 < a/b < 2/3

(2) b = 8

In the original condition, there are 2 variables (a,b) and 2 equations from the 2 conditions, making (C) our likely answer.
If we combine the 2 conditions, 1/2=12/24<a/b<16/24
When b-8, a/8=3a/24, from 12/24<3a/24<16/24, there is only a=5 that satisfies the inequality, so the condition is sufficient as unique answer is given.
The answer becomes (C).

For cases where we need 2 more equation, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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Re: If a and b are positive integers, is a/b = 5/8 ? [#permalink]

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New post 17 Mar 2017, 01:14
Hi,
I am confused with the option 2. My aproach is the following: if a/b = 5/8 and b=8, then we can substitute 8 for b and have an equality a/8 = 5/8, which can be solved for a. In this case we find that a = 5 and 5/8 = 5/8.
Appreciate your feedback.
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Re: If a and b are positive integers, is a/b = 5/8 ? [#permalink]

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New post 03 Oct 2017, 23:13
Rashad046 wrote:
Hi,
I am confused with the option 2. My aproach is the following: if a/b = 5/8 and b=8, then we can substitute 8 for b and have an equality a/8 = 5/8, which can be solved for a. In this case we find that a = 5 and 5/8 = 5/8.
Appreciate your feedback.


Hi Rashad046,
In the beginning I thought the same way you did, but then found out that "a/b = 5/8" is not given, it is the target question, so we don't know yet if a/b = 5/8, we need to find that out from the info in the 2 statements.
I hope I am not mistaken.
Thanks
AladdinT
Re: If a and b are positive integers, is a/b = 5/8 ?   [#permalink] 03 Oct 2017, 23:13
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