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31 May 2018, 06:03
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The sum of x and y is at least 2 but no more than 5. If the total of twice x and three times y is non-negative and no more than 40, which of the following expresses all possible values of y?
A. −4 ≤ y ≤ 36
B. −10 ≤ y ≤ 30
C. −10 ≤ y ≤ 36
D. 0 ≤ y ≤ 40
E. 2 ≤ y ≤ 5
A. −4 ≤ y ≤ 36
B. −10 ≤ y ≤ 30
C. −10 ≤ y ≤ 36
D. 0 ≤ y ≤ 40
E. 2 ≤ y ≤ 5
31 May 2018, 06:13
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The sum of x and y is at least 2 but no more than 5.
i.e., 2 ≤ (x + y) ≤ 5
If the total of twice x and three times y is non-negative and no more than 40
i.e., 0 ≤ 2x + 3y ≤ 40 ---- (1)
We have to find possible values of y.
We have range of values for (x + y). With this we can find range of values of 2x + 2y
4 ≤ 2x + 2y ≤ 10
Therefore, range of values for -2x - 2y is obtained by multiplying the entire inequality by -1. Note, the sign of the inequality will change.
-10 ≤ -2x - 2y ≤ -4 ---(2)
Add (1) and (2)
-10 ≤ y ≤ 36
Choice C.
i.e., 2 ≤ (x + y) ≤ 5
If the total of twice x and three times y is non-negative and no more than 40
i.e., 0 ≤ 2x + 3y ≤ 40 ---- (1)
We have to find possible values of y.
We have range of values for (x + y). With this we can find range of values of 2x + 2y
4 ≤ 2x + 2y ≤ 10
Therefore, range of values for -2x - 2y is obtained by multiplying the entire inequality by -1. Note, the sign of the inequality will change.
-10 ≤ -2x - 2y ≤ -4 ---(2)
Add (1) and (2)
-10 ≤ y ≤ 36
Choice C.
General Discussion
01 Jun 2018, 11:19
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Bunuel
The sum of x and y is at least 2 but no more than 5. If the total of twice x and three times y is non-negative and no more than 40, which of the following expresses all possible values of y?
A. −4 ≤ y ≤ 36
B. −10 ≤ y ≤ 30
C. −10 ≤ y ≤ 36
D. 0 ≤ y ≤ 40
E. 2 ≤ y ≤ 5
A. −4 ≤ y ≤ 36
B. −10 ≤ y ≤ 30
C. −10 ≤ y ≤ 36
D. 0 ≤ y ≤ 40
E. 2 ≤ y ≤ 5
We can create the following inequalities:
2 ≤ x + y ≤ 5
0 ≤ 2x + 3y ≤ 40
Multiplying the first inequality by -2, we have:
-4 ≥ -2x - 2y ≥ -10
-10 ≤ -2x - 2y ≤ -4
Adding this to 0 ≤ 2x + 3y ≤ 40, we have:
-10 ≤ y ≤ 36
Answer: C
