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# If x and y are two-digit integers such that x > 40 and y < 70, which

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Re: If x and y are two-digit integers such that x > 40 and y < 70, which [#permalink]
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for xy to be maximum, x and y must each have the largest possible value.
We know that x > 40 and y < 70.
Greatest possible 2 digit integer such that it is greater than 40 is 99, hence x = 99
Greatest possible 2 digit integer such that it is less than 70 is 69, hence x = 69
Therefore the maximum possible value of xy = 99*69 = 6831 which is closest to option D
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Re: If x and y are two-digit integers such that x > 40 and y < 70, which [#permalink]
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Bunuel wrote:
If x and y are two-digit integers such that x > 40 and y < 70, which of the following is closest to the maximum possible value of xy ?

(A) 700
(B) 2,800
(C) 4,000
(D) 7,000
(E) 28,000

PS21237

To maximize the value of xy we need to maximize the value of x and y.

Since both x and y are two-digit integers, let $$x = 99$$.

Since $$y < 70$$, let $$y = 69$$.

Since the answers are fairly spread apart, we can use $$100 * 70 = 7,000$$.

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Re: If x and y are two-digit integers such that x > 40 and y < 70, which [#permalink]

Solution

Given
In this question, we are given that
• The numbers x and y are two-digit integers such that x > 40 and y < 70

To find
We need to determine
• Among the given options, which one is the closest to the maximum value of xy

Approach and Working out
In order to maximize the value of x and y, we should consider individual maximum values of x and y respectively.
• As x > 40 and a 2-digit number, maximum value of x = 99
• As y < 70, maximum value of y = 69
• Hence, maximum value of xy = 99 * 69 = approx. 100 * 70 = 7000

Thus, option D is the correct answer.

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Re: If x and y are two-digit integers such that x > 40 and y < 70, which [#permalink]
Hi, shouldn't the maximum value be less than 7000 so it meets the condition?
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Re: If x and y are two-digit integers such that x > 40 and y < 70, which [#permalink]
Closest maximum value for (x) (y), x > 40 whereas y < 70. This is a trick question, it leads you to believe that to x must be slightly more than 40, in actual fact, the main clue is: both (x) and (y) are two digits integers. Thus, assume the maximum value of (x) = 99 approx. = 100 and (y) = 69 approx. = 70.

(x) (y) = 7,000

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Re: If x and y are two-digit integers such that x > 40 and y < 70, which [#permalink]
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Re: If x and y are two-digit integers such that x > 40 and y < 70, which [#permalink]
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