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# Three different numbers have a product that is greater than

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GMATH Teacher
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Three different numbers have a product that is greater than  [#permalink]

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20 Feb 2019, 07:11
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Difficulty:

75% (hard)

Question Stats:

45% (02:06) correct 55% (01:27) wrong based on 33 sessions

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GMATH practice exercise (Quant Class 16)

The product of three different numbers is greater than 1000. What is the value of the largest among them?

(1) The numbers are primes.
(2) The product of the numbers is less than 1310.

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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
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Re: Three different numbers have a product that is greater than  [#permalink]

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20 Feb 2019, 07:19
1) and 2) are clearly insufficient: there are endless possible results.
Let's try combined: we'll make a short list of prime numbers, starting with the lowest, and see if we can find more than one trio whse product is between 1000 and 1310:
2, 3, 5, 7, 9, 11, 13, 17...
the product of 9*11*13 is 99*13 - definitely in the range (even without calculating).
can we change this at all?
if we replace 13 with the next largest prime (17), it's too large: 99*17>1300
if we replace 9 with the next smallest (7): 77*13 = 770+210+21=980+21=1001 - in the range!
two possible solutions, not sufficient!
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Re: Three different numbers have a product that is greater than  [#permalink]

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20 Feb 2019, 11:50
fskilnik wrote:
GMATH practice exercise (Quant Class 16)

The product of three different numbers is greater than 1000. What is the value of the largest among them?

(1) The numbers are primes.
(2) The product of the numbers is less than 1310.

$$a < b < c$$

$$abc > 1000$$

$$? = c$$

$$\left( 1 \right)\,\,{\rm{primes}}\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,\left( {a,b,c} \right) = \left( {7,11,13} \right)\,\,\,\,\left[ {abc = 1001} \right]\,\,\,\,\, \Rightarrow \,\,\,? = 13 \hfill \cr \,{\rm{Take}}\,\,\left( {a,b,c} \right) = \left( {7,11,17} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 17 \hfill \cr} \right.$$

$$\left( 2 \right)\,\,abc < 1310\,\,\,\,\,\,\left\{ \matrix{ \,\left( {{\mathop{\rm Re}\nolimits} } \right){\rm{Take}}\,\,\left( {a,b,c} \right) = \left( {7,11,13} \right)\,\,\,\, \Rightarrow \,\,\,? = 13 \hfill \cr \,\left( {{\mathop{\rm Re}\nolimits} } \right){\rm{Take}}\,\,\left( {a,b,c} \right) = \left( {7,11,17} \right)\,\,\,\,\left[ {abc = 1309} \right]\,\,\,\,\, \Rightarrow \,\,\,? = 17 \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left( {\rm{E}} \right)$$

We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: Three different numbers have a product that is greater than  [#permalink]

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20 Feb 2019, 16:35
DavidTutorexamPAL wrote:
Let's try combined: we'll make a short list of prime numbers, starting with the lowest, and see if we can find more than one trio whse product is between 1000 and 1310:
2, 3, 5, 7, 9, 11, 13, 17...
the product of 9*11*13 is 99*13 - definitely in the range (even without calculating).

9 is not a prime number.
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Re: Three different numbers have a product that is greater than  [#permalink]

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20 Feb 2019, 16:39
To make calculation easy here, you can set two of the primes to 2 and 5. Then we'll know the information is not sufficient if we can find at least two different prime numbers between 100 and 131. And there are a few primes in that range (101 and 103, for example).
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Re: Three different numbers have a product that is greater than   [#permalink] 20 Feb 2019, 16:39
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