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# Math Revolution and GMAT Club Contest! If a, b, c are positive

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Retired Moderator
Joined: 22 Jun 2014
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Re: Math Revolution and GMAT Club Contest! If a, b, c are positive  [#permalink]

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01 Dec 2015, 12:45
1
We need to find the smallest possible value of "a", hence, it would best to check the lowest value first from the given option.

Can we get 33 on multiplication of three integers a,b,c for which a < b < c?

option (A): a = -33

abc = (-33)*(-1)*(1) here -33 < -1 < 1

Option (A) is the correct answer.
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Re: Math Revolution and GMAT Club Contest! If a, b, c are positive  [#permalink]

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02 Dec 2015, 00:03
1
If a, b, c are integers, 33 = abc, and a < b < c, what is the smallest possible value of a?

A. -33
B. -3
C. 1
D. 3
E. 11

Since a, b, c are integers, 33 = abc, and a < b < c

Possible values can be
a=-33
b=-1
c=1

Hence Ans: A
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Re: Math Revolution and GMAT Club Contest! If a, b, c are positive  [#permalink]

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03 Dec 2015, 10:53
1
QUESTION #3:

If a, b, c are integers, 33 = abc, and a < b < c, what is the smallest possible value of a?

A. -33
B. -3
C. 1
D. 3
E. 11

a*b*c=33 => two scenarios: 2 negatives and 1 positive or 3 positives
a< b < c => a min when a is negative < b (= negative) < c (= positive)
=> (a min = -33) < (b = -1) < (c=1)

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Re: Math Revolution and GMAT Club Contest! If a, b, c are positive  [#permalink]

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03 Dec 2015, 12:34
1
possible values for a, b, c are 1, 3, 11, 33 or -1, -3, -11, -33 (since a, b, c are integers) any combinations of those such that their product is 33
given a < b < c
min possible value for 'a' could be -33
(-33)*(-1)*(1) = 33 (which satisfies a < b < c)

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Joined: 02 Nov 2014
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Re: Math Revolution and GMAT Club Contest! If a, b, c are positive  [#permalink]

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03 Dec 2015, 13:27
1
QUESTION #3:

If a, b, c are integers, 33 = abc, and a < b < c, what is the smallest possible value of a?

A. -33
B. -3
C. 1
D. 3
E. 11

Soln: Since, integers $$a*b*c = 33$$ and $$a < b < c$$, in order to find the minimum value of $$a$$ we can simply look at the answer choices and try to equate $$a$$ to the lowest available value.

So, the question is: Can $$a$$ be as small as $$-33$$? Rearranging, we get, $$a*b*c = 33 = (-33) * (-1) * 1$$.
So that, $$a=-33, b=-1 & c=1.$$ and these values agree the condition a < b < c. So, smallest value of $$a = -33$$. We don't even need to check other options.

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Re: Math Revolution and GMAT Club Contest! If a, b, c are positive  [#permalink]

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04 Dec 2015, 06:01
1
answer : A (-33)

Since abc =33 and a<b<c.
a=-33
b=-1
c=1
abc = (-33)x(-1)x(1)=33
and also -33<-1<1.
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Re: Math Revolution and GMAT Club Contest! If a, b, c are positive  [#permalink]

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04 Dec 2015, 07:48
now 33 = 1*3*11

so, smallest value of a is 1

c..
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Posts: 35
Re: Math Revolution and GMAT Club Contest! If a, b, c are positive  [#permalink]

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04 Dec 2015, 23:42
1
abc=33, a<b<c.

Smallest possible value for a from answer choice is -33. Lets try -33 for a.

If a= -33, then b should be equal to -1 and c equal to 1 for both equations, abc=33, a<b<c to be satisfied.

Hence a = -33 is answer, which is choice A.
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Re: Math Revolution and GMAT Club Contest! If a, b, c are positive  [#permalink]

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05 Dec 2015, 00:03
1
If a, b, c are integers, 33 = abc, and a < b < c, what is the smallest possible value of a?

A. -33
B. -3
C. 1
D. 3
E. 11

By abc i guess it means axbxc.....

Since a,b,c are integers and different as a<b<c;
Therefore a= -33 ; b = -1 ; c = 1
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Re: Math Revolution and GMAT Club Contest! If a, b, c are positive  [#permalink]

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06 Dec 2015, 04:31
1
The smallest value of a is - 33 with a = -33, b = -1, c = 1.
Hence A.
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Re: Math Revolution and GMAT Club Contest! If a, b, c are positive  [#permalink]

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06 Dec 2015, 09:34
1
a b c all are integers.

none of them is zero as abc=33

and a<b<c

so answer is a*b*c= -33*-1*1
Math Expert
Joined: 02 Sep 2009
Posts: 58444
Re: Math Revolution and GMAT Club Contest! If a, b, c are positive  [#permalink]

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14 Dec 2015, 09:01
Bunuel wrote:

Math Revolution and GMAT Club Contest Starts!

QUESTION #3:

If a, b, c are integers, 33 = abc, and a < b < c, what is the smallest possible value of a?

A. -33
B. -3
C. 1
D. 3
E. 11

Check conditions below:

Math Revolution and GMAT Club Contest

The Contest Starts November 28th in Quant Forum

We are happy to announce a Math Revolution and GMAT Club Contest

For the following four (!) weekends we'll be publishing 4 FRESH math questions per weekend (2 on Saturday and 2 on Sunday).

To participate, you will have to reply with your best answer/solution to the new questions that will be posted on Saturday and Sunday at 9 AM Pacific.
Then a week later, the forum moderator will be selecting 2 winners who provided most correct answers to the questions, along with best solutions. Those winners will get 6-months access to GMAT Club Tests.

PLUS! Based on the answers and solutions for all the questions published during the project ONE user will be awarded with ONE Grand prize:

PS + DS course with 502 videos that is worth \$299!

All announcements and winnings are final and no whining GMAT Club reserves the rights to modify the terms of this offer at any time.

NOTE: Test Prep Experts and Tutors are asked not to participate. We would like to have the members maximize their learning and problem solving process.

Thank you!

MATH REVOLUTION OFFICIAL SOLUTION:

This type of question appears within a score range of 45 to 48. In terms of Integer, you have to find the “hidden 1” and consider negative numbers. Thus, the calculation would be, 33=(-33)(-1)(1), and -33 is the smallest possible value of a. So, A is the correct answer
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Re: Math Revolution and GMAT Club Contest! If a, b, c are positive  [#permalink]

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09 Sep 2019, 10:33
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Re: Math Revolution and GMAT Club Contest! If a, b, c are positive   [#permalink] 09 Sep 2019, 10:33

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# Math Revolution and GMAT Club Contest! If a, b, c are positive

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