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21 Feb 2025, 10:33
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C
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84% (02:11) correct
16%
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If x and y are integers such that 5 < |y| < 9 and 4 < |x|< 10, which of the following represents all possible values of xy ?
(A) −90 < xy < 20
(B) −36 < xy < −20 and 36 < xy < 90
(C) −90 < xy < −20 and 20 < xy < 90
(D) −50 < xy < 20 and −20 < xy < 50
(E) −36 < xy < −20 and 20 < xy < 36
Official Answer:
Plug In all possible values for x and y. Because the inequalities in the question stem are absolute values, the representation of all possible values of xy has a negative range and a positive range. The least possible negative value of xy is –90 and the greatest possible negative value is –20, so it can be written that –90 < xy < –20. The least possible positive value of xy is 20 and the greatest possible positive value is 90, so it can be written that 20 < xy < 90. Therefore, the possible values of xy are –90 < xy < –20 and 20 < xy < 90. The correct answer is (C)
(A) −90 < xy < 20
(B) −36 < xy < −20 and 36 < xy < 90
(C) −90 < xy < −20 and 20 < xy < 90
(D) −50 < xy < 20 and −20 < xy < 50
(E) −36 < xy < −20 and 20 < xy < 36
Official Answer:
Plug In all possible values for x and y. Because the inequalities in the question stem are absolute values, the representation of all possible values of xy has a negative range and a positive range. The least possible negative value of xy is –90 and the greatest possible negative value is –20, so it can be written that –90 < xy < –20. The least possible positive value of xy is 20 and the greatest possible positive value is 90, so it can be written that 20 < xy < 90. Therefore, the possible values of xy are –90 < xy < –20 and 20 < xy < 90. The correct answer is (C)
21 Feb 2025, 10:53
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anuragd99
| -9<y<-5 | -10<x<-4 |
| 5<y<9 | 4<x<10 |
From the two inequalities in second row, 20 < xy < 90. Only option C has this case.
Answer C.
21 Feb 2025, 20:04
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We can mutiply the absolute values
Therefore |a|*|b| = |ab|
From 5 < |y| < 9 and 4 < |x|< 10 we get 20<|xy|<90
1) |xy|<90 => -90<xy<90
2) |xy|>20 => xy> 20 or xy<-20
from 3 conditions we can get -90<xy<-20 and 20<xy<90
Therefore |a|*|b| = |ab|
From 5 < |y| < 9 and 4 < |x|< 10 we get 20<|xy|<90
1) |xy|<90 => -90<xy<90
2) |xy|>20 => xy> 20 or xy<-20
from 3 conditions we can get -90<xy<-20 and 20<xy<90
