-
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
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
(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
