If m, p, and t are positive integers and m<p<t, is the : GMAT Data Sufficiency (DS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 18 Jan 2017, 10:28

# STARTING SOON:

Open Admission Chat with MBA Experts of Personal MBA Coach - Join Chat Room to Participate.

### 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 June
Open Detailed Calendar

# If m, p, and t are positive integers and m<p<t, is the

Author Message
TAGS:

### Hide Tags

Manager
Joined: 13 Aug 2009
Posts: 203
Schools: Sloan '14 (S)
Followers: 3

Kudos [?]: 103 [1] , given: 16

If m, p, and t are positive integers and m<p<t, is the [#permalink]

### Show Tags

16 Nov 2009, 07:01
1
KUDOS
12
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

57% (02:26) correct 43% (01:10) wrong based on 356 sessions

### HideShow timer Statistics

If m, p, and t are positive integers and m<p<t, is the product mpt an even integer?

(1) t - p = p - m
(2) t - m = 16
[Reveal] Spoiler: OA
Forum Moderator
Status: mission completed!
Joined: 02 Jul 2009
Posts: 1426
GPA: 3.77
Followers: 180

Kudos [?]: 853 [0], given: 621

Re: If m, p, and t are positive integers and m<p<t, is the [#permalink]

### Show Tags

26 May 2010, 04:20
michigancat wrote:
For statement 1, you could have m, p, and t be 3, 5, and 7 respectively, in addition to 2, 3, and 4. So mpt can be odd or even. Insufficient.

.
Ooops you are wrong a bit cause from (2) t – m = 16, - > m=t-16 , and not as you stated m=16-t

clear, I am wrong as for (1).

_________________

Audaces fortuna juvat!

GMAT Club Premium Membership - big benefits and savings

Last edited by PTK on 26 May 2010, 04:25, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 36545
Followers: 7076

Kudos [?]: 93089 [9] , given: 10552

Re: If m, p, and t are positive integers and m<p<t, is the [#permalink]

### Show Tags

26 May 2010, 04:25
9
KUDOS
Expert's post
6
This post was
BOOKMARKED
Pkit wrote:
DS , Q. 76 page 313

If m, p, and t are positive integers and m < p < t, is the product mpt an even integer?
(1) t – p = p – m
(2) t – m = 16

My solution is:
(1) t+m=2p ->, $$(t+m)/2=p$$, p can not be odd since:
if t and m are even, then p is even , keep in mind that m < p < t, $$m<>t$$
if t and m are odd, p is even, keep in mind that m < p < t, $$m<>t$$,[(5+11)/2=8, but (5+5)/2=5 odd,but m<>t]
if t is even and m is odd, then p can not be odd , since (even+odd)/2 must give us integer, so P could not be odd, thus it is even.

Then, if:
mt= even*even=even
mt= odd*odd=odd
mt=even*odd=even

Then we know that P must be even, so either of results m*t when multiplied by even number P give us Even product, so the product m*p*t= even
Sufficient.

(2) not sufficinet.

I choose A, however the OG12th's answer choice is
[Reveal] Spoiler:
E

Am I wrong?

If m, p, and t are positive integers and m < p < t, is the product mpt an even integer?

For $$mpt$$ to be even at least one should be even (as m, p, and t are integers).

(1) $$t-p=p-m$$ --> $$\frac{t+m}{2}=p$$ --> this algebraic expression means that $$p$$ is halfway between $$t$$ and $$m$$ on the number line: $$----m-------p-------t----$$

So m, p, and t are evenly spaced. Does this imply that any integer must be even? Not necessarily. If $$p$$ is odd and $$m$$ and $$t$$ are some even constant below and above it, then all three will be odd. So we can have an YES as well as a NO answer. For example:
If $$m=1$$, $$p=3$$, $$t=5$$ the answer is NO;
If $$m=2$$, $$p=4$$, $$t=6$$ the answer is YES.

Not sufficient.

