It is currently 15 Dec 2017, 19:40

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

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

Hide Tags

Manager
Manager
User avatar
Joined: 13 Aug 2009
Posts: 199

Kudos [?]: 130 [0], given: 16

Schools: Sloan '14 (S)
If m, p, and t are positive integers and m<p<t, is the [#permalink]

Show Tags

New post 16 Nov 2009, 07:01
18
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

62% (01:32) correct 38% (01:07) wrong based on 443 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

Kudos [?]: 130 [0], given: 16

Expert Post
12 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42618

Kudos [?]: 135763 [12], given: 12708

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

Show Tags

New post 26 May 2010, 04:25
12
This post received
KUDOS
Expert's post
6
This post was
BOOKMARKED
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:

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

Two different answers. Not sufficient.

Answer: E.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135763 [12], given: 12708

Expert Post
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7800

Kudos [?]: 18137 [0], given: 236

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

Show Tags

New post 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

Kudos [?]: 18137 [0], given: 236

Manager
Manager
avatar
Joined: 03 Jun 2010
Posts: 136

Kudos [?]: 4 [0], given: 4

Location: Dubai, UAE
Schools: IE Business School, Manchester Business School, HEC Paris, Rotterdam School of Management, Babson College
GMAT ToolKit User
Re: If m, p, and t are positive integers and m<p<t, is the [#permalink]

Show Tags

New post 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.

Image Posted from GMAT ToolKit

Kudos [?]: 4 [0], given: 4

Intern
Intern
avatar
Joined: 14 Feb 2012
Posts: 40

Kudos [?]: 43 [0], given: 13

Location: Germany
Concentration: Technology, Strategy
GMAT Date: 06-13-2012
Re: If m, p, and t are positive integers and m<p<t, is the [#permalink]

Show Tags

New post 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?!?!

Kudos [?]: 43 [0], given: 13

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42618

Kudos [?]: 135763 [1], given: 12708

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

Show Tags

New post 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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135763 [1], given: 12708

Expert Post
2 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7800

Kudos [?]: 18137 [2], given: 236

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

Show Tags

New post 27 Mar 2012, 09:46
2
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
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

Kudos [?]: 18137 [2], given: 236

Intern
Intern
avatar
Joined: 31 Oct 2011
Posts: 19

Kudos [?]: 35 [0], given: 2

Schools: ESSEC '15 (A)
GMAT 1: 650 Q45 V35
Re: If m, p, and t are positive integers and m<p<t, is the [#permalink]

Show Tags

New post 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:

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

Two different answers. Not sufficient.

Answer: E.

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

Kudos [?]: 35 [0], given: 2

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42618

Kudos [?]: 135763 [1], given: 12708

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

Show Tags

New post 03 Dec 2012, 06:38
1
This post received
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:
\(m=2\), \(p=10\), \(t=18\) --> \(mpt=even\);
\(m=1\), \(p=9\), \(t=17\) --> \(mpt=odd\).
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135763 [1], given: 12708

Intern
Intern
User avatar
Joined: 29 Oct 2012
Posts: 11

Kudos [?]: 12 [0], given: 5

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

Show Tags

New post 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.

kindly advise.

Kudos [?]: 12 [0], given: 5

1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 22 Dec 2011
Posts: 295

Kudos [?]: 305 [1], given: 32

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

Show Tags

New post 08 Dec 2012, 00:34
1
This post received
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.

kindly advise.


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

Kudos [?]: 305 [1], given: 32

Intern
Intern
User avatar
Joined: 29 Oct 2012
Posts: 11

Kudos [?]: 12 [0], given: 5

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

Show Tags

New post 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.

Kudos [?]: 12 [0], given: 5

Intern
Intern
User avatar
Joined: 23 Dec 2011
Posts: 35

Kudos [?]: 22 [0], given: 26

Location: United States
Concentration: Technology, General Management
GPA: 3.83
WE: Programming (Computer Software)
Re: If m, p, and t are positive integers and m<p<t, is the [#permalink]

Show Tags

New post 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.

Two different answers. Not sufficient.

Answer: E.

Kudos [?]: 22 [0], given: 26

Manager
Manager
User avatar
B
Joined: 22 Jan 2014
Posts: 140

Kudos [?]: 78 [0], given: 145

WE: Project Management (Computer Hardware)
Re: If m, p, and t are positive integers and m<p<t, is the [#permalink]

Show Tags

New post 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.

Therefore, answer is E.

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

Illegitimi non carborundum.

Kudos [?]: 78 [0], given: 145

Manager
Manager
avatar
B
Joined: 10 Mar 2014
Posts: 237

Kudos [?]: 111 [0], given: 13

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

Show Tags

New post 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:

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

Two different answers. Not sufficient.

Answer: E.

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

Please clarify

Thanks.

Kudos [?]: 111 [0], given: 13

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42618

Kudos [?]: 135763 [0], given: 12708

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

Show Tags

New post 16 Aug 2014, 01:04
PathFinder007 wrote:
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:

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

Two different answers. Not sufficient.

Answer: E.

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

Please clarify

Thanks.


This does not change anything.

Try other numbers: m=2, p=10, t=18.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135763 [0], given: 12708

Expert Post
1 KUDOS received
Target Test Prep Representative
User avatar
S
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 1945

Kudos [?]: 1021 [1], given: 3

Location: United States (CA)
Re: If m, p, and t are positive integers and m<p<t, is the [#permalink]

Show Tags

New post 04 Apr 2017, 14:43
1
This post received
KUDOS
Expert's post
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


We are given that m, p, and t are positive integers with m < p < t, and we need to determine whether mpt is an even integer.

Statement One Alone:

t – p = p – m

Simplifying the equation in statement one, we have:

t – p = p – m

t + m = 2p

Since 2p must be even, we see that either t and m are both odd or t and m are both even. However, since we know nothing about p, p could be either odd or even. If t and m are both even, then regardless of whether p is odd or even, the product mpt will be even. However, if t and m are both odd and p is also odd, then mpt will be odd. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

t – m = 16

Since t – m = 16, we see that either t and m are both odd or t and m are both even. However, since we know nothing about p, statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using statements one and two, we still know only that either t and m are both odd or t and m are both even, and we still have no information regarding p. Thus, the two statements together are not sufficient.

Answer: E
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 1021 [1], given: 3

Director
Director
avatar
P
Joined: 14 Nov 2014
Posts: 623

Kudos [?]: 113 [0], given: 46

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

Show Tags

New post 04 Apr 2017, 22:37
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


Hi Bunuel , can you please check , is the below approach is fine....

1- t + m = 2p
we can have 2,2,2 -mpt=even
We can have 1,5,3 --mpt=odd

2- insuff clearly

Now solve 1 and 2
t+m = 2p-----------1
t-m = 16------------2

2t = 2p + 16
t = p +8

t and p can be even or odd ..so insuff

E ...

Kudos [?]: 113 [0], given: 46

Re: If m, p, and t are positive integers and m<p<t, is the   [#permalink] 04 Apr 2017, 22:37
Display posts from previous: Sort by

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

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


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.