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Post subject: GMAT Algebra Posted: Fri Jul 15, 2011 6:34 pm 

Joined: Sun May 30, 2010 3:15 am Posts: 424

T is the set of all numbers that can be written as the following sum involving distinct nonzero integers a, b, c and d: a/a + 2(b/b) + 3(c/c) + 4(d/d) + 5(abcd/abcd). What is the range of T? A. 15 B. 20 C. 28 D. 29 E. 30
(C) If a > 0, a / a = 1, but if 0 > a, a / a = –1 (because you have a positive number being divided by a negative number). This is also true for b/b, c/c and d/d. What about abcdabcd? It all depends on the number of negative variables among {a, b, c, d}: if one or three of these variables are negative, abcdabcd = –1. Otherwise, abcd/abcd = 1.
To find the range we are going find the largest possible value, and then find the smallest possible value. If each of these four variables is positive, we get 1 + 2 + 3 + 4 + 5 = 15, the greatest possible value of an element in T. To find the smallest possible value of T, we ideally need to get all the fractions negative. Regarding 5(abcd/abcd), it needs to be made negative, because of the five terms in the sum; it’s the one that has the greatest impact on the sum. This term will be –5 only if one or three variables are negative. If all four variables are negative, 5(abcd/abcd) will be 5. So, to find the smallest element in T, pick a positive value of a and let the other three variables be negative. The values for the fractions are then (+1), (2), (3), (4), (5). The corresponding value of the element in T is 1 – 2 – 3 – 4 – 5 = –13, and thus the range of T is 15 – (–13) = 28 (the difference between the highest value and the lowest one). The correct answer is C.  Shouldn't "0" be counted in the range, therefore making the answer 29?


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Gennadiy

Post subject: Re: GMAT Algebra Posted: Fri Jul 15, 2011 6:46 pm 

Joined: Sun May 30, 2010 2:23 am Posts: 498

No, the range of a set is the difference between its largest element and the smallest one.
EXAMPLES: The range of {1, 2, 3, 4, 5} is 5 – 1 = 4 The range of {1, 4, 5} is 5 – 1 = 4 The range of {2.5, 0, 1} is 1 – (2.5) = 3.5
In our case the set is {13, ... some elements ... , 15}, so its range is 15 – (13) = 15 + 13 = 28. The main idea is that we do NOT have to find all the elements, but just the smallest and the largest ones.
Note:  when a question deals with integers in its statement, it might NOT be all about integers.  the "range of a function" is a completely different term, which means the set of all the values a function possesses.


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ccheng

Post subject: Re: GMAT Algebra Posted: Mon Oct 17, 2011 2:25 pm 

Joined: Mon Oct 10, 2011 1:25 pm Posts: 7


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Gennadiy

Post subject: Re: GMAT Algebra Posted: Mon Oct 17, 2011 3:16 pm 

Joined: Sun May 30, 2010 2:23 am Posts: 498


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fedana

Post subject: Re: math (t.4, qt.22): sets, algebra Posted: Fri Mar 23, 2012 4:44 pm 

Joined: Mon Nov 26, 2012 4:59 pm Posts: 8

This is a very good question.


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Robert.Delane

Post subject: Re: GMAT Algebra Posted: Wed Aug 22, 2012 4:35 pm 

Joined: Tue Nov 27, 2012 7:29 am Posts: 12

Why are we assuming the real numbers can be 1, 2, 3, 4, 5 only? Why not 6, 7, 8, 9, 10 or any other number combination?


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Gennadiy

Post subject: Re: GMAT Algebra Posted: Wed Aug 22, 2012 4:41 pm 

Joined: Sun May 30, 2010 2:23 am Posts: 498


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dave

Post subject: Re: GMAT Algebra Posted: Fri Nov 02, 2012 5:53 pm 

Joined: Mon Nov 26, 2012 5:39 pm Posts: 11

If we take a positive value for a, abc/abc is going to become positive and 3(abc/abc) = 3 not 3.


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Gennadiy

Post subject: Re: GMAT Algebra Posted: Fri Nov 02, 2012 6:02 pm 

Joined: Sun May 30, 2010 2:23 am Posts: 498


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questioner

Post subject: Re: GMAT Algebra Posted: Sun Aug 18, 2013 6:52 am 

Joined: Sun May 30, 2010 3:15 am Posts: 424

The correct answer should be 29 instead of 28: 15  (13) + 1, because 15 and 13 are both in the range inclusive.


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