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T is the set of all numbers that can be written as the follo
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01 Dec 2013, 17:34
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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
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Re: T is the set of all numbers that can be written as the follo
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02 Dec 2013, 01:30
honchos wrote: 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 \(\frac{x}{x}\) is 1 when \(x>0\) and 1 when \(x<0\). For example, if \(x=2\), then \(\frac{x}{x}=1\) and if \(x=2\), then \(\frac{x}{x}=1\). Thus the maximum value of \(\frac{a}{a} + 2(\frac{b}{b}) + 3(\frac{c}{c}) + 4(\frac{d}{d}) + 5(\frac{abcd}{abcd})\) is obtained when each of a, b, c and d are positive: 1+2+3+4+5=15. As for the minimum value: notice that all a, b, c, d and abcd cannot simultaneously be negative. For example if a, b, c and d are negative then abcd will be positive. Thus the minimum value is obtained when a is positive and b, c and d are negative: 12345=13. The range = 15  (13) = 28. Answer: C.
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Re: T is the set of all numbers that can be written as the follo
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29 Jan 2014, 03:33
Am I missing sth? 12345 is 14 and not 13, right? so the correct answer would be D



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Re: T is the set of all numbers that can be written as the follo
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29 Jan 2014, 05:51



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Re: T is the set of all numbers that can be written as the follo
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07 Jul 2014, 10:32
Bunuel wrote: honchos wrote: 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 \(\frac{x}{x}\) is 1 when \(x>0\) and 1 when \(x<0\). For example, if \(x=2\), then \(\frac{x}{x}=1\) and if \(x=2\), then \(\frac{x}{x}=1\). Thus the maximum value of \(\frac{a}{a} + 2(\frac{b}{b}) + 3(\frac{c}{c}) + 4(\frac{d}{d}) + 5(\frac{abcd}{abcd})\) is obtained when each of a, b, c and d are positive: 1+2+3+4+5=15. As for the minimum value: notice that all a, b, c, d and abcd cannot simultaneously be negative. For example if a, b, c and d are negative then abcd will be positive. Thus the minimum value is obtained when a is positive and b, c and d are negative: 12345=13. The range = 15  (13) = 28. Answer: C. Hey Bunuel..there are many values in between that we can never achieve..say 0..so how is range defined in such cases...is it just the maxmin..
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Re: T is the set of all numbers that can be written as the follo
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07 Jul 2014, 10:35
JusTLucK04 wrote: Bunuel wrote: honchos wrote: 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 \(\frac{x}{x}\) is 1 when \(x>0\) and 1 when \(x<0\). For example, if \(x=2\), then \(\frac{x}{x}=1\) and if \(x=2\), then \(\frac{x}{x}=1\). Thus the maximum value of \(\frac{a}{a} + 2(\frac{b}{b}) + 3(\frac{c}{c}) + 4(\frac{d}{d}) + 5(\frac{abcd}{abcd})\) is obtained when each of a, b, c and d are positive: 1+2+3+4+5=15. As for the minimum value: notice that all a, b, c, d and abcd cannot simultaneously be negative. For example if a, b, c and d are negative then abcd will be positive. Thus the minimum value is obtained when a is positive and b, c and d are negative: 12345=13. The range = 15  (13) = 28. Answer: C. Hey Bunuel..there are many values in between that we can never achieve..say 0..so how is range defined in such cases...is it just the maxmin.. Yes, the range is always the difference between the largest and smallest.
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Re: T is the set of all numbers that can be written as the follo
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12 Jul 2017, 18:49
Bunuel wrote: honchos wrote: 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 \(\frac{x}{x}\) is 1 when \(x>0\) and 1 when \(x<0\). For example, if \(x=2\), then \(\frac{x}{x}=1\) and if \(x=2\), then \(\frac{x}{x}=1\). Thus the maximum value of \(\frac{a}{a} + 2(\frac{b}{b}) + 3(\frac{c}{c}) + 4(\frac{d}{d}) + 5(\frac{abcd}{abcd})\) is obtained when each of a, b, c and d are positive: 1+2+3+4+5=15. As for the minimum value: notice that all a, b, c, d and abcd cannot simultaneously be negative. For example if a, b, c and d are negative then abcd will be positive. Thus the minimum value is obtained when a is positive and b, c and d are negative: 12345=13. The range = 15  (13) = 28. Answer: C. I took abcd as a 4 digit number. Bunuel , could you please edit the question and replace abcd with a*b*c*d , for clarity.
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Re: T is the set of all numbers that can be written as the follo
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12 Jul 2017, 21:24
rekhabishop wrote: Bunuel wrote: honchos wrote: 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 \(\frac{x}{x}\) is 1 when \(x>0\) and 1 when \(x<0\). For example, if \(x=2\), then \(\frac{x}{x}=1\) and if \(x=2\), then \(\frac{x}{x}=1\). Thus the maximum value of \(\frac{a}{a} + 2(\frac{b}{b}) + 3(\frac{c}{c}) + 4(\frac{d}{d}) + 5(\frac{abcd}{abcd})\) is obtained when each of a, b, c and d are positive: 1+2+3+4+5=15. As for the minimum value: notice that all a, b, c, d and abcd cannot simultaneously be negative. For example if a, b, c and d are negative then abcd will be positive. Thus the minimum value is obtained when a is positive and b, c and d are negative: 12345=13. The range = 15  (13) = 28. Answer: C. I took abcd as a 4 digit number. Bunuel , could you please edit the question and replace abcd with a*b*c*d , for clarity. If abcd were a 4digit number if would have been mentioned explicitly. Without that, abcd can only be a*b*c*d since only multiplication sign (*) is usually omitted.
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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.
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Re: T is the set of all numbers that can be written as the follo
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13 Jul 2017, 21:53
honchos wrote: 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 How to think in such a problem: "T is the set of all numbers that can be written as the following sum" Makes me think that T can take a limited number of values. Else the set would have infinite elements and we will not be able to define the range. a/a + 2(b/b) + 3(c/c) + 4(d/d) + 5(abcd/abcd) Seeing this, I recall that x/x will be 1 or 1 depending on whether x is positive or negative. It can take no other value. So to maximise the sum (to get range), we should make all such expressions 1. This happens when all a, b, c and d are positive. The sum will be 1 + 2 + 3 + 4 + 5 = 15 To minimise the sum we should try to make as many terms negative as possible. But abcd will become positive if all a, b, c and d are negative. So we should keep 'a' positive and make all rest negative. 1  2 3  4 5 = 13 Note that it doesn't matter what the actual values of a, b, c and d are. a/a will always be only 1 or 1. Range = 15  (13) = 28
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Re: T is the set of all numbers that can be written as the follo
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14 Jul 2017, 19:22
I am wondering why no one asked why we are considering "a" positive, why not b or c or d ? well the answer is: as we are looking for minimum value we should add as less as possible, thus á is considered +ve value.



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