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

 It is currently 20 Nov 2019, 08:09

### 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, b, c, d and e are integers and p=2^a3^b and q=2^c3

Author Message
TAGS:

### Hide Tags

Senior Manager
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 439
Location: United Kingdom
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
If a, b, c, d and e are integers and p=2^a3^b and q=2^c3  [#permalink]

### Show Tags

09 Jan 2012, 21:58
5
47
00:00

Difficulty:

25% (medium)

Question Stats:

68% (01:11) correct 32% (01:42) wrong based on 913 sessions

### HideShow timer Statistics

Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 36, 0.72, and 3.005 are terminating decimals.

If a, b, c, d and e are integers and $$p = 2^a3^b$$ and $$q = 2^c3^d5^e$$, is p/q a terminating decimal?

(1) a > c
(2) b > d

_________________
Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730
Math Expert
Joined: 02 Sep 2009
Posts: 59180
Re: If a, b, c, d and e are integers and p=2^a3^b and q=2^c3  [#permalink]

### Show Tags

13 Jan 2012, 16:36
32
13
enigma123 wrote:
If a, b, c, d and e are integers and p = 2^a3^b and q = 2^c3^d5^e, is p/q a terminating decimal?
(1) a > c
(2) b > d

Any idea what is the concept behind this question to get a answer B?

Theory:
Reduced fraction $$\frac{a}{b}$$ (meaning that fraction is already reduced to its lowest term) can be expressed as terminating decimal if and only $$b$$ (denominator) is of the form $$2^n5^m$$, where $$m$$ and $$n$$ are non-negative integers. For example: $$\frac{7}{250}$$ is a terminating decimal $$0.028$$, as $$250$$ (denominator) equals to $$2*5^3$$. Fraction $$\frac{3}{30}$$ is also a terminating decimal, as $$\frac{3}{30}=\frac{1}{10}$$ and denominator $$10=2*5$$.

Note that if denominator already has only 2-s and/or 5-s then it doesn't matter whether the fraction is reduced or not.

For example $$\frac{x}{2^n5^m}$$, (where x, n and m are integers) will always be the terminating decimal.

We need reducing in case when we have the prime in denominator other then 2 or 5 to see whether it could be reduced. For example fraction $$\frac{6}{15}$$ has 3 as prime in denominator and we need to know if it can be reduced.

BACK TO THE ORIGINAL QUESTION:
If a, b, c, d and e are integers and p = 2^a3^b and q = 2^c3^d5^e, is p/q a terminating decimal?

Question: is $$\frac{2^a*3^b}{2^c*3^d*5^e}$$ a terminating decimal? The question basically asks whether we cans reduce 3^d in the denominator so to have only powers of 2 and 5 left, which can be rephrased is b (the power of 3 in the nominator) greater than or equal to d (the power of 3 in the denominator): is b>=d?

(1) a > c. Not sufficient.
(2) b > d. Sufficient.

Hope it helps.
_________________
Senior Manager
Joined: 28 Apr 2012
Posts: 267
Location: India
Concentration: Finance, Technology
GMAT 1: 650 Q48 V31
GMAT 2: 770 Q50 V47
WE: Information Technology (Computer Software)
Re: If a, b, c, d and e are integers and p=2^a3^b and q=2^c3  [#permalink]

### Show Tags

28 Jul 2012, 09:10
4
1
enigma123 wrote:
If a, b, c, d and e are integers and p = 2^a3^b and q = 2^c3^d5^e, is p/q a terminating decimal?
(1) a > c
(2) b > d

Any idea what is the concept behind this question to get a answer B?

Of all the theories.

