Last visit was: 21 Jun 2024, 01:26 It is currently 21 Jun 2024, 01:26
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 93895
Own Kudos [?]: 633522 [24]
Given Kudos: 82410
Send PM
Most Helpful Reply
GMAT Club Legend
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6806
Own Kudos [?]: 30600 [9]
Given Kudos: 799
Location: Canada
Send PM
General Discussion
avatar
Manager
Manager
Joined: 10 Aug 2015
Posts: 95
Own Kudos [?]: 240 [1]
Given Kudos: 20
Send PM
Manager
Manager
Joined: 14 Sep 2013
Status:Just redeemed Kudos for GMAT Club Test !!
Posts: 88
Own Kudos [?]: 48 [1]
Given Kudos: 38
Location: Bangladesh
GMAT 1: 530 Q40 V23
GPA: 3.56
WE:Analyst (Commercial Banking)
Send PM
Re: If a and b are positive integers, is a/b = 5/8 ? [#permalink]
1
Kudos
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.
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10138
Own Kudos [?]: 16872 [1]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Re: If a and b are positive integers, is a/b = 5/8 ? [#permalink]
1
Bookmarks
Expert Reply
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.
Intern
Intern
Joined: 23 Apr 2016
Posts: 2
Own Kudos [?]: 10 [0]
Given Kudos: 9
Send PM
Re: If a and b are positive integers, is a/b = 5/8 ? [#permalink]
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.
avatar
Intern
Intern
Joined: 03 Oct 2017
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 0
Send PM
Re: If a and b are positive integers, is a/b = 5/8 ? [#permalink]
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
Manager
Manager
Joined: 17 Jan 2014
Posts: 51
Own Kudos [?]: 10 [0]
Given Kudos: 85
Location: India
Concentration: Operations, Marketing
WE:Supply Chain Management (Manufacturing)
Send PM
Re: If a and b are positive integers, is a/b = 5/8 ? [#permalink]
GMATPrepNow

Bunuel

FROM QUES. STEM IS CLEAR THAT 5/8 = 0.625 THEN IT IS DIRECTLY SHOWS IN THE STATEMENT 1. THAT VALUE F A/B LIES BETWEEN 0.5 TO 66.6.

IMO - ANSWER IS A

GMATPrepNow wrote:
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
Math Expert
Joined: 02 Sep 2009
Posts: 93895
Own Kudos [?]: 633522 [0]
Given Kudos: 82410
Send PM
Re: If a and b are positive integers, is a/b = 5/8 ? [#permalink]
Expert Reply
gsmina wrote:
GMATPrepNow

Bunuel

FROM QUES. STEM IS CLEAR THAT 5/8 = 0.625 THEN IT IS DIRECTLY SHOWS IN THE STATEMENT 1. THAT VALUE F A/B LIES BETWEEN 0.5 TO 66.6.

IMO - ANSWER IS A

GMATPrepNow wrote:
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


The question asks: IS a/b = 5/8?

For (1) a/b can certainly be 5/8, because 5/8 is between 1/2 and 2/3 but a/b can also be any other number between 1/2 and 2/3, for example, 0.6. So, (1) is not sufficient.
GMAT Club Legend
GMAT Club Legend
Joined: 03 Oct 2013
Affiliations: CrackVerbal
Posts: 4931
Own Kudos [?]: 7744 [0]
Given Kudos: 218
Location: India
Send PM
Re: If a and b are positive integers, is a/b = 5/8 ? [#permalink]
In this question, the fact that a and b are positive integers is what makes the question easier to deal with. Had this constraint not been given, this question would have been much more difficult to solve.

We are to find out if \(\frac{a}{b}\) = \(\frac{5}{8}\) i.e. if a and b are in the ratio of 5:8.

From statement I, we know that \(\frac{a}{b}\) is greater than 0.5 but lesser than 0.67. Clearly, one possible value that \(\frac{a}{b}\) can take is \(\frac{5}{8}\) i.e. 0.625.
But, unfortunately, this is not the only value that is in between 0.5 and 0.67. \(\frac{5}{9}\) is also in the same range.

Therefore, statement I is insufficient to answer the question. Answer options A and D can be eliminated. Possible answer options are B, C or E.

From statement II, we know nothing about a. We only know that b = 8. This is surely insufficient to answer the question.
Answer option B can be eliminated.

Combining both statements I and II, with b = 8, the only way in which \(\frac{a}{b}\) can be greater than 0.5 but lesser than 0.67 is by having a = 5.

If a = 4, b = 8, a/b = ½ which violates the condition given in statement I. Any value of a<4 will bring the value of a/b below ½, which is not acceptable.

If a = 6, b = 8, a/b = ¾ which violates the condition given in statement I. Any value of a>6 will increase the value of a/b beyond 0.67, which is not acceptable again.

Therefore, the only possible value for a is 5. When a = 5 and b = 8, \(\frac{a}{b}\) = \(\frac{5}{8}\). The combination of statements is sufficient.
The correct answer option is C.

Hope this helps!
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10138
Own Kudos [?]: 16872 [1]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Re: If a and b are positive integers, is a/b = 5/8 ? [#permalink]
1
Bookmarks
Expert Reply
Forget the conventional way to solve DS questions.

We will solve this DS question using the variable approach.

(DS) This is a 2 variables question with Condition(1) with 1 equation and Condition (2) with 1 equation

We are aware that each condition would usually give us an equation, resulting in a total of 2 equations, one each from condition (1), and condition (2). Since we need 2 equations to match the number of variables and equations in the original condition, an equal number of equations and variables should logically give us an answer C.

To master the Variable Approach, visit https://www.mathrevolution.com and check our lessons and proven techniques to score high in DS questions.

Step 1 of the Variable Approach: Modifying and rechecking the original condition and the question.

=> We have to find whether \(\frac{a }{ b}\) = \(\frac{5 }{ 8}\)

Second and the third step of Variable Approach: From the original condition, we have 2 variables (f and m). To match the number of variables with the number of equations, we need 2 equations. Since conditions (1) and (2) will provide 1 equation each, C would most likely be the answer.

The answer is C because the number of variables and equations is 2. You should never get this question wrong as it is a basic, 30-39 level question.

Let’s take a look at both conditions together

Condition 1: \(\frac{1 }{2} < \frac{a }{ b} < \frac{2 }{3}\) and Condition 2: b = 8

=> \(\frac{1 }{ 2} < \frac{a }{ 8} < \frac{2 }{ 3}\)

=> 4 < a < \(\frac{16 }{ 3}\)

=> 4 < a < 5.33

a being integer will have value as 5. Hence, a = 5 and b = 8.

Is \(\frac{a }{ b} = \frac{5 }{ 8}\) - YES

The answer is unique YES according to CMT(1), so the conditions combined are sufficient.

Both conditions (1) and (2) together are sufficient.

So, C is the correct answer.

Answer: C
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 33636
Own Kudos [?]: 839 [0]
Given Kudos: 0
Send PM
Re: If a and b are positive integers, is a/b = 5/8 ? [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
Re: If a and b are positive integers, is a/b = 5/8 ? [#permalink]
Moderator:
Math Expert
93895 posts