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

 It is currently 20 Nov 2018, 07:45

### 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

## Events & Promotions

###### Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
• ### All GMAT Club Tests are Free and open on November 22nd in celebration of Thanksgiving Day!

November 22, 2018

November 22, 2018

10:00 PM PST

11:00 PM PST

Mark your calendars - All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA)
• ### Free lesson on number properties

November 23, 2018

November 23, 2018

10:00 PM PST

11:00 PM PST

Practice the one most important Quant section - Integer properties, and rapidly improve your skills.

# M31-47

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 50714

### Show Tags

20 Jun 2015, 10:58
00:00

Difficulty:

95% (hard)

Question Stats:

43% (02:17) correct 57% (02:29) wrong based on 46 sessions

### HideShow timer Statistics

If $$a$$ and $$b$$ are single-digit positive numbers and $$\frac{a}{b}$$ is NOT a recurring decimal, what is the value of $$a$$?

(1) $$-\frac{1}{3} > -\frac{a}{b} > -\frac{4}{5}$$

(2) $$b$$ is equal to the sum of its positive divisors excluding $$b$$ itself.

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 50714

### Show Tags

20 Jun 2015, 10:58
Official Solution:

If $$a$$ and $$b$$ are single-digit positive numbers and $$\frac{a}{b}$$ is NOT a recurring decimal, what is the value of $$a$$?

$$a$$ and $$b$$ are single-digit positive numbers means that $$a$$ and $$b$$ can be 1, 2, 3, 4, 5, 6, 7, 8, or 9.

(1) $$-\frac{1}{3} > -\frac{a}{b} > -\frac{4}{5}$$

Simplify by multiplying by -1: $$\frac{1}{3} < \frac{a}{b} < \frac{4}{5}$$

Convert to decimals $$0.(3) < \frac{a}{b} < 0.8$$.

Since $$\frac{a}{b}$$ is NOT a recurring decimal, then it can be 0.4 ($$a = 2$$, $$b = 5$$), 0.5 ($$a = 1$$, $$b = 2$$), ... Not sufficient.

(2) $$b$$ is equal to the sum of its positive divisors excluding $$b$$ itself.

From single digit numbers only 6 satisfies this condition: $$6 = 1 + 2 + 3$$. Since $$\frac{a}{b}$$ is NOT a recurring decimal, then $$\frac{a}{6}$$ can be $$\frac{3}{6} = 0.5$$, $$\frac{6}{6} = 1$$, or $$\frac{9}{6} = 1.5$$. Not sufficient.

(1)+(2) From (2) $$\frac{a}{b}$$ can be $$\frac{3}{6} = 0.5$$, $$\frac{6}{6} = 1$$, or $$\frac{9}{6} = 1.5$$. Only one of which is between 0.(3) and 0.8, namely 0.5. Sufficient.

_________________
Intern
Joined: 14 Apr 2013
Posts: 2

### Show Tags

01 Sep 2016, 00:27

From single digit numbers only 6 satisfies this condition: 6=1+2+3.

However, 3 is also valid: 3 = 1+2.

What am I missing here? Thanks in advance
Math Expert
Joined: 02 Sep 2009
Posts: 50714

### Show Tags

01 Sep 2016, 02:35
z0rpia wrote:

From single digit numbers only 6 satisfies this condition: 6=1+2+3.

However, 3 is also valid: 3 = 1+2.

What am I missing here? Thanks in advance

(2) says: b is equal to the sum of its positive divisors excluding b itself.

2 is not a divisor of 3. So, 3 does NOT equal to the sum of its positive divisors excluding b itself. 3 has only one positive divisor excluding 3 itself namely 1.
_________________
SVP
Joined: 26 Mar 2013
Posts: 1887

### Show Tags

02 Sep 2016, 01:50
Bunuel wrote:

Since $$\frac{a}{b}$$ is NOT a recurring decimal, then it can be 0.4 ($$a = 2$$, $$b = 5$$), 0.5 ($$a = 1$$, $$b = 2$$), ... Not sufficient.

Does 3/5 & 7/10 satisfy fact 1? I think so as they are 0.6 & 0.7 respectively. Did not you consider them fro certain reason?
Math Expert
Joined: 02 Sep 2009
Posts: 50714

### Show Tags

02 Sep 2016, 02:55
Mo2men wrote:
Bunuel wrote:

Since $$\frac{a}{b}$$ is NOT a recurring decimal, then it can be 0.4 ($$a = 2$$, $$b = 5$$), 0.5 ($$a = 1$$, $$b = 2$$), [highlight]... Not sufficient.[/highlight]

Does 3/5 & 7/10 satisfy fact 1? I think so as they are 0.6 & 0.7 respectively. Did not you consider them fro certain reason?

a/b can be 3/5. You can see ... part in the solution above, which indicates that there are some other values of a/b possible.

a/b cannot be 7/10, because 10 is not a single digit number.
_________________
Manager
Joined: 28 Jun 2018
Posts: 56
GMAT 1: 490 Q39 V18
GMAT 2: 640 Q47 V30
GMAT 3: 670 Q50 V31
GMAT 4: 700 Q49 V36
GPA: 4

### Show Tags

30 Oct 2018, 03:49
A quick tip -

To make sure of statement 2 faster. You can use terminating decimals theory. Because recurring decimals are basically non-terminating. So check if the denominator of any number is having multiples of 2 or 5 after u reduce fraction to lowest form.

Example-
We can simply eliminate 1/6 , 2/6 , 4/6 , 5/6, 7/6 and 8/6 because they have no denominator divisible by 2 and 5.
4/6 when reduced gives 2/3.
8/6 gives 4/3. and so on.

Hey Bunuel
To check statement 2 and make sure that we do have a recurring decimal. We can use terminating decimals theory right?
M31-47 &nbs [#permalink] 30 Oct 2018, 03:49
Display posts from previous: Sort by

# M31-47

Moderators: chetan2u, Bunuel

 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®.