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If the product of 5 different positive integers is less than 200, what

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If the product of 5 different positive integers is less than 200, what  [#permalink]

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New post 20 Jun 2018, 01:48
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[GMAT math practice question]

If the product of 5 different positive integers is less than 200, what is the greatest possible value for the largest of these 5 integers?

A. 3
B. 6
C. 7
D. 8
E. 9

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Re: If the product of 5 different positive integers is less than 200, what  [#permalink]

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New post 20 Jun 2018, 02:44
MathRevolution wrote:
[GMAT math practice question]

If the product of 5 different positive integers is less than 200, what is the greatest possible value for the largest of these 5 integers?

A. 3
B. 6
C. 7
D. 8
E. 9


All 5 are different positive integers, so largest has to be at least 5..
Nearest in choice is 6..
Moreover take the smallest possible value for other 4 so 1*2*3*4=24
The fifth will be <200/24..
100/11=25/3=8+1/3..
Thus the largest will be 8 and value will be
8*1*4*3*2=192<200

D
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Re: If the product of 5 different positive integers is less than 200, what  [#permalink]

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New post 20 Jun 2018, 02:53
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a*b*c*d*e < 200

Let us consider 'e' is largest integer
Since all are positive integers, for 'e' to be largest --> a,b,c,d should be smallest.

Given that all integers different, 4 lowest positive integers are 1,2,3,4

1*2*3*4*e < 200

e < (200/24)

e < 8.33

Since 'e' is highest integer, answer is 8
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Re: If the product of 5 different positive integers is less than 200, what  [#permalink]

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New post 20 Jun 2018, 03:03
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MathRevolution wrote:
[GMAT math practice question]

If the product of 5 different positive integers is less than 200, what is the greatest possible value for the largest of these 5 integers?

A. 3
B. 6
C. 7
D. 8
E. 9

To MAXIMIZE the largest integer, MINIMIZE the other four integers.
Since the integers must be positive and distinct, the smallest possible option for the other four integers is as follows:
1*2*3*4 = 24.
We can PLUG IN THE ANSWERS, which represent the value of the largest integer.
Of the five answer choices -- 3, 6, 7, 8, 9 -- the largest that can be multiplied by 24 to yield a product less than 200 is 8:
24*8 = 192.


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Re: If the product of 5 different positive integers is less than 200, what  [#permalink]

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New post 21 Jun 2018, 17:10
MathRevolution wrote:
[GMAT math practice question]

If the product of 5 different positive integers is less than 200, what is the greatest possible value for the largest of these 5 integers?

A. 3
B. 6
C. 7
D. 8
E. 9


To maximize the largest of the 5 integers, we minimize the values of the smallest 4 integers. Since they are positive and are different from each other, they must be 1, 2, 3, and 4. The product of the first four integers is 1 x 2 x 3 x 4 = 24.

The largest integer that could multiply 24 and produce a product that is less than 200 is 8, since 24 x 8 = 192.

Answer: D
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Re: If the product of 5 different positive integers is less than 200, what  [#permalink]

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New post 22 Jun 2018, 00:45
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The greatest possible value of the largest of the integers occurs when the other integers are as small as possible.
In other words, the other four integers should be \(1,2,3\), and \(4\).

We try different values for the fifth integer:
\(1*2*3*4*5 = 120\)
\(1*2*3*4*6 = 144\)
\(1*2*3*4*7 = 168\)
\(1*2*3*4*8 = 192\)
\(1*2*3*4*9 = 216\)

The largest product that is less than \(200\) occurs when the fifth integer is \(8\).
Thus, the greatest possible value of the largest integer is \(8\).

Therefore, the answer is D.
Answer: D
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Re: If the product of 5 different positive integers is less than 200, what  [#permalink]

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New post 02 Aug 2018, 01:32
This is how i solved it:
take prime factors of 200 = 2^3 * 5^2
look at the given options - you can A,B,C,E because with the prime factors - it s not possible.
So it is 8
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Re: If the product of 5 different positive integers is less than 200, what &nbs [#permalink] 02 Aug 2018, 01:32
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