GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 16 Aug 2018, 12:46

### 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

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

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47946
If a and b are positive integers, is a/b = 5/8 ?  [#permalink]

### Show Tags

29 Oct 2015, 01:16
00:00

Difficulty:

75% (hard)

Question Stats:

52% (01:32) correct 48% (01:20) wrong based on 289 sessions

### HideShow timer Statistics

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.

_________________
Manager
Joined: 10 Aug 2015
Posts: 103
Re: If a and b are positive integers, is a/b = 5/8 ?  [#permalink]

### Show Tags

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
Manager
Status: Just redeemed Kudos for GMAT Club Test !!
Joined: 14 Sep 2013
Posts: 93
GMAT 1: 530 Q40 V23
GPA: 3.56
WE: Analyst (Commercial Banking)
Re: If a and b are positive integers, is a/b = 5/8 ?  [#permalink]

### Show Tags

30 Oct 2015, 08:08
1
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.
_________________

______________
KUDOS please, if you like the post or if it helps
"Giving kudos" is a decent way to say "Thanks"

Master with structure - Numerical comparison [source: economist.com] https://gmatclub.com/forum/master-with-structure-numerical-comparison-233657.html#p1801987

CEO
Joined: 12 Sep 2015
Posts: 2703
Re: If a and b are positive integers, is a/b = 5/8 ?  [#permalink]

### Show Tags

30 Oct 2015, 08:21
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

Cheers,
Brent
_________________

Brent Hanneson – Founder of gmatprepnow.com

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6020
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If a and b are positive integers, is a/b = 5/8 ?  [#permalink]

### Show Tags

01 Nov 2015, 00:35
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.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Intern
Joined: 23 Apr 2016
Posts: 2
Re: If a and b are positive integers, is a/b = 5/8 ?  [#permalink]

### Show Tags

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.
Intern
Joined: 03 Oct 2017
Posts: 1
Re: If a and b are positive integers, is a/b = 5/8 ?  [#permalink]

### Show Tags

03 Oct 2017, 23:13
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.

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
Re: If a and b are positive integers, is a/b = 5/8 ? &nbs [#permalink] 03 Oct 2017, 23:13
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.