Among 1/2, 1/3 and 1/5, only 1/3 is non terminating. So if we don't have 3 in the denominator then only p/q will be terminating.
b>d, ensures we have no "3" left in the denominator, hence the decimal is terminating.
(it holds true for 7,11,13....)
_________________
"Appreciation is a wonderful thing. It makes what is excellent in others belong to us as well."
― Voltaire

Press Kudos, if I have helped.
Thanks!
##### General Discussion
Manager
Joined: 18 Dec 2011
Posts: 50
Re: If a, b, c, d and e are integers and p=2^a3^b and q=2^c3  [#permalink]

### Show Tags

09 Jan 2012, 23:16
IMO B, explanation:

p/q= 2^(a-c)3^(b-d)/ 5^e

For p/q to be a terminating decimal, b should be greater than or equal to 0, hence b greater than d ie 2 is sufficient.
Intern
Joined: 07 Jan 2012
Posts: 6
Location: United States
WE: Marketing (Other)
Re: If a, b, c, d and e are integers and p=2^a3^b and q=2^c3  [#permalink]

### Show Tags

09 Jan 2012, 23:32
1
1
As I understand, in order to be a non-terminating decimal we should be able to convert a number into X/99 format. If b>d then there is no way we can get 99 in the denominator and hence it will always be a terminating decimal. Thus, B is an answer.
Senior Manager
Status: Finally Done. Admitted in Kellogg for 2015 intake
Joined: 25 Jun 2011
Posts: 439
Location: United Kingdom
GMAT 1: 730 Q49 V45
GPA: 2.9
WE: Information Technology (Consulting)
Re: If a, b, c, d and e are integers and p=2^a3^b and q=2^c3  [#permalink]

### Show Tags

16 Jan 2012, 16:39
1
Bunuel - you are a LEGEND. Many thanks for the lovely explanation.
_________________
Best Regards,
E.

MGMAT 1 --> 530
MGMAT 2--> 640
MGMAT 3 ---> 610
GMAT ==> 730
Intern
Joined: 18 Jun 2012
Posts: 31
Re: If a, b, c, d and e are integers and p=2^a3^b and q=2^c3  [#permalink]

### Show Tags

28 Jul 2012, 05:34
@Bunuel

What if e=0 ? Will it be a terminating decimal ?
Math Expert
Joined: 02 Sep 2009
Posts: 59180
Re: If a, b, c, d and e are integers and p=2^a3^b and q=2^c3  [#permalink]

### Show Tags

28 Jul 2012, 05:54
smartmanav wrote:
@Bunuel

What if e=0 ? Will it be a terminating decimal ?

You mean for (2)? In this case the denominator will have only 2's in it, and if the denominator has only 2's or only 5's in it, it still will be a terminating decimal.
_________________
Intern
Joined: 28 Aug 2012
Posts: 38
Location: Austria
GMAT 1: 770 Q51 V42
Re: If a, b, c, d and e are integers and p=2^a3^b and q=2^c3  [#permalink]

### Show Tags

Updated on: 02 Sep 2012, 06:29
2
The question here is, whether b >= d.
Why is that? p and q are given in their prime factorization. If q has more twos and/or fives in its prime factorisation than p, it won't result in a non-terminating decimal, Remainder of 2 can only be 1: 1/2=0.5 and remainders of 5 result in: 1/5=0.2, 2/5=0.4 3/5=0.6 and 4/5=0.8.

However, this is not the case with the 3. If q has more threes than p, you can cancel all of the threes in the numerator, but there will remain some threes in the denominator, resulting in a non-terminating decimal, because 1/3=0.33333 and 2/3=0.666666

Statement (1) gives us no information about b and d.
Statement (2) does. There are fewer threes in the denominator. They will cancel with some of the threes in the numerator. Therefore, this statement is sufficient. We know that p/q will be a terminating decimal.

I hope my explanation is good enough.

Originally posted by Zinsch123 on 02 Sep 2012, 06:20.
Last edited by Zinsch123 on 02 Sep 2012, 06:29, edited 2 times in total.
Intern
Joined: 29 Aug 2012
Posts: 25
Schools: Babson '14
GMAT Date: 02-28-2013
Re: If a, b, c, d and e are integers and p=2^a3^b and q=2^c3  [#permalink]

### Show Tags

04 Nov 2012, 23:02
what if b = -2 & d = -3 , then we have a case for terminating decimal ?? because the denominator now would be in 2^m * 5^n form.
Director
Joined: 22 Mar 2011
Posts: 584
WE: Science (Education)
Re: If a, b, c, d and e are integers and p=2^a3^b and q=2^c3  [#permalink]

### Show Tags

05 Nov 2012, 11:44
2
himanshuhpr wrote:
what if b = -2 & d = -3 , then we have a case for terminating decimal ?? because the denominator now would be in 2^m * 5^n form.

