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# Four different prime numbers, each less than 20, are multiplied togeth

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Senior Manager
Joined: 02 Jan 2017
Posts: 295
Four different prime numbers, each less than 20, are multiplied togeth  [#permalink]

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23 Feb 2017, 20:27
1
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Difficulty:

25% (medium)

Question Stats:

74% (01:29) correct 26% (01:28) wrong based on 95 sessions

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Four different prime numbers, each less than 20, are multiplied together. What is the greatest possible result?
○A○ 21,879
○B○ 28,728
○C○ 40,755
○D○ 46,189
○E○ 49,742
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Re: Four different prime numbers, each less than 20, are multiplied togeth  [#permalink]

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23 Feb 2017, 22:51
vikasp99 wrote:
Four different prime numbers, each less than 20, are multiplied together. What is the greatest possible result?
○A○ 21,879
○B○ 28,728
○C○ 40,755
○D○ 46,189
○E○ 49,742

Prime numbers less than 20 are {2,3,5,7,11,13,17,19}

Biggest required product = 11*13*17*19=46189

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Four different prime numbers, each less than 20, are multiplied togeth  [#permalink]

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23 Feb 2017, 23:05
1
vikasp99 wrote:
Four different prime numbers, each less than 20, are multiplied together. What is the greatest possible result?
○A○ 21,879
○B○ 28,728
○C○ 40,755
○D○ 46,189
○E○ 49,742

To get the greatest possible result, we must consider prime numbers 19, 17, 13 and 11.
The product of the units digit of each of the above numbers => 9*7*3*1 will result in a number with 9 at its unit digit (Only A and D are possible options)
Use approximation to get 19*17*13*11 => 20*20*10*10 = 40000 (D is close enough)

Hence option D is correct
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Re: Four different prime numbers, each less than 20, are multiplied togeth  [#permalink]

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26 Feb 2017, 12:59
2
Hi All,

This question is built around several Number Properties - and the answer choices are 'spread out' enough that you don't really have to do a lot of 'heavy math' to get to the correct answer.

To start, we have to identify the 4 largest PRIMES that are less than 20. They are: 19, 17, 13 and 11.

Next, notice how they are all ODD integers. When we take the product of 4 odd numbers, we end up with an ODD number. Eliminate Answers B and E. Since none of the 4 primes ends in a '5', the product will NOT end in a '5' - so we can eliminate Answer C.

There is such a big difference in the two remaining answers (21,879 and 46,189) that we can estimate the product. Let's 'round up' the 19 and 17 to 20 and 20. Let's 'round down' the 13 and 11 to 10 and 10. This gives us....

(20(20)(10)(10) = (400)(100) = 40,000

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Re: Four different prime numbers, each less than 20, are multiplied togeth  [#permalink]

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03 Apr 2017, 05:54
Great way to solve Rich!
I solved it by a rather conventional method:
To maximize the product, take the bigger nos. (prime nos.)
11,13,17,19
Their product is 46189.
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Re: Four different prime numbers, each less than 20, are multiplied togeth  [#permalink]

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09 Jan 2019, 11:37
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Re: Four different prime numbers, each less than 20, are multiplied togeth   [#permalink] 09 Jan 2019, 11:37
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