(2) $$t-m=16$$. Clearly not sufficient. No info about $$p$$.

(1)+(2) Second statement says that the distance between $$m$$ and $$t$$ is 16, so as from (1) $$m$$, $$p$$, and $$t$$ are evenly spaced, then the distance between $$m$$ and $$p$$ and the distance between$$p$$ and $$t$$ must 8. But again we can have two different answers:

$$m=0$$, $$p=8$$, $$t=16$$ --> $$mpt=even$$;
$$m=1$$, $$p=9$$, $$t=17$$ --> $$mpt=odd$$.

Hope it's clear.
_________________
Forum Moderator
Status: mission completed!
Joined: 02 Jul 2009
Posts: 1426
GPA: 3.77
Followers: 180

Kudos [?]: 853 [0], given: 621

Re: If m, p, and t are positive integers and m<p<t, is the [#permalink]

### Show Tags

26 May 2010, 04:35
Bunuel wrote:
Pkit wrote:
DS , Q. 76 page 313

Hope it's clear.

Thank you Bunuel, now it is clear for me.
_________________

Audaces fortuna juvat!

GMAT Club Premium Membership - big benefits and savings

Senior Manager
Joined: 19 Oct 2010
Posts: 271
Location: India
GMAT 1: 560 Q36 V31
GPA: 3
Followers: 7

Kudos [?]: 75 [0], given: 27

Re: If m, p, and t are positive integers and m<p<t, is the [#permalink]

### Show Tags

11 Sep 2011, 02:22
Really good question..
_________________

petrifiedbutstanding

Intern
Joined: 04 Jun 2011
Posts: 16
Concentration: Finance
GMAT 1: 710 Q50 V36
GPA: 3.37
WE: Analyst (Mutual Funds and Brokerage)
Followers: 0

Kudos [?]: 8 [0], given: 5

Re: If m, p, and t are positive integers and m<p<t, is the [#permalink]

### Show Tags

18 Jan 2012, 08:18
I thought the same thing, I'm glad this post is still around.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7121
Location: Pune, India
Followers: 2133

Kudos [?]: 13639 [0], given: 222

Re: If m, p, and t are positive integers and m<p<t, is the [#permalink]