Yes, $$p/q$$ will be a terminating decimal. For $$b = -2$$ and $$d = -3, b > d.$$

Since $$p/q = 2^{a-c}3^{b-d}5^{-e}$$, the given ratio is a terminating decimal if and only if $$b-d\geq{0}$$ or $$b\geq{d}.$$ Which means there is no factor of 3 in the denominator, only factors of 2 and/or 5, if at all. If in addition $$a\geq{c}$$ and $$e\leq{0}$$, the given ratio is in fact an integer, which is a terminating decimal.
_________________
PhD in Applied Mathematics
Love GMAT Quant questions and running.
Manager
Joined: 10 Sep 2014
Posts: 61
Re: If a, b, c, d and e are integers and p=2^a3^b and q=2^c3  [#permalink]

### Show Tags

25 Oct 2014, 23:58
1
Hi Bunuel,

Quick question on this rule.
How about 1/15? it can be written as 1/2^0 * 3 * 5. The denominator has 5, but the fraction is not a terminating decimal. Can you please explain why?

Bunuel wrote:
enigma123 wrote:
If a, b, c, d and e are integers and p = 2^a3^b and q = 2^c3^d5^e, is p/q a terminating decimal?
(1) a > c
(2) b > d

Any idea what is the concept behind this question to get a answer B?

Theory:
Reduced fraction $$\frac{a}{b}$$ (meaning that fraction is already reduced to its lowest term) can be expressed as terminating decimal if and only $$b$$ (denominator) is of the form $$2^n5^m$$, where $$m$$ and $$n$$ are non-negative integers. For example: $$\frac{7}{250}$$ is a terminating decimal $$0.028$$, as $$250$$ (denominator) equals to $$2*5^3$$. Fraction $$\frac{3}{30}$$ is also a terminating decimal, as $$\frac{3}{30}=\frac{1}{10}$$ and denominator $$10=2*5$$.

Note that if denominator already has only 2-s and/or 5-s then it doesn't matter whether the fraction is reduced or not.

For example $$\frac{x}{2^n5^m}$$, (where x, n and m are integers) will always be the terminating decimal.

We need reducing in case when we have the prime in denominator other then 2 or 5 to see whether it could be reduced. For example fraction $$\frac{6}{15}$$ has 3 as prime in denominator and we need to know if it can be reduced.

BACK TO THE ORIGINAL QUESTION:
If a, b, c, d and e are integers and p = 2^a3^b and q = 2^c3^d5^e, is p/q a terminating decimal?

Question: is $$\frac{2^a*3^b}{2^c*3^d*5^e}$$ a terminating decimal? The question basically asks whether we cans reduce 3^d in the denominator so to have only powers of 2 and 5 left, which can be rephrased is b (the power of 3 in the nominator) greater than or equal to d (the power of 3 in the denominator): is b>=d?

(1) a > c. Not sufficient.
(2) b > d. Sufficient.

Hope it helps.

_________________
Press KUDOs if you find my explanation helpful
Math Expert
Joined: 02 Sep 2009
Posts: 59180
Re: If a, b, c, d and e are integers and p=2^a3^b and q=2^c3  [#permalink]

### Show Tags

26 Oct 2014, 06:32
1
1
TARGET730 wrote:
Hi Bunuel,

Quick question on this rule.
How about 1/15? it can be written as 1/2^0 * 3 * 5. The denominator has 5, but the fraction is not a terminating decimal. Can you please explain why?

Bunuel wrote:
enigma123 wrote:
If a, b, c, d and e are integers and p = 2^a3^b and q = 2^c3^d5^e, is p/q a terminating decimal?
(1) a > c
(2) b > d

Any idea what is the concept behind this question to get a answer B?

Theory:
Reduced fraction $$\frac{a}{b}$$ (meaning that fraction is already reduced to its lowest term) can be expressed as terminating decimal if and only $$b$$ (denominator) is of the form $$2^n5^m$$, where $$m$$ and $$n$$ are non-negative integers. For example: $$\frac{7}{250}$$ is a terminating decimal $$0.028$$, as $$250$$ (denominator) equals to $$2*5^3$$. Fraction $$\frac{3}{30}$$ is also a terminating decimal, as $$\frac{3}{30}=\frac{1}{10}$$ and denominator $$10=2*5$$.

