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If x and y are integers and x + xy + y = 5, which of the following cou
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17 Apr 2023, 01:37
17 Apr 2023, 01:37
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If x and y are integers and x + xy + y = 5, which of the following could be the value of the product of x and y?
Indicate all that apply
–14
–2
0
2
12
Indicate all that apply
–14
–2
0
2
12
Re: If x and y are integers and x + xy + y = 5, which of the following cou
[#permalink]
26 May 2023, 22:45
26 May 2023, 22:45
Expert Reply
OE
It is given that 𝑥 and 𝑦 are integers such that 𝑥 + 𝑥𝑦 + 𝑦 = 5. (eqn.1)
We have to find the possible values of 𝑥𝑦.
Since the answer choices represents the possible values of 𝑥𝑦, so let us check if they
are satisfying the given conditions,
A. -14
If 𝑥𝑦 = −14 then equation 1 reduces to 𝑥 + 𝑦 − 14 = 5 i.e. 𝑥 + 𝑦 = 19
We don’t have integers which will give a sum 19 and the product -14 as the factors
of -14 are 1, -1, 2, -2, 7, -7, 14 and -14. Hence, A is not the answer.
B. -2
If 𝑥𝑦 = −2 then equation 1 reduces to 𝑥 + 𝑦 − 2 = 5 i.e. 𝑥 + 𝑦 = 7
We don’t have integers which will give a sum 7 and the product -2 as the factors of -2 are 1, -1, 2 and -2. Hence, B is not the answer.
C. 0
If 𝑥𝑦 = 0 then equation 1 reduces to 𝑥 + 𝑦 + 0 = 5 i.e. 𝑥 + 𝑦 = 5
We need integers which will give a sum 5 and the product 0 i.e. 𝑥 and 𝑦 are 0 and 5.
Hence, C is the answer.
D. 2
If 𝑥𝑦 = 2 then equation 1 reduces to 𝑥 + 𝑦 + 2 = 5 i.e. 𝑥 + 𝑦 = 3
We need integers which will give a sum 3 and the product 2 i.e. 𝑥 and 𝑦 are 1 and 2.
Hence, D is the answer.
E. 12
If 𝑥𝑦 = 12 then equation 1 reduces to 𝑥 + 𝑦 + 12 = 5 i.e. 𝑥 + 𝑦 = −7
We need integers which will give a sum -7 and the product 12 i.e. 𝑥 and 𝑦 are -3 and -4.
Hence, E is the answer.
Ans. (C, D, E)
It is given that 𝑥 and 𝑦 are integers such that 𝑥 + 𝑥𝑦 + 𝑦 = 5. (eqn.1)
We have to find the possible values of 𝑥𝑦.
Since the answer choices represents the possible values of 𝑥𝑦, so let us check if they
are satisfying the given conditions,
A. -14
If 𝑥𝑦 = −14 then equation 1 reduces to 𝑥 + 𝑦 − 14 = 5 i.e. 𝑥 + 𝑦 = 19
We don’t have integers which will give a sum 19 and the product -14 as the factors
of -14 are 1, -1, 2, -2, 7, -7, 14 and -14. Hence, A is not the answer.
B. -2
If 𝑥𝑦 = −2 then equation 1 reduces to 𝑥 + 𝑦 − 2 = 5 i.e. 𝑥 + 𝑦 = 7
We don’t have integers which will give a sum 7 and the product -2 as the factors of -2 are 1, -1, 2 and -2. Hence, B is not the answer.
C. 0
If 𝑥𝑦 = 0 then equation 1 reduces to 𝑥 + 𝑦 + 0 = 5 i.e. 𝑥 + 𝑦 = 5
We need integers which will give a sum 5 and the product 0 i.e. 𝑥 and 𝑦 are 0 and 5.
Hence, C is the answer.
D. 2
If 𝑥𝑦 = 2 then equation 1 reduces to 𝑥 + 𝑦 + 2 = 5 i.e. 𝑥 + 𝑦 = 3
We need integers which will give a sum 3 and the product 2 i.e. 𝑥 and 𝑦 are 1 and 2.
Hence, D is the answer.
E. 12
If 𝑥𝑦 = 12 then equation 1 reduces to 𝑥 + 𝑦 + 12 = 5 i.e. 𝑥 + 𝑦 = −7
We need integers which will give a sum -7 and the product 12 i.e. 𝑥 and 𝑦 are -3 and -4.
Hence, E is the answer.
Ans. (C, D, E)
gmatclubot
Re: If x and y are integers and x + xy + y = 5, which of the following cou [#permalink]
26 May 2023, 22:45
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