### Show Tags

19 Jan 2012, 02:21
Yes, number properties theory is simple but its application can get really tricky. The worst thing is that you don't even realize that there was a trick in the question and that you have messed up! You might very confidently mark A here and move on! This is a perfect example of trickery of number properties on GMAT.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Manager Joined: 03 Jun 2010 Posts: 138 Location: Dubai, UAE Schools: IE Business School, Manchester Business School, HEC Paris, Rotterdam School of Management, Babson College Followers: 2 Kudos [?]: 4 [0], given: 4 Re: If m, p, and t are positive integers and m<p<t, is the [#permalink] ### Show Tags 23 Jan 2012, 05:29 Ok this is my take, take statement 1, t+m/2= p which means that t+m/2 equals an integer and the only way that is possible is when t+m are either both odd or both even since if they are odd and even that doesn't given an integer. Secondly, if t+m is either both odd or both even the result will be even hence p= even. But statement 1 insufficient because we dont know whether t+m are both odd or even. There BCE Now let's take statement 2 We have no information about p so insufficient. Hence CE Now both statements taken together We still can't conclude that t and m are either odd or even since that will determine whether the product is even. So E. Do let me know if my solution makes sense to people. Posted from GMAT ToolKit Intern Joined: 14 Feb 2012 Posts: 40 Location: Germany Concentration: Technology, Strategy GMAT Date: 06-13-2012 Followers: 0 Kudos [?]: 34 [0], given: 13 Re: If m, p, and t are positive integers and m<p<t, is the [#permalink] ### Show Tags 27 Mar 2012, 08:35 Hey! I need help with this one. It's obvious that each statement alone is not sufficient, but I'm struggling with both statements together not sufficient. From (1) we know that p=(t+m)/2 From (2) we know that t-m=16 -> following this info, you can say that either both t and m are even or both are odd. Now putting it together, since t+m will be even and and saying that (t+m)/2 will be even, too, we can say that it will be even?!?! Math Expert Joined: 02 Sep 2009 Posts: 36545 Followers: 7076 Kudos [?]: 93089 [1] , given: 10552 Re: If m, p, and t are positive integers and m<p<t, is the [#permalink] ### Show Tags 27 Mar 2012, 08:57 1 This post received KUDOS Expert's post andih wrote: Hey! I need help with this one. It's obvious that each statement alone is not sufficient, but I'm struggling with both statements together not sufficient. From (1) we know that p=(t+m)/2 From (2) we know that t-m=16 -> following this info, you can say that either both t and m are even or both are odd. Now putting it together, since t+m will be even and and saying that (t+m)/2 will be even, too, we can say that it will be even?!?! Not sure understood your question correctly. Anyway, check the examples provided in this post: if-m-p-and-t-are-positive-integers-and-m-p-t-is-the-product-mpt-an-even-integer-126259.html#p729805 Hope they'll help to clear your doubts. _________________ Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7121 Location: Pune, India Followers: 2133 Kudos [?]: 13639 [2] , given: 222 Re: If m, p, and t are positive integers and m<p<t, is the [#permalink] ### Show Tags 27 Mar 2012, 09:46 2 This post received KUDOS Expert's post andih wrote: Hey! I need help with this one. It's obvious that each statement alone is not sufficient, but I'm struggling with both statements together not sufficient. From (1) we know that p=(t+m)/2 From (2) we know that t-m=16 -> following this info, you can say that either both t and m are even or both are odd. Now putting it together, since t+m will be even and and saying that (t+m)/2 will be even, too, we can say that it will be even?!?! We need to find whether at least one of m, p and t is even. S1: p = (t+m)/2 tells us that (t+m) is even since p has to be integer. So all we know is that t and m are both either odd or both even (since their sum is even). It doesn't say anything about p i.e. whether p is even or odd. p could be odd e.g. (4+2)/2 = 3 or (5+1)/2 = 3 or it could be even e.g. (8+4)/2 = 6 or (7+5)/2 = 6 etc. S2: t - m = 16 tells us that t and m are either both odd or both even (because the difference between them is even).We again don't know whether they are even. e.g. 18 - 2 = 16 or 17 - 1 = 16. We also don't know whether p is even. Using both statements, 2p = t+m, 16 = t - m. Add them to get p+8 = t. If t is odd, p is also odd. If t is even, p is also even. So basically, all 3 variables are either odd or all three are even. But we do not know whether they are even. Hence not sufficient. Answer (E) _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Intern
Joined: 31 Oct 2011
Posts: 19
Schools: ESSEC '15 (A)
GMAT 1: 650 Q45 V35
Followers: 0

Kudos [?]: 31 [0], given: 2

Re: If m, p, and t are positive integers and m<p<t, is the [#permalink]

### Show Tags

03 Dec 2012, 06:27
Bunuel wrote:
Pkit wrote:
DS , Q. 76 page 313

If m, p, and t are positive integers and m < p < t, is the product mpt an even integer?
(1) t – p = p – m
(2) t – m = 16

My solution is:
(1) t+m=2p ->, $$(t+m)/2=p$$, p can not be odd since:
if t and m are even, then p is even , keep in mind that m < p < t, $$m<>t$$
if t and m are odd, p is even, keep in mind that m < p < t, $$m<>t$$,[(5+11)/2=8, but (5+5)/2=5 odd,but m<>t]
if t is even and m is odd, then p can not be odd , since (even+odd)/2 must give us integer, so P could not be odd, thus it is even.

Then, if:
mt= even*even=even
mt= odd*odd=odd
mt=even*odd=even

Then we know that P must be even, so either of results m*t when multiplied by even number P give us Even product, so the product m*p*t= even
Sufficient.

(2) not sufficinet.

