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If a, b, and c are different constants, how many different numbers y
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02 May 2024, 01:30
02 May 2024, 01:30
1
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Expert Reply
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A
B
C
D
E
Difficulty:
85%
(hard)
Question Stats:
29% (00:52) correct
71%
(00:59)
wrong
based on 136
sessions
If \(a\), \(b\), and \(c\) are different constants, how many different numbers \(y\) are there such that \(a*y + b = c\)?
A. 0
B. 1
C. 2
D. Infinitely many
E. Cannot be determined from the given information
A. 0
B. 1
C. 2
D. Infinitely many
E. Cannot be determined from the given information
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Re: If a, b, and c are different constants, how many different numbers y
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05 May 2024, 22:30
05 May 2024, 22:30
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Expert Reply
Official Solution:
If \(a\), \(b\), and \(c\) are different constants, how many different numbers \(y\) are there such that \(a*y + b = c\)?
A. 0
B. 1
C. 2
D. Infinitely many
E. Cannot be determined from the given information
Given \(c\) and \(b\) are different numbers, then \(c - b \neq 0\), this means \(a*y = c - b = some \ nonzero \ number\).
If \(a = 0\), then no value of \(y\) can satisfy this equation, as \(0*y = nonzero \ number\) has no solutions for \(y\).
If \(a \neq 0\), then only 1 value of \(y\) can satisfy this equation, since in this case \(y = \frac{c - b}{a}\).
Therefore, there is either one solution or no solution, depending on the value of \(a\).
Answer: E
If \(a\), \(b\), and \(c\) are different constants, how many different numbers \(y\) are there such that \(a*y + b = c\)?
A. 0
B. 1
C. 2
D. Infinitely many
E. Cannot be determined from the given information
Given \(c\) and \(b\) are different numbers, then \(c - b \neq 0\), this means \(a*y = c - b = some \ nonzero \ number\).
If \(a = 0\), then no value of \(y\) can satisfy this equation, as \(0*y = nonzero \ number\) has no solutions for \(y\).
If \(a \neq 0\), then only 1 value of \(y\) can satisfy this equation, since in this case \(y = \frac{c - b}{a}\).
Therefore, there is either one solution or no solution, depending on the value of \(a\).
Answer: E
General Discussion
Joined: 25 Oct 2017
Posts: 153
Given Kudos: 717
GMAT Focus 1:
655 Q87 V80 DI80
655 Q87 V80 DI80
GMAT 1: 690 Q49 V35
Re: If a, b, and c are different constants, how many different numbers y
[#permalink]
02 May 2024, 07:00
02 May 2024, 07:00
2
Kudos
If a ≠ 0, then y will have only one value.
But, if a = 0 then y can have infinitely many values.
Cannot be determined with given info. Option E
But, if a = 0 then y can have infinitely many values.
Cannot be determined with given info. Option E
