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If x and y are positive integers, and (4x)/(3y) is an integer, which
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04 Jul 2023, 01:30
04 Jul 2023, 01:30
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If x and y are positive integers, and \(\frac{4x}{3y}\) is an integer, which of the following must be true?
I. x is a multiple of 4.
II. y is a multiple of 3.
III. x·y is a multiple of 3.
A. I only
B. II only
C. III only
D. I and II only
E. I, II and III
I. x is a multiple of 4.
II. y is a multiple of 3.
III. x·y is a multiple of 3.
A. I only
B. II only
C. III only
D. I and II only
E. I, II and III
Senior Manager
Joined: 16 Jan 2022
Posts: 250
Given Kudos: 1014
Location: India
GPA: 4
WE:Analyst (Computer Software)
Re: If x and y are positive integers, and (4x)/(3y) is an integer, which
[#permalink]
04 Jul 2023, 05:43
04 Jul 2023, 05:43
1
Kudos
Asked: which of the following must be true?
Given: x and y are integers and \(\frac{4x}{3y}\) = integer.
Solution: The best way to solve a MBT question is to find the values for which the statement is false.
Now we can write 4x/3y = k (Where k is a positive integer) -> 4x = 3y * k -- (1)
I. x is a multiple of 4.
x can be 3 and y can be 4, and we would get an integer. Hence, statement I is not always true.
II. y is a multiple of 3.
Similar to statement I we can use x as 3 and y as 4, we get an integer. Hence, statement II is not always true.
III. xy is a multiple of 3.
Yes, this can be true. We can take the above values of x as 3 and y as 4, and we will get xy as a multiple of 3.
We can check this for other values too, and in each case, we will get a Yes. eg. x can be 9 and y can be 12, and we will get a Yes.
Answer: C.
Given: x and y are integers and \(\frac{4x}{3y}\) = integer.
Solution: The best way to solve a MBT question is to find the values for which the statement is false.
Now we can write 4x/3y = k (Where k is a positive integer) -> 4x = 3y * k -- (1)
I. x is a multiple of 4.
x can be 3 and y can be 4, and we would get an integer. Hence, statement I is not always true.
II. y is a multiple of 3.
Similar to statement I we can use x as 3 and y as 4, we get an integer. Hence, statement II is not always true.
III. xy is a multiple of 3.
Yes, this can be true. We can take the above values of x as 3 and y as 4, and we will get xy as a multiple of 3.
We can check this for other values too, and in each case, we will get a Yes. eg. x can be 9 and y can be 12, and we will get a Yes.
Answer: C.
Manager
Joined: 09 Jun 2020
Posts: 249
Given Kudos: 171
Location: India
GMAT 1: 720 Q50 V36 
GPA: 4
Re: If x and y are positive integers, and (4x)/(3y) is an integer, which
[#permalink]
05 Jul 2023, 01:49
05 Jul 2023, 01:49
Approach : Given, x and y are positive integers, and \(\frac{4x}{3y}\) is also an integer. For any fraction to be integer denominator should divide into numerator such that no remainder is left.
Stmt 1: x is a multiple of 4. If x is a multiple of 4 say 8, even then \(\frac{4x}{3y}\) is not an integer.
Stmt 2: y is a multiple of 3. If y is a multiple of 3 say 6, even then \(\frac{4x}{3y}\) is not an integer.
Stmt 3: x·y is a multiple of 3. If xy = 3k where k an integer.
Then \(\frac{4x}{3y}\) = \(\frac{4 (3k)}{3y^2 }\) and if y = 2 then condition satisfied.
Hence C is the answer.
Stmt 1: x is a multiple of 4. If x is a multiple of 4 say 8, even then \(\frac{4x}{3y}\) is not an integer.
Stmt 2: y is a multiple of 3. If y is a multiple of 3 say 6, even then \(\frac{4x}{3y}\) is not an integer.
Stmt 3: x·y is a multiple of 3. If xy = 3k where k an integer.
Then \(\frac{4x}{3y}\) = \(\frac{4 (3k)}{3y^2 }\) and if y = 2 then condition satisfied.
Hence C is the answer.
Bunuel wrote:
If x and y are positive integers, and \(\frac{4x}{3y}\) is an integer, which of the following must be true?
I. x is a multiple of 4.
II. y is a multiple of 3.
III. x·y is a multiple of 3.
A. I only
B. II only
C. III only
D. I and II only
E. I, II and III
I. x is a multiple of 4.
II. y is a multiple of 3.
III. x·y is a multiple of 3.
A. I only
B. II only
C. III only
D. I and II only
E. I, II and III
