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

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

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29 Nov 2015, 09:57
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65% (00:54) correct 35% (00:56) wrong based on 334 sessions

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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!

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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.

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

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29 Nov 2015, 10:16
2
abc=33 and a<b<c,
so (-33)(-1)(1)=33

The smallest possible value of a will be -33.

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

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29 Nov 2015, 10:21
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

Given : a * b * c = 33.
33 is a Positive Odd number. Side Note: Thus, all 3 numbers will be odd.
Prime factorization will also give you numbers. 1, 3, 11. The 3 numbers will be combination of these 3 numbers with possible variation in sign(+/-).

We could have any 2 digits as negative. --> negative * negative * positive. We have negative values in answer option, so eliminate C, D and E from answer choices.
-33 * -1 * 1 = 33.

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

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29 Nov 2015, 10:22
1

First, break this question. Since a<b<c and abc=33, what are the different possible factors of 33 that can help us find a, b and c. Remember, a, b and c are integers and could be both positive or negative. The different factors are 33, 11, 3 and 1 (these values can be both positive and negative). The least of these would be -33. Can we make 'a' -33 and still achieve the conditions in the question. ? Yes -> a=-33, b=-1 and c=1 - in this case, abc=33 and a<b<c as well. Hence -33 is the smallest value of a.
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Re: Math Revolution and GMAT Club Contest! If a, b, c are positive  [#permalink]

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29 Nov 2015, 11:00
1
the factors of 33 are -33, -11, -3, -1, 1, 3, 11, 33.

From the above, the least value of a such that abc to be 33 and a< b<c is -33.
In this case b=-1 and c=1
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Re: Math Revolution and GMAT Club Contest! If a, b, c are positive  [#permalink]

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Updated on: 29 Nov 2015, 11:51
1
It says abc=33 and a<b<c
checking numbers -> a=-33, b=-1, c=1
Sol. A. -33

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Last edited by Nightfury14 on 29 Nov 2015, 11:51, edited 2 times in total.
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Re: Math Revolution and GMAT Club Contest! If a, b, c are positive  [#permalink]

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29 Nov 2015, 11:16
1
The three factors of 33 are 1, 3 and 11. With no positive/negative restrictions on a b and c, some of the factors can also be negative
with a<b<c: possible values for a, b and c that yield 33 are:

a: -11, -3 or 1
b: -3, -1 or 3
c: 1 , 11 or 11

Since -11 is not in the answer choices, the smallest value for a is therefore -3:
$$(-3)*(-1)*11=33$$
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Re: Math Revolution and GMAT Club Contest! If a, b, c are positive  [#permalink]

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29 Nov 2015, 11:35
The correct answer is A here.
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Re: Math Revolution and GMAT Club Contest! If a, b, c are positive  [#permalink]

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29 Nov 2015, 11:54
Solution: 1X3X11=33 (given that : abc=33) where it also satisfy the condition a<b<c.
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Re: Math Revolution and GMAT Club Contest! If a, b, c are positive  [#permalink]

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29 Nov 2015, 12:04
1
if abc=33 and a<b<c
then, a can be -33, and b can be -1 while c is 1.
-33* -1 * 1 = 33.
thus, the minimal value of a can be -33.
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Re: Math Revolution and GMAT Club Contest! If a, b, c are positive  [#permalink]

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29 Nov 2015, 22:24
1
If a, b, c are integers, 33 = abc, and a < b < c, what is the smallest possible value of a?

a * b * c = -33 * -1 * 1 = 33. So the smallest value of a can be -33.

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

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30 Nov 2015, 07:09
1

if a= -33 , b = -1 and c=1
then abc= 33
Hence, smallest value of a = -33
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Re: Math Revolution and GMAT Club Contest! If a, b, c are positive  [#permalink]

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30 Nov 2015, 08:41
1
Option a!

The integers can be (-33)*(-1)*(1); a<b<c
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Re: Math Revolution and GMAT Club Contest! If a, b, c are positive  [#permalink]

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30 Nov 2015, 11:21
-33 cannot be answer as a is smallest and to make +33, we need atleast -1...

out of remaining 4, minimum is -3... which works with -3, -1 and 11....

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

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30 Nov 2015, 11:49
1
Using the given options,
If a=-33, b=-1, c=1, then a<b<c
And abc=33
So smallest value of a=-33
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Re: Math Revolution and GMAT Club Contest! If a, b, c are positive  [#permalink]

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30 Nov 2015, 11:49
Using the given options,
If a=-33, b=-1, c=1, then a<b<c
And abc=33
So smallest value of a=-33
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Re: Math Revolution and GMAT Club Contest! If a, b, c are positive  [#permalink]

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30 Nov 2015, 23:36
1

Now, (-33)(-1)(+1) =33 and this satisfier a<b<c

So, the answer is A (-33)
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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, 02:52
1
As abc=33 and a<b<c, Factors of 33 are 1,3,11,33 .abc can be -33*-1*1. here a =-33 is the lowest possible value
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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, 10:13
1
Given abc= 33.

This could mean that either a, b and c all are positive or 2 of them are negative.
Since we're asked to find the minimum possible value of a, we will work with negative numbers.
-33, -1 and 1. a=-33.

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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, 11:52
If a, b, c are integers, 33 = abc, and a < b < c, what is the smallest possible value of a?

a < b < c = 1 < 3 < 11

So, a = 1

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Re: Math Revolution and GMAT Club Contest! If a, b, c are positive   [#permalink] 01 Dec 2015, 11:52

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