If the integer x is divisible by 3 but not by 2, then which one of the : Problem Solving (PS)

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Bunuel

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If the integer x is divisible by 3 but not by 2, then which one of the [#permalink]

Updated on: 19 Oct 2022, 11:26

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If the integer x is divisible by 3 but not by 2, then which one of the following expressions is NEVER an integer?

(A) (x + 1)/2
(B) x/7
(C) x^2/3
(D) x^3/3
(E) x/24

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Originally posted by Bunuel on 13 Jun 2017, 10:54.
Last edited by Bunuel on 19 Oct 2022, 11:26, edited 2 times in total.

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Re: If the integer x is divisible by 3 but not by 2, then which one of the [#permalink]

13 Jun 2017, 11:01

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Bunuel wrote:

If the integer x is divisible by 3 but not by 2, then which one of the following expressions is NEVER an integer?

(A) (x + 1)/2
(B) x/7
(C) x^2/3
(D) x^3/3
(E) x/24

Odd divided by even is never an integer.

Let x = 3
(A) $\frac{(x + 1)}{2} = \frac{(3 + 1)}{2} = \frac{4}{2} = 2$
(B)$\frac{x}{7} = \frac{3}{7}$ ---------- Not integer
(C) $\frac{{x^2}}{3}$ = $\frac{3^2}{3} = \frac{9}{3} = 3$
(D) $\frac{x^3}{3} = \frac{3^3}{3} = \frac{27}{3} = 9$
(E) $\frac{x}{24} = \frac{3}{24} = \frac{1}{8}$ ------------ Not integer

B, C and D eliminated.

Let x = 21
(B) $\frac{x}{7} = \frac{21}{7} = 3$
(E) $\frac{x}{24} = \frac{21}{24} = \frac{7}{8}$ --------- Not integer. Answer E...

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Abhishek009

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Re: If the integer x is divisible by 3 but not by 2, then which one of the [#permalink]

13 Jun 2017, 11:35

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Leo8 wrote:

+ E

If x is not divisible by 2 then it won't be divisible by 24 either

Good observation , for the number to be divisible by 24 we must have the numerator as a multiple of both 2 and 3 , which contradicts the statement -

Quote:

the integer x is divisible by 3 but not by 2

Thus, answer must be (E)
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Re: If the integer x is divisible by 3 but not by 2, then which one of the [#permalink]

18 Jun 2017, 14:08

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E
A) If X is not divisible by 2, it means that it is odd, hence (X+1)/2 is always an integer
B) X/7 could be true if the X is 21, 63, 105...
C) X^2/3 is always an integer 3^2/3=3 9^2/3=27 etc
D) The same logic as in C. 3^3/3=9
E) Will never be an integer as X doesn't contain any even factor(not divisible by 2), while 24 has 3 2s

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m1033512

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Re: If the integer x is divisible by 3 but not by 2, then which one of the [#permalink]

22 Mar 2019, 00:25

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[quote="bharat8484"]what if we take X as 240 for option E.?[/quote]

X can not be 240 as we have to find the value of x which is NOT divisible by 2 .

240 is divisible by 2 , hence x can not take this value . This is the given condtion in question.

award kudos if helpful

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Re: If the integer x is divisible by 3 but not by 2, then which one of the [#permalink]

13 Jun 2017, 11:22

+ E

If x is not divisible by 2 then it won't be divisible by 24 either

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Re: If the integer x is divisible by 3 but not by 2, then which one of the [#permalink]

18 Jun 2017, 04:06

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We are looking for an odd multiple of 3.

Evaluating option 3, just take the example of to be 9

9/24 is not an integer. Hence, E
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Re: If the integer x is divisible by 3 but not by 2, then which one of the [#permalink]

18 Jun 2017, 11:26

IMO, E

In this question you are looking for X divided by some even number (or X+-1 divided by 3)

B, C, D do not have either of these

A) (X+1)/2 -> if our x is divisible by 3 and not 2, then it is odd so (X+-1) is always divisible by 2

E) X/24 -> 24 is even so this is not possible, and thus is our answer

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Re: If the integer x is divisible by 3 but not by 2, then which one of the [#permalink]

21 Jun 2017, 01:53

for this to hold true,
x is an odd multiple of 3

statement 1: x + 1 is even hence divisible by 3 - can be an integer
statement 2: if x is 21, x/7 is an integer
Statement 3: x^2/3 always an integer as x is a multiple of 3, so x^2 is a multiple of 3
Statement 4: same as above, x is a multiple of 3, x^3 is a multiple of 3 hence x^3/3 is an integer

Statement 5- correct answer- not an integer as 24 has two even integers and hence x is odd - CAN NEVER BE AN INTEGER

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Re: If the integer x is divisible by 3 but not by 2, then which one of the [#permalink]

12 Jul 2017, 06:28

Bunuel wrote:

If the integer x is divisible by 3 but not by 2, then which one of the following expressions is NEVER an integer?

(A) (x + 1)/2
(B) x/7
(C) x^2/3
(D) x^3/3
(E) x/24

x is divisible by 3 and not by 2. So x is odd multiple of 3
so, lets get down to choices to check which one is an integer and which is not.

(A) x+1 is even and hence (x+1)/2 = I
(B) x/7 may be an integer or may be not. We can't say anything based on the data available with us.
(C) x^2 must be a multiple of 3. So, x^2/3 = I
(D) x^3 must be a multiple of 3. So, x^3/3 = I
(E) 24 = 2*2*2*3 since x is odd multiple of 3. x is not divisible by 24. Hence x/24 is not integer.

Answer E.

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Re: If the integer x is divisible by 3 but not by 2, then which one of the [#permalink]

16 Jul 2017, 17:17

Expert Reply

Bunuel wrote:

If the integer x is divisible by 3 but not by 2, then which one of the following expressions is NEVER an integer?

(A) (x + 1)/2
(B) x/7
(C) x^2/3
(D) x^3/3
(E) x/24

Because x is divisible by 3 and not 2, x must be an odd multiple of 3, such as 3 or 9.

Since 24 is an even number, x/24 will NEVER be an integer.

Answer: E
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Re: If the integer x is divisible by 3 but not by 2, then which one of the [#permalink]

04 Feb 2019, 08:31

Bunuel wrote:

If the integer x is divisible by 3 but not by 2, then which one of the following expressions is NEVER an integer?

(A) (x + 1)/2
(B) x/7
(C) x^2/3
(D) x^3/3
(E) x/24

x / 3 ! by 2

x = 3 , 9, 15 , 21

x/24, will never give an integer for the present conditions, since it is 12*2 (this goes against the question)

E
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bharat8484

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Re: If the integer x is divisible by 3 but not by 2, then which one of the [#permalink]

21 Mar 2019, 22:59

what if we take X as 240 for option E.?

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Re: If the integer x is divisible by 3 but not by 2, then which one of the [#permalink]

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Re: If the integer x is divisible by 3 but not by 2, then which one of the [#permalink]

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