Note that if denominator already has only 2-s and/or 5-s then it doesn't matter whether the fraction is reduced or not.

For example $$\frac{x}{2^n5^m}$$, (where x, n and m are integers) will always be the terminating decimal.

We need reducing in case when we have the prime in denominator other then 2 or 5 to see whether it could be reduced. For example fraction $$\frac{6}{15}$$ has 3 as prime in denominator and we need to know if it can be reduced.

BACK TO THE ORIGINAL QUESTION:
If a, b, c, d and e are integers and p = 2^a3^b and q = 2^c3^d5^e, is p/q a terminating decimal?

Question: is $$\frac{2^a*3^b}{2^c*3^d*5^e}$$ a terminating decimal? The question basically asks whether we cans reduce 3^d in the denominator so to have only powers of 2 and 5 left, which can be rephrased is b (the power of 3 in the nominator) greater than or equal to d (the power of 3 in the denominator): is b>=d?

(1) a > c. Not sufficient.
(2) b > d. Sufficient.

Hope it helps.

1/15 = 1/(3*5). For a reduced fraction to be terminating, the denominator of the fraction should NOT have any prime but 2 or/and 5.

Check Terminating and Recurring Decimals Problems in our Special Questions Directory.

Hope it helps.
_________________
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8158
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: If a, b, c, d and e are integers and p=2^a3^b and q=2^c3  [#permalink]

### Show Tags

06 Dec 2015, 11:31
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.

Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 36, 0.72, and 3.005 are terminating decimals.

If a, b, c, d and e are integers and p = 2^a3^b and q = 2^c3^d5^e, is p/q a terminating decimal?

(1) a > c
(2) b > d

We can derive from p/q=2^a3^b/2^c3^d5^e, that b>=d as the denominator has to be of only 2 or 5 out of the prime factors, so 3 is eliminated and (B) hence becomes the answer.

Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.
_________________
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 \$79 for 1 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Manager
Joined: 21 Feb 2017
Posts: 70
Re: If a, b, c, d and e are integers and p=2^a3^b and q=2^c3  [#permalink]

### Show Tags

21 Sep 2017, 11:45
Bunuel wrote:
NamVu1990 wrote:
This question needs some editing, i first read the question as: p = $$2^{(3a)^{b}$$ and q = $$2^{(3c)^{(5d)^{e}}$$

So I answer D because the denominator consists of 2 only so the decimal will terminate regardless

_______________
Edited. Thank you.

Hi Bunuel,

I have a doubt. If denominator has only 2 or 5 with any power will terminate irrespective of numerator (I mean whether numerator is integer or not?) If so can please explain why answer is C for below question? In explanation it was mentioned that if P=1/6 then result will be something. But my question is p is a factor of 100.. So how can one assume 1/6 as value of p .. Aren't factors always positive integers?

I tried to find this question on gmatclub but could get any information. If it is repeating I will correct my mistake.

Is P/Q a terminating decimal?
(1) P is a factor of 100 (2) Q is a factor of 100
Math Expert
Joined: 02 Sep 2009
Posts: 59180
Re: If a, b, c, d and e are integers and p=2^a3^b and q=2^c3  [#permalink]

### Show Tags

21 Sep 2017, 12:04
goalMBA1990 wrote:
Bunuel wrote:
NamVu1990 wrote:
This question needs some editing, i first read the question as: p = $$2^{(3a)^{b}$$ and q = $$2^{(3c)^{(5d)^{e}}$$

So I answer D because the denominator consists of 2 only so the decimal will terminate regardless

_______________
Edited. Thank you.

Hi Bunuel,

I have a doubt. If denominator has only 2 or 5 with any power will terminate irrespective of numerator (I mean whether numerator is integer or not?) If so can please explain why answer is C for below question? In explanation it was mentioned that if P=1/6 then result will be something. But my question is p is a factor of 100.. So how can one assume 1/6 as value of p .. Aren't factors always positive integers?

I tried to find this question on gmatclub but could get any information. If it is repeating I will correct my mistake.