I choose A, however the OG12th's answer choice is
[Reveal] Spoiler:
E

Am I wrong?

If m, p, and t are positive integers and m < p < t, is the product mpt an even integer?

For $$mpt$$ to be even at least one should be even (as m, p, and t are integers).

(1) $$t-p=p-m$$ --> $$\frac{t+m}{2}=p$$ --> this algebraic expression means that $$p$$ is halfway between $$t$$ and $$m$$ on the number line: $$----m-------p-------t----$$

So m, p, and t are evenly spaced. Does this imply that any integer must be even? Not necessarily. If $$p$$ is odd and $$m$$ and $$t$$ are some even constant below and above it, then all three will be odd. So we can have an YES as well as a NO answer. For example:
If $$m=1$$, $$p=3$$, $$t=5$$ the answer is NO;
If $$m=2$$, $$p=4$$, $$t=6$$ the answer is YES.

Not sufficient.

(2) $$t-m=16$$. Clearly not sufficient. No info about $$p$$.

(1)+(2) Second statement says that the distance between $$m$$ and $$t$$ is 16, so as from (1) $$m$$, $$p$$, and $$t$$ are evenly spaced, then the distance between $$m$$ and $$p$$ and the distance between$$p$$ and $$t$$ must 8. But again we can have two different answers:

$$m=0$$, $$p=8$$, $$t=16$$ --> $$mpt=even$$;
$$m=1$$, $$p=9$$, $$t=17$$ --> $$mpt=odd$$.

Hope it's clear.

Bunuel, great explanation but in my humble opinion I don't think you can take m=0 since it says that m p and t are positive integer
Math Expert
Joined: 02 Sep 2009
Posts: 36545
Followers: 7076

Kudos [?]: 93089 [1] , given: 10552

Re: If m, p, and t are positive integers and m<p<t, is the [#permalink]

### Show Tags

03 Dec 2012, 06:38
1
KUDOS
Expert's post
Maxswe wrote:

Bunuel, great explanation but in my humble opinion I don't think you can take m=0 since it says that m p and t are positive integer

Correct, but it does not affect the answer. Consider:
$$m=2$$, $$p=10$$, $$t=18$$ --> $$mpt=even$$;
$$m=1$$, $$p=9$$, $$t=17$$ --> $$mpt=odd$$.
_________________
Intern
Joined: 29 Oct 2012
Posts: 11
Followers: 0

Kudos [?]: 10 [0], given: 5

Re: If m, p, and t are positive integers and m<p<t, is the [#permalink]

### Show Tags

07 Dec 2012, 23:48
Hi,

Can someone help me find where I'm wrong in solving the following Q:

Q: If m,p and t are positive integers and m<p<t, is the product mpt an even integer?
1. t-p=p-m
2. t-m= 16

O.A (E)

My interpretation:

Q: For "mpt" to be an even integer atleast one of the three numbers should be even. to find if any one of m,p or t is even.

1. t-p=p-m

so, t+m=2p
t+m/2 = p

if t+m is divisible by 2 and results in an integer 'p', then 'p' has to be a multiple of '2' which is even. hence 'mpt' should be even. SUFFICIENT

we are down to Options A or D.

2. t-m=16.

this only says the diff of t and m is even. so t and m are either both 'odd' or both 'even'. INSUFFICIENT.

So the correct Answer ( in my opinion) is A.

Senior Manager
Joined: 22 Dec 2011
Posts: 298
Followers: 3

Kudos [?]: 233 [1] , given: 32

Re: If m, p, and t are positive integers and m<p<t, is the [#permalink]

### Show Tags

08 Dec 2012, 00:34
1
KUDOS
imk wrote:
Hi,

Can someone help me find where I'm wrong in solving the following Q:

Q: If m,p and t are positive integers and m<p<t, is the product mpt an even integer?
1. t-p=p-m
2. t-m= 16

O.A (E)

My interpretation:

Q: For "mpt" to be an even integer atleast one of the three numbers should be even. to find if any one of m,p or t is even.

