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The product of three different numbers is greater than 1000.

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by fskilnik@GMATH » Wed Feb 20, 2019 6:01 am

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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.

Answer: [spoiler] ___(E)__[/spoiler]
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by fskilnik@GMATH » Wed Feb 20, 2019 10:34 am
fskilnik@GMATH 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.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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