Is P/Q a terminating decimal?
(1) P is a factor of 100 (2) Q is a factor of 100

1. When it's mentioned "reduced fraction a/b", it's implied that both a and b are integers.
2. Only positive integers can be factors on the GMAT, so I don't know why the solution you mention considers 1/6 as a factor. I would not trust such source.
_________________
Manager
Joined: 21 Feb 2017
Posts: 70
Re: If a, b, c, d and e are integers and p=2^a3^b and q=2^c3  [#permalink]

### Show Tags

21 Sep 2017, 12:12
Bunuel wrote:
goalMBA1990 wrote:
Bunuel wrote:
[quote="NamVu1990"]This question needs some editing, i first read the question as: p = $$2^{(3a)^{b}$$ and q = $$2^{(3c)^{(5d)^{e}}$$

So I answer D because the denominator consists of 2 only so the decimal will terminate regardless

_______________
Edited. Thank you.

Hi Bunuel,

I have a doubt. If denominator has only 2 or 5 with any power will terminate irrespective of numerator (I mean whether numerator is integer or not?) If so can please explain why answer is C for below question? In explanation it was mentioned that if P=1/6 then result will be something. But my question is p is a factor of 100.. So how can one assume 1/6 as value of p .. Aren't factors always positive integers?

I tried to find this question on gmatclub but could get any information. If it is repeating I will correct my mistake.

Is P/Q a terminating decimal?
(1) P is a factor of 100 (2) Q is a factor of 100

1. When it's mentioned "reduced fraction a/b", it's implied that both a and b are integers.
2. Only positive integers can be factors on the GMAT, so I don't know why the solution you mention considers 1/6 as a factor. I would not trust such source.[/quote]
Thank you very much for clarification. So answer we would be B for above question. Correct?

Sent from my XT1663 using GMAT Club Forum mobile app
Math Expert
Joined: 02 Sep 2009
Posts: 59180
Re: If a, b, c, d and e are integers and p=2^a3^b and q=2^c3  [#permalink]

### Show Tags

21 Sep 2017, 12:16
goalMBA1990 wrote:

Thank you very much for clarification. So answer we would be B for above question. Correct?

Sent from my XT1663 using GMAT Club Forum mobile app

It should be mentioned that p and q are positive integers, and in this case yes.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 59180
Re: If a, b, c, d and e are integers and p=2^a3^b and q=2^c3  [#permalink]

### Show Tags

21 Sep 2017, 12:23
goalMBA1990 wrote:
Thank you very much for clarification. So answer we would be B for above question. Correct?

Sent from my XT1663 using GMAT Club Forum mobile app

In the below question:
Is P/Q a terminating decimal?

(1) P is a factor of 100
(2) Q is a factor of 100

Does the solution mention that p can be 1/6 for the first statement or for the second? If for (2), then yes p could be 1/6 and in this case (2) is not sufficient. When combined, since p is a factor of 100, then it must be an integer, thus p/q will be terminating decimal and the answer would be C.
_________________
Manager
Joined: 21 Feb 2017
Posts: 70
Re: If a, b, c, d and e are integers and p=2^a3^b and q=2^c3  [#permalink]

### Show Tags

21 Sep 2017, 19:30
Bunuel wrote:
goalMBA1990 wrote:
Thank you very much for clarification. So answer we would be B for above question. Correct?

Sent from my XT1663 using GMAT Club Forum mobile app

In the below question:
Is P/Q a terminating decimal?

(1) P is a factor of 100
(2) Q is a factor of 100

Does the solution mention that p can be 1/6 for the first statement or for the second? If for (2), then yes p could be 1/6 and in this case (2) is not sufficient. When combined, since p is a factor of 100, then it must be an integer, thus p/q will be terminating decimal and the answer would be C.

Whether it is mentioned or not, how any fraction become factor of any integer? How can we assume fraction for P or Q?

Sent from my XT1663 using GMAT Club Forum mobile app
Re: If a, b, c, d and e are integers and p=2^a3^b and q=2^c3   [#permalink] 21 Sep 2017, 19:30

Go to page    1   2    Next  [ 27 posts ]

Display posts from previous: Sort by