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If b, c and d are even integers, and Y is an odd integer, wh
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10 Mar 2020, 05:34
10 Mar 2020, 05:34
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If \(b\), \(c\) and \(d\) are even integers, and \(Y\) is an odd integer, which of the following CANNOT be true?
A) \(\frac{b}{cd} = Y\)
B) \((\frac{b}{c})(d) = Y\)
C) \(\frac{b + c}{d} = Y\)
D) \(\frac{Y – b}{c} = d\)
E) \(\frac{b + c + d}{2} = Y\)
Let's eliminate answer choices that COULD be true.
A) \(\frac{12}{(2)(2)} = 3\). ELIMINATE A
B) \((\frac{2}{4})(6) = 3\). ELIMINATE B
C) \(\frac{2 + 4}{2} = 3\). ELIMINATE C
D) \(\frac{Y – b}{c} = d\)
E) \(\frac{2 + 2 + 2}{2} = 3\). ELIMINATE E
By the process of elimination, the correct answer must be D
ASIDE: Here's why answer choice D is correct
If Y is ODD and b is EVEN, then Y - b = ODD - EVEN = ODD
So, (Y – b)/c = d becomes ODD/c = d
Multiply both sides by c to get: ODD = cd
Since c and d are both EVEN, we get: ODD = (EVEN)(EVEN), which can never be true
Answer: D
Cheers,
Brent
A) \(\frac{b}{cd} = Y\)
B) \((\frac{b}{c})(d) = Y\)
C) \(\frac{b + c}{d} = Y\)
D) \(\frac{Y – b}{c} = d\)
E) \(\frac{b + c + d}{2} = Y\)
Let's eliminate answer choices that COULD be true.
A) \(\frac{12}{(2)(2)} = 3\). ELIMINATE A
B) \((\frac{2}{4})(6) = 3\). ELIMINATE B
C) \(\frac{2 + 4}{2} = 3\). ELIMINATE C
D) \(\frac{Y – b}{c} = d\)
E) \(\frac{2 + 2 + 2}{2} = 3\). ELIMINATE E
By the process of elimination, the correct answer must be D
ASIDE: Here's why answer choice D is correct
If Y is ODD and b is EVEN, then Y - b = ODD - EVEN = ODD
So, (Y – b)/c = d becomes ODD/c = d
Multiply both sides by c to get: ODD = cd
Since c and d are both EVEN, we get: ODD = (EVEN)(EVEN), which can never be true
Answer: D
Cheers,
Brent
Re: If b, c and d are even integers, and Y is an odd integer, wh
[#permalink]
10 Mar 2020, 11:01
10 Mar 2020, 11:01
There are certain rules that we need to remember.
1. Anything multiplied by Even is even.
2. Even + Even = Even
3. \(\frac{Even}{Even}\) = Even or Odd. For example, \(\frac{6}{2} = 3\) and \(\frac{4}{2} = 2\)
Now, let's see the options.
Option A: \(\frac{b}{cd} = Y\)
Assuming value of b = 12 and c = d = 2, we get \(\frac{12}{2 \times 2} = 3\)
Option B: \((\frac{b}{c})(d) = Y\)
This is a tricky option as one might think that \(\frac{Even}{Even}\) can be Even or Odd and when it is multiplied by Even, it will always result in Even.
Let's disprove this!
Assume value of b = 6 and c = 4 and d = 2, we get \(\frac{6}{4 } \times 2 = 3\)
Option B can be true.
Option C: \(\frac{b + c}{d} = Y\)
B+C = even + even = even. Now as we have seen in option A, \(\frac{Even}{Even}\) can be odd. So, this option is also possible.
Option D: \(\frac{Y – b}{c} = d\)
Rearranging the terms, we get \(Y = cd + b\)
Now, cd = even \(\times\) even = even and B = even. So, EVEN + EVEN can never be ODD. Option D CANNOT be true.
Option E: \(\frac{b + c + d}{2} = Y\)
B + C + D = even + even + even = even
Now \(\frac{Even}{2}\) can be ODD.
OA, D
1. Anything multiplied by Even is even.
2. Even + Even = Even
3. \(\frac{Even}{Even}\) = Even or Odd. For example, \(\frac{6}{2} = 3\) and \(\frac{4}{2} = 2\)
Now, let's see the options.
Option A: \(\frac{b}{cd} = Y\)
Assuming value of b = 12 and c = d = 2, we get \(\frac{12}{2 \times 2} = 3\)
Option B: \((\frac{b}{c})(d) = Y\)
This is a tricky option as one might think that \(\frac{Even}{Even}\) can be Even or Odd and when it is multiplied by Even, it will always result in Even.
Let's disprove this!
Assume value of b = 6 and c = 4 and d = 2, we get \(\frac{6}{4 } \times 2 = 3\)
Option B can be true.
Option C: \(\frac{b + c}{d} = Y\)
B+C = even + even = even. Now as we have seen in option A, \(\frac{Even}{Even}\) can be odd. So, this option is also possible.
Option D: \(\frac{Y – b}{c} = d\)
Rearranging the terms, we get \(Y = cd + b\)
Now, cd = even \(\times\) even = even and B = even. So, EVEN + EVEN can never be ODD. Option D CANNOT be true.
Option E: \(\frac{b + c + d}{2} = Y\)
B + C + D = even + even + even = even
Now \(\frac{Even}{2}\) can be ODD.
OA, D
GreenlightTestPrep wrote:
If \(b\), \(c\) and \(d\) are even integers, and \(Y\) is an odd integer, which of the following CANNOT be true?
A) \(\frac{b}{cd} = Y\)
B) \((\frac{b}{c})(d) = Y\)
C) \(\frac{b + c}{d} = Y\)
D) \(\frac{Y – b}{c} = d\)
E) \(\frac{b + c + d}{2} = Y\)
A) \(\frac{b}{cd} = Y\)
B) \((\frac{b}{c})(d) = Y\)
C) \(\frac{b + c}{d} = Y\)
D) \(\frac{Y – b}{c} = d\)
E) \(\frac{b + c + d}{2} = Y\)
Re: If b, c and d are even integers, and Y is an odd integer, wh
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23 Jul 2023, 09:39
23 Jul 2023, 09:39
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