1. t-p=p-m

so, t+m=2p
t+m/2 = p

if t+m is divisible by 2 and results in an integer 'p', then 'p' has to be a multiple of '2' which is even. hence 'mpt' should be even. SUFFICIENT

we are down to Options A or D.

2. t-m=16.

this only says the diff of t and m is even. so t and m are either both 'odd' or both 'even'. INSUFFICIENT.

So the correct Answer ( in my opinion) is A.

Hi. please post the OA inside the spoilers to give other a fair shot at the problem. Thanks.

you have said -> "if t+m is divisible by 2 and results in an integer 'p', then 'p' has to be a multiple of '2' which is even. hence 'mpt' should be even. SUFFICIENT"

P can or cannot be a multiple of 2, t+m is a multiple of 2.
Take t=3 m =3 then t+m = 6, which is multiple of 2, and p can be 3 so that t+m = 2 (p) = 3+3 = 2 * 3
tmp = odd
if we take t = m = 6 then tmp = Even
t+m = 2p then only 2 things we can deduct
both t and m are both odd or Even, as E+O would result in Odd,which cannot be a multiple of 2

HTH

Cheers
Intern
Joined: 29 Oct 2012
Posts: 11
Followers: 0

Kudos [?]: 10 [0], given: 5

Re: If m, p, and t are positive integers and m<p<t, is the [#permalink]

### Show Tags

08 Dec 2012, 00:41
Thank you. How silly of me to miss that point. I was thinking of the odd numerator and totally wiped out the possibility that even/even can be an odd integer. btw point noted. this is my first post. Sorry that I gave the answer away.
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13437
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: If m, p, and t are positive integers and m<p<t, is the [#permalink]

### Show Tags

17 Feb 2014, 01:00
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.
_________________
Intern
Joined: 23 Dec 2011
Posts: 39
Location: United States
Concentration: Technology, General Management
GPA: 3.83
WE: Programming (Computer Software)
Followers: 1

Kudos [?]: 15 [0], given: 26

Re: If m, p, and t are positive integers and m<p<t, is the [#permalink]

### Show Tags

05 Jul 2014, 00:23
f m, p, and t are positive integers and m < p < t, is the product mpt an even integer?

For mpt to be even at least one should be even (as m, p, and t are integers).

(1) t-p=p-m --> \frac{t+m}{2}=p --> this algebraic expression means that p is halfway between t and m on the number line: ----m-------p-------t----

So m, p, and t are evenly spaced. Does this imply that any integer must be even? Not necessarily. If p is odd and m and t are some even constant below and above it, then all three will be odd. So we can have an YES as well as a NO answer. For example:
If m=1, p=3, t=5 the answer is NO;
If m=2, p=4, t=6 the answer is YES.

Not sufficient.

(2) t-m=16. Clearly not sufficient. No info about p.

(1)+(2) Second statement says that the distance between m and t is 16, so as from (1) m, p, and t are evenly spaced, then the distance between m and p and the distance betweenp and t must 8. But again we can have two different answers:

m=0, p=8, t=16 --> mpt=even;
m=1, p=9, t=17 --> mpt=odd.

Manager
Joined: 22 Jan 2014
Posts: 138
WE: Project Management (Computer Hardware)
Followers: 0

Kudos [?]: 53 [0], given: 135

Re: If m, p, and t are positive integers and m<p<t, is the [#permalink]

### Show Tags

06 Jul 2014, 05:14
h2polo wrote:
If m, p, and t are positive integers and m<p<t, is the product mpt an even integer?

(1) t - p = p - m
(2) t - m = 16

1) t-m = 2p
or t-m = even
so, t,m = (even,even) or (odd,odd)
and p can be even or odd
so A alone is not sufficient.

2) t-m = 16
t,m = (17,1) or (18,2) ....
again the same condition and p is unknown.
so B alone is also insufficient.

