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20 Feb 2019, 07:11
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E
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Difficulty:
75%
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Question Stats:
47% (02:12) correct
53%
(01:50)
wrong
based on 76
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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.
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.
20 Feb 2019, 07:19
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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!
answer E
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!
answer E
20 Feb 2019, 11:50
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fskilnik
\(a < b < c\)
\(abc > 1000\)
\(? = c\)
\(\left( 1 \right)\,\,{\rm{primes}}\,\,\,\left\{ \matrix{\\
\,{\rm{Take}}\,\,\left( {a,b,c} \right) = \left( {7,11,13} \right)\,\,\,\,\left[ {abc = 1001} \right]\,\,\,\,\, \Rightarrow \,\,\,? = 13 \hfill \cr \\
\,{\rm{Take}}\,\,\left( {a,b,c} \right) = \left( {7,11,17} \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 17 \hfill \cr} \right.\)
\(\left( 2 \right)\,\,abc < 1310\,\,\,\,\,\,\left\{ \matrix{\\
\,\left( {{\mathop{\rm Re}\nolimits} } \right){\rm{Take}}\,\,\left( {a,b,c} \right) = \left( {7,11,13} \right)\,\,\,\, \Rightarrow \,\,\,? = 13 \hfill \cr \\
\,\left( {{\mathop{\rm Re}\nolimits} } \right){\rm{Take}}\,\,\left( {a,b,c} \right) = \left( {7,11,17} \right)\,\,\,\,\left[ {abc = 1309} \right]\,\,\,\,\, \Rightarrow \,\,\,? = 17 \hfill \cr} \right.\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left( {\rm{E}} \right)\)
We follow the notations and rationale taught in the GMATH method.
Regards,
Fabio.
