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If 3 < x < 8 and 5 < y < 11, which of the following represents all the

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Bunuel
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If 3 < x < 8 and 5 < y < 11, which of the following represents all the [#permalink] New post   08 Jun 2018, 11:51
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If 3 < x < 8 and 5 < y < 11, which of the following represents all the possible values of xy?

A. 3 < xy < 11
B. 8 < xy < 19
C. 15 < xy < 88
D. 24 < xy < 55
E. 33 < xy < 40
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C
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Re: If 3 < x < 8 and 5 < y < 11, which of the following represents all the [#permalink] New post   08 Jun 2018, 12:10
Option C:

The ranges of X and Y are given and they are not Integers. So min value of X could be very close to 3 and so does the max. value. And the same rule applies to Y as well.

Multiplying the Min (x,y) and max(x,y) would give the range. 15<xy<88.
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Re: If 3 < x < 8 and 5 < y < 11, which of the following represents all the [#permalink] New post   08 Jun 2018, 12:11
Bunuel wrote:
If 3 < x < 8 and 5 < y < 11, which of the following represents all the possible values of xy?

A. 3 < xy < 11
B. 8 < xy < 19
C. 15 < xy < 88
D. 24 < xy < 55
E. 33 < xy < 40


Given, 3 < x < 8 & 5 < y <11, assuming x & y are integers, we get values for

x = 4,5,6,7
y = 6,7,8,9,10

Now maximum xy = 7 * 10 = 70 & minimum xy = 6 * 4 = 24

Only Answer C, can accommodate these values.

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GyM
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Re: If 3 < x < 8 and 5 < y < 11, which of the following represents all the [#permalink] New post   08 Jun 2018, 12:17
Bunuel wrote:
If 3 < x < 8 and 5 < y < 11, which of the following represents all the possible values of xy?

A. 3 < xy < 11
B. 8 < xy < 19
C. 15 < xy < 88
D. 24 < xy < 55
E. 33 < xy < 40



Max x = 8
Max y = 11
So max value will be 88

lowest value x = 3
lowest value y = 5
lowest value will be 15


Option C reflects that <15xy<88. Thus Option C is the best answer.
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Re: If 3 < x < 8 and 5 < y < 11, which of the following represents all the [#permalink] New post   08 Jun 2018, 12:48
Expert Reply

Solution



Given:
    • 3 < x < 8
    • 5 < y < 11

To find:
    • Out of the given options, which one represents all the possible values of xy

Approach and Working:
In this case, the possible values that define xy can be identified by the extreme possible values of x and y

To find the minimum value:
    • As x > 3, we can assume the value of x is very close to 3, or almost equal to 3
    • Similarly, as y > 5, we can assume the value of y is very close to 5, or almost equal to 5
    • Therefore, the value of xy should be greater than 3 *5
      o Or, xy > 15

To find the maximum value:
    • As x < 8, we can assume the value of x is very close to 8, or almost equal to 8
    • Similarly, as y < 11, we can assume the value of y is very close to 11, or almost equal to 11
    • Therefore, the value of xy should be less than 8 * 11
      Or, xy < 88

Hence, the correct answer is option C.

Answer: C
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Re: If 3 < x < 8 and 5 < y < 11, which of the following represents all the [#permalink] New post   08 Jun 2018, 12:51
Bunuel wrote:
If 3 < x < 8 and 5 < y < 11, which of the following represents all the possible values of xy?

A. 3 < xy < 11
B. 8 < xy < 19
C. 15 < xy < 88
D. 24 < xy < 55
E. 33 < xy < 40


The minimum value range for xy is when x = 3 and y = 5. Here, xy will be 15.
The maximum value range of xy is when x = 8 and y = 11. Here, xy will be 88.

Therefore, the range which represents all possible value of xy is 15 < xy < 88(Option C)
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Re: If 3 < x < 8 and 5 < y < 11, which of the following represents all the [#permalink] New post   08 Jun 2018, 19:04
Bunuel wrote:
If 3 < x < 8 and 5 < y < 11, which of the following represents all the possible values of xy?

A. 3 < xy < 11
B. 8 < xy < 19
C. 15 < xy < 88
D. 24 < xy < 55
E. 33 < xy < 40


Given, 3 < x < 8----------(1) & 5 < y < 11------------(2)

Multiplying (1) & (2), we have

15 < xy < 88

Ans. option (C)
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Re: If 3 < x < 8 and 5 < y < 11, which of the following represents all the [#permalink]
08 Jun 2018, 19:04
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