(1)+(2)
t+m = 2p
t-m = 16
solving; t-p = 8
t,p = (100,92) or (101,93) ...
when (t,p) = (100,92) then m = even and m*t*p = even
when (t,p) = (101,93) then m = odd and m*t*p = odd
hence (1)+(2) also is insufficient.

------------------
+1 if you liked my solution. Tx.
_________________

Illegitimi non carborundum.

Manager
Joined: 10 Mar 2014
Posts: 236
Followers: 1

Kudos [?]: 80 [0], given: 13

Re: If m, p, and t are positive integers and m<p<t, is the [#permalink]

### Show Tags

15 Aug 2014, 22:58
Bunuel wrote:
Pkit wrote:
DS , Q. 76 page 313

If m, p, and t are positive integers and m < p < t, is the product mpt an even integer?
(1) t – p = p – m
(2) t – m = 16

My solution is:
(1) t+m=2p ->, $$(t+m)/2=p$$, p can not be odd since:
if t and m are even, then p is even , keep in mind that m < p < t, $$m<>t$$
if t and m are odd, p is even, keep in mind that m < p < t, $$m<>t$$,[(5+11)/2=8, but (5+5)/2=5 odd,but m<>t]
if t is even and m is odd, then p can not be odd , since (even+odd)/2 must give us integer, so P could not be odd, thus it is even.

Then, if:
mt= even*even=even
mt= odd*odd=odd
mt=even*odd=even

Then we know that P must be even, so either of results m*t when multiplied by even number P give us Even product, so the product m*p*t= even
Sufficient.

(2) not sufficinet.

I choose A, however the OG12th's answer choice is
[Reveal] Spoiler:
E

Am I wrong?

If m, p, and t are positive integers and m < p < t, is the product mpt an even integer?

For $$mpt$$ to be even at least one should be even (as m, p, and t are integers).

(1) $$t-p=p-m$$ --> $$\frac{t+m}{2}=p$$ --> this algebraic expression means that $$p$$ is halfway between $$t$$ and $$m$$ on the number line: $$----m-------p-------t----$$

So m, p, and t are evenly spaced. Does this imply that any integer must be even? Not necessarily. If $$p$$ is odd and $$m$$ and $$t$$ are some even constant below and above it, then all three will be odd. So we can have an YES as well as a NO answer. For example:
If $$m=1$$, $$p=3$$, $$t=5$$ the answer is NO;
If $$m=2$$, $$p=4$$, $$t=6$$ the answer is YES.

Not sufficient.

(2) $$t-m=16$$. Clearly not sufficient. No info about $$p$$.

(1)+(2) Second statement says that the distance between $$m$$ and $$t$$ is 16, so as from (1) $$m$$, $$p$$, and $$t$$ are evenly spaced, then the distance between $$m$$ and $$p$$ and the distance between$$p$$ and $$t$$ must 8. But again we can have two different answers:

$$m=0$$, $$p=8$$, $$t=16$$ --> $$mpt=even$$;
$$m=1$$, $$p=9$$, $$t=17$$ --> $$mpt=odd$$.

Hope it's clear.

HI Bunuel,

In above example why you are considering m=0? as in question stem it is said that m,p, and t are positive integers. So How m can be 0

Thanks.
Re: If m, p, and t are positive integers and m<p<t, is the   [#permalink] 15 Aug 2014, 22:58

Go to page    1   2    Next  [ 24 posts ]

Similar topics Replies Last post
Similar
Topics:
1 If p is a positive integer, Is integer m a multiple of 6? 4 05 Dec 2016, 23:46
If m and n are positive integers, what is the value of p? 2 07 Feb 2016, 09:45
11 If p, m, and n are positive integers, n is odd, and p = m^2 9 24 Feb 2014, 07:44
6 If m and n are positive integers, and if p and q are differe 2 22 Mar 2012, 19:52
If m, p, and t are positive integers and m < p < t, is 2 31 Jul 2007, 08:43
Display posts from previous: Sort by