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If the product of 5 different positive integers is less than

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If the product of 5 different positive integers is less than

by Max@Math Revolution » Wed Jun 20, 2018 12:35 am

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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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by GMATGuruNY » Wed Jun 20, 2018 1:58 am
Max@Math Revolution 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.

The correct answer is D.
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by Jeff@TargetTestPrep » Thu Jun 21, 2018 4:15 pm
Max@Math Revolution wrote:
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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by Max@Math Revolution » Thu Jun 21, 2018 11:33 pm
=>
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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