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pran21
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If w, x, y and z are four positive integers,then is (w+x)(y-z) an odd Updated on: 03 Sep 2014, 11:30
Originally posted by pran21 on 03 Sep 2014, 11:01.
Last edited by Bunuel on 03 Sep 2014, 11:30, edited 1 time in total.
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61% (02:49) correct 39% (02:41) wrong based on 161 sessions

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If w, x, y and z are four positive integers,then is (w+x)(y-z) an odd number?

(1) w + x + y is an even number.
(2) x + y - z is an odd number.
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E
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If w, x, y and z are four positive integers,then is (w+x)(y-z) an odd 03 Sep 2014, 14:32
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pran21
If w, x, y and z are four positive integers,then is (w+x)(y-z) an odd number?

(1) w + x + y is an even number.
(2) x + y - z is an odd number.
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Dear pran21,
I'm happy to help.

Consider these two sets.

Set #1 = {w = 1, x = 2, y = 3, z = 2}
Satisfies both statements.
(w+x)(y-z) = 3*1 = 3 is odd

Set #2 = {w = 2, x = 2, y = 2, z = 1}
Satisfies both statements.
(w+x)(y-z) = 4*1 = 4 is even

We can satisfy both statements, yet answer the prompt question either way. Even combined, both statements are insufficient.
Answer = (E)

Does this make sense?
Mike :-)
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If w, x, y and z are four positive integers,then is (w+x)(y-z) an odd 11 Sep 2014, 07:58
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pran21
If w, x, y and z are four positive integers,then is (w+x)(y-z) an odd number?

(1) w + x + y is an even number.
(2) x + y - z is an odd number.
Dear pran21,
I'm happy to help.

Consider these two sets.

Set #1 = {w = 1, x = 2, y = 3, z = 2}
Satisfies both statements.
(w+x)(y-z) = 3*1 = 3 is odd

Set #2 = {w = 2, x = 2, y = 2, z = 1}
Satisfies both statements.
(w+x)(y-z) = 4*1 = 4 is even

We can satisfy both statements, yet answer the prompt question either way. Even combined, both statements are insufficient.
Answer = (E)

Does this make sense?
Mike :-)
Show more

Hii Mike,
great solution..!! could u please tell me,how did u substitute nos in 2nd set so that the outcome was an even integer?is there any technique for substituting nos ?did u randomly choose them?m jus asking because trying to randomly insert various integers until the outcome turns out to be even doesnt seem to be a productive idea.. :shock:
Thanks..! :)
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If w, x, y and z are four positive integers,then is (w+x)(y-z) an odd 11 Sep 2014, 10:57
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vards

Hi Mike,
great solution..!! could u please tell me,how did u substitute nos in 2nd set so that the outcome was an even integer?is there any technique for substituting nos ?did u randomly choose them?m just asking because trying to randomly insert various integers until the outcome turns out to be even doesnt seem to be a productive idea.. :shock:
Thanks..! :)
Show more
Dear yards,
I'm happy to respond. :-) You asked "How did you substitute numbers in the second set so that the outcome was an even integer?" Of course, once I had numbers that worked, I just plugged them in. I believe what you meant to ask was: how did I create that particular combination of numbers? How did I go about generating a set which would satisfy both statements and produce an even output in the prompt?
This is very subtle. This involves number sense. See:
https://magoosh.com/gmat/2012/number-sense-for-the-gmat/
Number sense is a very right-brain process, which involves many subtle pattern-matching skills. There's absolutely no way to spell out the "recipe" for number sense: it is something one has to develop over time, and that blog article gives some recommendations. Here are just a few considerations I used.
(1) if we want an even product, only one of the factors has to be even. The other factor can be anything, even or odd --- as long as just one factor is even, the product will be even. That's a big idea.
(2) with that in mind, I made w = x = 2, so that would definitely be even
(3) with those numbers, I had to make y even, to satisfy statement #1
(4) all this meant I had to make x odd, to satisfy statement #2
That was my reasoning, and that's an example of working with number-sense. How would a student know where to start this process? Again, that's a deeply right-brain skill, and comes only will repeated practice, especially from simply playing with arithmetic and being curious about the patterns of numbers. For example, in this problem, there are 16 possible sets, where each entry is either 1 or 2. It might be worthwhile to go through all 16 possibilities, and for each one, see: does it satisfy statement #1? does it satisfy statement #2? what does it do to the prompt? Part of number sense comes from just playing with numbers, just out of sheer curiosity, even if it is entirely irrelevant to the problem. Play is a state of mind that has nothing to do with any goal.
You may find this blog article helpful as well:
https://magoosh.com/gmat/2013/how-to-do- ... th-faster/

