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QOTD#17 If x is divisible by 78, which of the following must
[#permalink]
22 Nov 2016, 16:41

Expert Reply

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Question Stats:

If x is divisible by 78, which of the following must be divisible by x?

Indicate all possible values.

A. \(\frac{x}{78}\)

B. \(x\)

C. \(x+78\)

D. \(78-x\)

E. \(78x\)

F. \(78x+78\)

_________________

Indicate all possible values.

A. \(\frac{x}{78}\)

B. \(x\)

C. \(x+78\)

D. \(78-x\)

E. \(78x\)

F. \(78x+78\)

Drill 4

Question: 12

Page: 295

Question: 12

Page: 295

_________________

Sandy

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Re: QOTD#17 If x is divisible by 78, which of the following must
[#permalink]
12 Jun 2017, 09:06

5

sandy wrote:

Explanation

There are variables in the answer choices, so Plug In. Try x = 78. You can eliminate choices (A) and (D). Now try a weird number: 0. Eliminate choice (G). Try one more number: 156, which is double 78. This time you can eliminate choices (C) and (E). A number is divisible by itself and a multiple of a number is divisible by that number, so the correct answers are choices (B) and (F).

Hence options B and F are correct.

There are variables in the answer choices, so Plug In. Try x = 78. You can eliminate choices (A) and (D). Now try a weird number: 0. Eliminate choice (G). Try one more number: 156, which is double 78. This time you can eliminate choices (C) and (E). A number is divisible by itself and a multiple of a number is divisible by that number, so the correct answers are choices (B) and (F).

Hence options B and F are correct.

Your solution is Incorrect.

Let me explain this ==>

Here question is asking us => "Which of the following is divisible by x"

Option 1) x/78 => Let x=78 => x/78 = 1 and 1 is not divisible by 78 => REJECT.

Option 2) x/x =1 => Accept

Option 3) (x+78)/x => 1+(78/x) => Is x= 78 => OK else if x=78*2 => Not OK => REJECT.

Option 4) (78-x)/x => 78/x - 1 => If x=78 => OK else if x=78*2 => Not OK => REJECT.

Option 5) 78x/x => 78 => ALWAYS an integer.=> ACCEPT

(You cannot plus in x as zero as division by zero is considered to be illegal on the GRE. You can take any value of x => and this will always be 78 which is an integer)

Option 6) (78x +78)/x => 78 + 78/x => If x = 78 => OK else if x=78*2 = Not OK => REJECT.

Hence the Correct answer choices must be B and E

Smash that B and E

Regards

Stone Cold

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Re: QOTD#17 If x is divisible by 78, which of the following must
[#permalink]
22 Nov 2016, 16:44

Expert Reply

Explanation

There are variables in the answer choices, so Plug In. Try x = 78. You can eliminate choices (A) and (D). Now try a weird number: 0. Eliminate choice (G). Try one more number: 156, which is double 78. This time you can eliminate choices (C) and (E). A number is divisible by itself and a multiple of a number is divisible by that number, so the correct answers are choices (B) and (F).

Hence options B and F are correct.

_________________

Sandy

If you found this post useful, please let me know by pressing the Kudos Button

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There are variables in the answer choices, so Plug In. Try x = 78. You can eliminate choices (A) and (D). Now try a weird number: 0. Eliminate choice (G). Try one more number: 156, which is double 78. This time you can eliminate choices (C) and (E). A number is divisible by itself and a multiple of a number is divisible by that number, so the correct answers are choices (B) and (F).

Hence options B and F are correct.

_________________

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Re: QOTD#17 If x is divisible by 78, which of the following must
[#permalink]
13 Dec 2016, 07:04

Why (E) can't be an answer?

Re: QOTD#17 If x is divisible by 78, which of the following must
[#permalink]
15 Jan 2017, 04:32

Hi Sandy, can you give me a detailed working for the above question.. Thanks

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Re: QOTD#17 If x is divisible by 78, which of the following must
[#permalink]
15 Jan 2017, 15:31

Expert Reply

shikha0611 wrote:

Hi Sandy, can you give me a detailed working for the above question.. Thanks

Again plugging is the best strategy for these questions. We plug 78 and 0 as values of x.

Regards,

_________________

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QOTD#17 If x is divisible by 78, which of the following must
[#permalink]
17 Apr 2021, 00:09

1

sandy wrote:

If x is divisible by 78, which of the following must be divisible by x?

Indicate all possible values.

A. \(\frac{x}{78}\)

B. \(x\)

C. \(x+78\)

D. \(78-x\)

E. \(78x\)

F. \(78x+78\)

Indicate all possible values.

A. \(\frac{x}{78}\)

B. \(x\)

C. \(x+78\)

D. \(78-x\)

E. \(78x\)

F. \(78x+78\)

sandy

I think it must be B and E only

Here is why:

If \(x\) is divisible by \(78\) then \(x\) must have all the factors of \(78\) i.e. \(2, 3\) and \(13\)

Let \(x = 78a = (1)(3)(13)a\)

A. \(\frac{x}{78x} = \frac{1}{78}\) - NO

B. \(\frac{x}{x} = 1\) - YES

C. \(\frac{(x+78)}{x} = \frac{(78a + 78)}{78a} = \frac{(a + 1)}{a}\) - NO

D. \(\frac{(78 - x)}{x} = \frac{(78 - 78a)}{78a} = \frac{(1 - a)}{a}\) - NO

E. \(\frac{78x}{x} = 78\) - YES

F. \(\frac{(78x+78)}{x} = \frac{78(x + 1)}{78a} = \frac{(x + 1)}{a}\) - NO

Hence, option B and E

_________________

I hope this helps!

Regards:

Karun Mendiratta

Founder and Quant Trainer

Prepster Education, Delhi, India

https://www.instagram.com/prepster_education/

Regards:

Karun Mendiratta

Founder and Quant Trainer

Prepster Education, Delhi, India

https://www.instagram.com/prepster_education/

Re: QOTD#17 If x is divisible by 78, which of the following must
[#permalink]
17 Apr 2021, 00:38

Expert Reply

KarunMendiratta wrote:

sandy wrote:

If x is divisible by 78, which of the following must be divisible by x?

Indicate all possible values.

A. \(\frac{x}{78}\)

B. \(x\)

C. \(x+78\)

D. \(78-x\)

E. \(78x\)

F. \(78x+78\)

Indicate all possible values.

A. \(\frac{x}{78}\)

B. \(x\)

C. \(x+78\)

D. \(78-x\)

E. \(78x\)

F. \(78x+78\)

sandy

I think it must be B and E only

Here is why:

If \(x\) is divisible by \(78\) then \(x\) must have all the factors of \(78\) i.e. \(2, 3\) and \(13\)

Let \(x = 78a = (1)(3)(13)a\)

A. \(\frac{x}{78x} = \frac{1}{78}\) - NO

B. \(\frac{x}{x} = 1\) - YES

C. \(\frac{(x+78)}{x} = \frac{(78a + 78)}{78a} = \frac{(a + 1)}{a}\) - NO

D. \(\frac{(78 - x)}{x} = \frac{(78 - 78a)}{78a} = \frac{(1 - a)}{a}\) - NO

E. \(\frac{78x}{x} = 78\) - YES

F. \(\frac{(78x+78)}{x} = \frac{78(x + 1)}{78a} = \frac{(x + 1)}{a}\) - NO

Hence, option B and E

Princeton has a lot of mistakes

Sandy is no longer among us. Only Carcass and GreenlightTestPrep

_________________

Re: QOTD#17 If x is divisible by 78, which of the following must
[#permalink]
16 Aug 2023, 03:11

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