Odds/Evens: If m, p, and t are positive integers and m <

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II: Master | Next Rank: 500 Posts; Posts: 400; Joined: Mon Dec 10, 2007 1:35 pm; Location: London, UK; Thanked: 19 times; GMAT Score:680

by II » Tue Apr 29, 2008 3:22 pm

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

Interested in figuring out alternative approaches to solve this. In particular the plugging-in numbers approach ... I struggled to find "smart" numbers to use here under the 2-minute per question timeline. This is my weakness in number properties DS questions ... under the time pressure I struggle to get the smart numbers quickly.

My approach:
For a product of integers to be even, at least one of those integers needs to be even. So the question is asking: is either one of m, p, or t even ?

I looked at statement 2, which was the "easy" statement here. So we have our BD/ACE grid.
t could be 20, and m could be 4 here, which would answer yes to our question.
t could be 19, and m could be 3, which would answer no to our question.
So this is INSUFF, and we can cross out BD.

Statement 1: t – p = p – m
Let m=2, p=4, and t=6. Here 6-4=4-2 ... and this answers YES
Let m=1, p=3, and t=5. Here 5-3=3-1 ... and this answers NO
So this INSUFF, and we can cross out A.
So we are left with answer choices C and E.

With (1) and (2) together, we still cannot find out for certain whether at least one of m, p, or t is even.
Let m=4, p=12, t=20
Let m=3, p=11, t=19
These satify both the criteria in both statements and the criteria in Q-stem but dont enable us to answer the question sufficiently. So INSUFF, and E is the final answer.

This quite a lengthy approach, especially when under real test conditions, where thinking of numbers can take up valuable time.
Are there better approaches to tackle this problem ?

Thanks in advance for sharing.
II

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Source: Beat The GMAT — Data Sufficiency | Tue Apr 29, 2008 3:22 pm

luvaduva: Senior | Next Rank: 100 Posts; Posts: 84; Joined: Tue Feb 05, 2008 8:52 pm; Thanked: 8 times

by luvaduva » Tue Apr 29, 2008 5:25 pm

"For a product of integers to be even, at least one of those integers needs to be even. So the question is asking: is either one of m, p, or t even ? "

That is exactly what we look for.

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

-don't know if p is even or odd, but 2p is even.
-don't know if m is even or odd
t = 2p - even = even
t = 2p - odd = odd
N/S

(2)
t - m = 16
t = 16 +m
-don't know if m is even or odd
t = 16 + odd = odd
t = 16 = even = even
N/S

(1) and (2)

t = 2p - m
t = 16 + m

2p - m = 16 + m

16 = 2(p - m)
8 = p - m

-don't know whether p or m are even or odd.

N/S

Not sure if this is a lot quicker, but it seems better than picking numbers.

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II: Master | Next Rank: 500 Posts; Posts: 400; Joined: Mon Dec 10, 2007 1:35 pm; Location: London, UK; Thanked: 19 times; GMAT Score:680

by II » Tue Apr 29, 2008 11:31 pm

I agree luvaduva. I like your approach. I think is key to have multiple approaches in your toolbox when tackling the GMAT.

Thanks for your input.
II

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nh8404052006: Senior | Next Rank: 100 Posts; Posts: 48; Joined: Wed Aug 27, 2008 9:58 am

by nh8404052006 » Sat Dec 13, 2008 8:48 am

My approach:
From (2), we know t and m are 16 apart, that implies if t is odd then m is also odd. By the same reasoning, if t is even, then m is also even.
If both t and m are even, the product must be even. If both t and m are odd, we cannot say whether the product is even or odd, since we have no idea what p is.i.e Statement (2) is insufficient.

From Statement (1), we only know p is the midpoint of t and m. But from statement (1), we can extrapolate that t - m must be even. If t - m is odd, then p is not an integer. Now, we come to the situation very similar to that of statement (2), we therefore, can say statement (1) is insufficient.

If we consider both statements together, still no new information is available, thus, the answer is E.

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logitech: Legendary Member; Posts: 2134; Joined: Mon Oct 20, 2008 11:26 pmFollowed by: 25 members; Thanked: 237 times; GMAT Score:730

Re: Odds/Evens: If m, p, and t are positive integers and m &

by logitech » Wed Jan 14, 2009 11:17 am

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

(1) t – p = p – m

This says p is in the middle

3 5 7

2 4 6

so insuf

(2) t – m = 16

this says their range is 16 insuf

together

1 9 17

2 10 18

Insuf

LGTCH
---------------------
"DON'T LET ANYONE STEAL YOUR DREAM!"

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rahul.s: Master | Next Rank: 500 Posts; Posts: 324; Joined: Thu Dec 24, 2009 6:29 amFollowed by: 1 member; Thanked: 17 times

by rahul.s » Mon Jan 11, 2010 9:52 pm

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

(1) t ï¿½ p = p ï¿½ m

This says p is in the middle

3 5 7

2 4 6

so insuf

(2) t ï¿½ m = 16

this says their range is 16 insuf

together

1 9 17

2 10 18

Insuf

Brilliant approach Logitech! Simple and easy to understand. Thank you

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bhumika.k.shah: Legendary Member; Posts: 941; Joined: Sun Dec 27, 2009 12:28 amFollowed by: 1 member; Thanked: 20 times

by bhumika.k.shah » Sun Jan 17, 2010 1:01 am

rahul.s wrote:
logitech wrote:If m, p, and t are positive integers and m < p < t, is the product mpt an even integer?

(1) t ï¿½ p = p ï¿½ m

This says p is in the middle

3 5 7

2 4 6

so insuf

(2) t ï¿½ m = 16

this says their range is 16 insuf

together

1 9 17

2 10 18

Insuf
Brilliant approach Logitech! Simple and easy to understand. Thank you

i agree

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vkanwal: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Tue Nov 03, 2009 9:14 pm

by vkanwal » Thu May 27, 2010 1:43 am

@logitech

Even i went ahead with same approach and was able to reach conclusion in few seconds .Its short an straight .
Wherever we can use direct numbers to check conditions .we shall not be hesitant in doing so .It saves time (which is too precious

)).

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krusta80: Master | Next Rank: 500 Posts; Posts: 143; Joined: Mon Mar 14, 2011 3:13 amFollowed by: 5 members; Thanked: 34 times

by krusta80 » Fri Mar 02, 2012 5:03 pm

[email protected] wrote:st1 : t-p =p-m
st2 : t-m = 16

both not sufficient (reasons same as above )

but if combining 1 and 2 yields :
t+m = 2p (from 1)
t= m+16 (from 2)

substituting t from 2 in 1
2m + 16 =2p
2m + 2(8)= 2(p)
in this case all are even and hence mpt =even

why cant we choose C ???

Just because m and p have even coefficients doesn't mean that they are even.

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Jeff@TargetTestPrep: GMAT Instructor; Posts: 1462; Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members; Location: New York, NY; Thanked: 39 times

by Jeff@TargetTestPrep » Wed Dec 13, 2017 11:14 am

II 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

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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