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x and y are integers such that 8 w x w 10 and x + y = 4. Which of
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19 Sep 2024, 01:25
19 Sep 2024, 01:25
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52% (01:51) correct
48% (01:50) wrong based on 25 sessions
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x and y are integers such that \(–8 \leq x \leq 10\) and \(x + y = –4\). Which of the following can be the values of xy?
A. xy = 0
B. xy = –9
C. xy = 9
D. x=1/y
E. xy=130
A. xy = 0
B. xy = –9
C. xy = 9
D. x=1/y
E. xy=130
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Re: x and y are integers such that 8 w x w 10 and x + y = 4. Which of
[#permalink]
12 Dec 2024, 01:23
12 Dec 2024, 01:23
Expert Reply
We know $\(x\)$ and $\(y\)$ are integers such that $\(-8 \leq x \leq 10 \& x+y=-4\)$; we need to check from the options that which can be the value of the product $\(x y\)$.
From the options we would need $\(-8 \leq x \leq 10 \& x+y=-4\)$
A) $\(x y=0-\)$ which can be true for $\(x=0\)$ and $\(y=-4\)$ or for $\(x=-4\)$ and $\(y=0\)$.
B) $\(x y=-9\)$ - which cannot be the product of $\(x\)$ and $\(y\)$ as $\(-9=(-1 \times 9) /(-3 \times 3)\)$ cannot be the ralues of $\(x\)$ and $\(y\)$ as the sum of $\(x\)$ and $\(y\)$ needs to be -4 .
C) $\(x y=9\)$ - which cannot be the product of $\(x\)$ and $\(y\)$ as $\(9=(1 \times 9) /(3 \times 3) /(-1 \times-9) /(-3 \times-3)\)$ cannot be the values of $\(x\)$ and $\(y\)$ as the sum of $\(x\)$ and $y$ needs to be -4
D) $\(x=\frac{1}{y} \Rightarrow x y=1-\)$ which cannot be the product of $\(x\)$ and $\(y\)$ as $\(1=(1 \times 1) /(-1 \times-1)\)$ cannot be he values of $\(x\)$ and $\(y\)$ as $\(x+y=-4\)$
E) $\(x y=130\)$ - which cannot be the product of $\(x\)$ and $\(y\)$ as $\(130=(10 \times 13) /(-26 \times-5) /(-10 \times-13) /(26 \times 5)\)$ etc cannot be the values of $\(x\)$ and $\(y\)$ as the um of $\(x\)$ and $\(y\)$ needs to be - 4
Note: - Since a single answer is needed for this question, we do not need to check the remaining ptions once we get the correct answer.
From the options we would need $\(-8 \leq x \leq 10 \& x+y=-4\)$
A) $\(x y=0-\)$ which can be true for $\(x=0\)$ and $\(y=-4\)$ or for $\(x=-4\)$ and $\(y=0\)$.
B) $\(x y=-9\)$ - which cannot be the product of $\(x\)$ and $\(y\)$ as $\(-9=(-1 \times 9) /(-3 \times 3)\)$ cannot be the ralues of $\(x\)$ and $\(y\)$ as the sum of $\(x\)$ and $\(y\)$ needs to be -4 .
C) $\(x y=9\)$ - which cannot be the product of $\(x\)$ and $\(y\)$ as $\(9=(1 \times 9) /(3 \times 3) /(-1 \times-9) /(-3 \times-3)\)$ cannot be the values of $\(x\)$ and $\(y\)$ as the sum of $\(x\)$ and $y$ needs to be -4
D) $\(x=\frac{1}{y} \Rightarrow x y=1-\)$ which cannot be the product of $\(x\)$ and $\(y\)$ as $\(1=(1 \times 1) /(-1 \times-1)\)$ cannot be he values of $\(x\)$ and $\(y\)$ as $\(x+y=-4\)$
E) $\(x y=130\)$ - which cannot be the product of $\(x\)$ and $\(y\)$ as $\(130=(10 \times 13) /(-26 \times-5) /(-10 \times-13) /(26 \times 5)\)$ etc cannot be the values of $\(x\)$ and $\(y\)$ as the um of $\(x\)$ and $\(y\)$ needs to be - 4
Note: - Since a single answer is needed for this question, we do not need to check the remaining ptions once we get the correct answer.
gmatclubot
Re: x and y are integers such that 8 w x w 10 and x + y = 4. Which of [#permalink]
12 Dec 2024, 01:23
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