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For integers a, b, and c, if ab = bc, then which of the foll [#permalink]
 11 Feb 2013, 10:54
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For integers a, b, and c, if ab = bc, then which of the following must also be true? A. a = c B. a^2*b=b*c^2 C. a/c = 1 D. abc > bc E. a + b + c = 0
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Last edited by Bunuel on 11 Feb 2013, 15:22, edited 1 time in total.
Edited the question.
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Re: For integers a, b, and c, if ab = bc, then which of the foll [#permalink]
11 Feb 2013, 15:22
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emmak wrote: For integers a, b, and c, if ab = bc, then which of the following must also be true?
A. a = c
B. a^2*b=b*c^2
C. a/c = 1
D. abc > bc
E. a + b + c = 0 ab = bc --> ab-bc=0 --> b(a-c)=0--> b=0 or a=c. A. a = c. If b=0, then this option is not necessarily true. B. a^2*b=b*c^2 --> b(a^2-c^2)=0 --> b(a-c)(a+c)=0. Now, since b=0 or a=c, then b(a-c)(a+c) does equal to zero. So, we have that this options must be true. C. a/c = 1. If b=0, then this option is not necessarily true. D. abc > bc. If b=0, then this option is not true. E. a + b + c = 0. If b=0, then this option is not necessarily true (if b=0 then a+c can take any value this option is not necessarily true.). Answer: B.
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Re: For integers a, b, and c, if ab = bc, then which of the foll [#permalink]
12 Mar 2013, 05:08
b(a-c)=0 => b=0 or a=c
You can see B in an easier way:
Inequalities hold when we raise them to power on both sides. so a^2= c^2. => b.a^2= b.c^2. Thus B follows right away.
I agree with other explainations by Bunuel.
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Re: For integers a, b, and c, if ab = bc, then which of the foll [#permalink]
11 Jun 2013, 20:47
Bunuel wrote: emmak wrote: For integers a, b, and c, if ab = bc, then which of the following must also be true?
A. a = c
B. a^2*b=b*c^2
C. a/c = 1
D. abc > bc
E. a + b + c = 0 ab = bc --> ab-bc=0 --> b(a-c)=0--> b=0 or a=c. B. a^2*b=b*c^2 --> b(a^2-c^2)=0 --> b(a-c)(a+c)=0. Now, since b=0 or a=c, then b(a-c)(a+c) does equal to zero. So, we have that this options must be true. Answer: B. for answer choice B, could you also say that if a = -c it also equals zero? Also, why do all of the possible answers equaling zero in choice B mean that B must be true?
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Re: For integers a, b, and c, if ab = bc, then which of the foll [#permalink]
11 Jun 2013, 21:21
dhlee922 wrote: Bunuel wrote:
ab = bc --> ab-bc=0 --> b(a-c)=0--> b=0 or a=c.
B. a^2*b=b*c^2 --> b(a^2-c^2)=0 --> b(a-c)(a+c)=0. Now, since b=0 or a=c, then b(a-c)(a+c) does equal to zero. So, we have that this options must be true.
Answer: B.
for answer choice B, could you also say that if a = -c it also equals zero? The point here is that analyzing the initial equation ab = bc, we know that either b = 0 or a = c. Plugging in either of these values results in b(a-c)(a+c) being equal to zero. I think you're confusion comes from extracting "a = -c" from "b(a-c)(a+c) = 0" as opposed to extracting information from the original equation ab = bc (which is what we need to do). dhlee922 wrote: Also, why do all of the possible answers equaling zero in choice B mean that B must be true? Continuing from above: So recall that from the first equation, b = 0 or a = c. The expanded term b(a-c)(a+c) is an alternate expression for the second option; i.e, the fact that both of the possible necessary truths (b = 0; a = c) lead to b(a-c)(a+c) = 0 means that the equivalent expression, a^2 * b = b * c^2 must also be true. I hope that's clear!
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Re: For integers a, b, and c, if ab = bc, then which of the foll [#permalink]
12 Jun 2013, 15:29
i'm still a little confused by the answer choices.
is it because the question stem equates to B=0 OR A=C
so for answer choice A, A doesnt have to equal C because the B equaling 0 will just make the whole expression 0
but then for answer choice B, since B=0 OR A=C, since 1 or the 3 groups in parentheses will be 0, it will make the whole expression 0, therefore B must be true?
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Re: For integers a, b, and c, if ab = bc, then which of the foll [#permalink]
12 Jun 2013, 15:34
dhlee922 wrote: i'm still a little confused by the answer choices.
is it because the question stem equates to B=0 OR A=C
so for answer choice A, A doesnt have to equal C because the B equaling 0 will just make the whole expression 0
but then for answer choice B, since B=0 OR A=C, since 1 or the 3 groups in parentheses will be 0, it will make the whole expression 0, therefore B must be true? Yes, exactly. We know that or b=0 or a-c=0 ( or both) . We can rewrite B as b(a-c)(a+c), and since at least one of the terms is 0, the whole expression is 0.
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Re: For integers a, b, and c, if ab = bc, then which of the foll [#permalink]
12 Jun 2013, 15:38
dhlee922 wrote: i'm still a little confused by the answer choices.
is it because the question stem equates to B=0 OR A=C
so for answer choice A, A doesnt have to equal C because the B equaling 0 will just make the whole expression 0
but then for answer choice B, since B=0 OR A=C, since 1 or the 3 groups in parentheses will be 0, it will make the whole expression 0, therefore B must be true? Yes, for A, if b=0, then a may or may not equal to c. As for B, since b=0 or a=c (a-c=0), then b(a-c)(a+c)=0 must be true, since either the first or the second multiple (or both) is 0. Hope it's clear.
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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders
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. NEW!!! ,11 Mixed Questions NEW!!!, 12 Fresh Meat NEW!!!
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Re: For integers a, b, and c, if ab = bc, then which of the foll [#permalink]
12 Jun 2013, 15:49
yes, thank you everyone for your replies! geez, i find this one to be pretty tricky, but it's only 600-700 level, ugh
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Re: For integers a, b, and c, if ab = bc, then which of the foll
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12 Jun 2013, 15:49
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