One of the many ironies of studying for the GMAT: if one has the very tangible goal of a good GMAT score, an essential part of achieving that goal comes from letting go of having a goal in a number of different ways in one's studies. If one stays locked in goal-oriented mode, in some ways that actually impedes achieving the goal. See:
https://magoosh.com/gmat/2014/getting-a-good-gmat-score/

Does all this make sense?
Mike :-)
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If w, x, y and z are four positive integers,then is (w+x)(y-z) an odd 17 May 2016, 22:31
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mikemcgarry
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Hi Mike,
great solution..!! could u please tell me,how did u substitute nos in 2nd set so that the outcome was an even integer?is there any technique for substituting nos ?did u randomly choose them?m just asking because trying to randomly insert various integers until the outcome turns out to be even doesnt seem to be a productive idea.. :shock:
Thanks..! :)
Dear yards,
I'm happy to respond. :-) You asked "How did you substitute numbers in the second set so that the outcome was an even integer?" Of course, once I had numbers that worked, I just plugged them in. I believe what you meant to ask was: how did I create that particular combination of numbers? How did I go about generating a set which would satisfy both statements and produce an even output in the prompt?
This is very subtle. This involves number sense. See:
https://magoosh.com/gmat/2012/number-sense-for-the-gmat/
Number sense is a very right-brain process, which involves many subtle pattern-matching skills. There's absolutely no way to spell out the "recipe" for number sense: it is something one has to develop over time, and that blog article gives some recommendations. Here are just a few considerations I used.
(1) if we want an even product, only one of the factors has to be even. The other factor can be anything, even or odd --- as long as just one factor is even, the product will be even. That's a big idea.
(2) with that in mind, I made w = x = 2, so that would definitely be even
(3) with those numbers, I had to make y even, to satisfy statement #1
(4) all this meant I had to make x odd, to satisfy statement #2
That was my reasoning, and that's an example of working with number-sense. How would a student know where to start this process? Again, that's a deeply right-brain skill, and comes only will repeated practice, especially from simply playing with arithmetic and being curious about the patterns of numbers. For example, in this problem, there are 16 possible sets, where each entry is either 1 or 2. It might be worthwhile to go through all 16 possibilities, and for each one, see: does it satisfy statement #1? does it satisfy statement #2? what does it do to the prompt? Part of number sense comes from just playing with numbers, just out of sheer curiosity, even if it is entirely irrelevant to the problem. Play is a state of mind that has nothing to do with any goal.
You may find this blog article helpful as well:
https://magoosh.com/gmat/2013/how-to-do- ... th-faster/

One of the many ironies of studying for the GMAT: if one has the very tangible goal of a good GMAT score, an essential part of achieving that goal comes from letting go of having a goal in a number of different ways in one's studies. If one stays locked in goal-oriented mode, in some ways that actually impedes achieving the goal. See:
https://magoosh.com/gmat/2014/getting-a-good-gmat-score/

Does all this make sense?
Mike :-)
Show more


Mike,

I did evaluate on paper all the 16 possibilities. The results are revealing:
Of 16 possible combinations,
1) statement 1 is valid 8 times and so is statement 2 .. Half the times.
2) The expression (w+x)(y-z) is true only 4 times
among these 4 instances,
one instance of each of the following can be found
-statement. #1 is true
-statement. #2 is true
- both # 1 and 2 is true
- both #1 and 2 is false ..
Wow!! the truth is spread evenly across truth and false states of both statements. What a great question!
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If w, x, y and z are four positive integers,then is (w+x)(y-z) an odd 28 Jan 2024, 12:21
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