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The square of an even number equals 6 less than 5 times the number. Wh

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The square of an even number equals 6 less than 5 times the number. Wh  [#permalink]

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New post Updated on: 30 Dec 2017, 00:02
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The square of an even number equals 6 less than 5 times the number. Which of the following is the square of the number?

A) 2

B) 3

C) 4

D) 6

E) 9

Originally posted by fc2262a on 29 Dec 2017, 16:14.
Last edited by Bunuel on 30 Dec 2017, 00:02, edited 2 times in total.
Renamed the topic.
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Re: The square of an even number equals 6 less than 5 times the number. Wh  [#permalink]

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New post 29 Dec 2017, 18:43
fc2262a , Please read carefully, and follow, our Rules for Posting, here. Thanks.
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Re: The square of an even number equals 6 less than 5 times the number. Wh  [#permalink]

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New post 29 Dec 2017, 19:23
fc2262a wrote:
The square of an even number equals 6 less than 5 times the number. Which of the following is the square of the number?

A) 2 B) 3 C) 4 D) 6 E) 9



Follow rules as applicable here..

As for your question, choices itself give out answer..
You are looking for square of even number as ANSWER
Only 4 fits in
D

Algebraically..
Number=n
\(n^2=5n-6.....n^2-5n+6=0....n^2-3n-2n+6=0.....(n-2)(n-3)=0\)
So n can be 2 or 3, but it is even so 2
Square of 2=4
D
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Re: The square of an even number equals 6 less than 5 times the number. Wh  [#permalink]

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New post Updated on: 30 Dec 2017, 00:02
fc2262a wrote:
The square of an even number equals 6 less than 5 times the number. Which of the following is the square of the number?

A) 2

B) 3

C) 4

D) 6

E) 9



There are two methods of solving this question. Let me talk about the quick one first and then I will talk about the usual approach to solve this question.

Method 1:



We are asked to find the square of the number.

We also know from the question stem that the given "number" is an even number.

If the "number" is even, then the square of the number will also be "even" (keep in mind, we need to find this square).

Look at the answer options, we have only one number, which is even as well as square of number and that is 4.

Thus, the correct answer is Option C. :)


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Originally posted by EgmatQuantExpert on 29 Dec 2017, 23:57.
Last edited by EgmatQuantExpert on 30 Dec 2017, 00:02, edited 1 time in total.
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Re: The square of an even number equals 6 less than 5 times the number. Wh  [#permalink]

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New post 30 Dec 2017, 00:01
fc2262a wrote:
The square of an even number equals 6 less than 5 times the number. Which of the following is the square of the number?

A) 2

B) 3

C) 4

D) 6

E) 9


Method 2 :



The methodical way to solve this question would be assume the given number to be "\(x\)".

Keep in mind that we need to find "\(x^2\)"

Approach:

According to the question stem :

\(x^2 = 5x - 6\)
\(x^2 - 5x + 6 = 0\)
\(x^2 - 3x - 2x + 6 = 0\)
\((x-3) (x-2) = 0\)

Since it is given that \(x\) is an even number, we can discard \(x = 3\) and conclude that the given number has to be \(2\).

Since we need to find the square of the number, the correct answer should be \(x^2 = 2^2 = 4\).

Correct Option : C


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Re: The square of an even number equals 6 less than 5 times the number. Wh  [#permalink]

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New post 20 Jan 2018, 22:22
N^2 = 5N - 6
N^2 - 5N + 6 = 0
(N - 3)(N - 2) = 0
N can be 3, or 2

But the question says N is an even number. Hence, N has to be 2.
The square of 2 is 4. Thus Option C is the correct answer.
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Re: The square of an even number equals 6 less than 5 times the number. Wh  [#permalink]

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New post 21 Jan 2018, 08:06
fc2262a wrote:
The square of an even number equals 6 less than 5 times the number. Which of the following is the square of the number?

A) 2

B) 3

C) 4

D) 6

E) 9



this wording is very confusing for me, "The square of an even number equals 6 less than 5 times the number." so I understand it like this --- the square of an even number equals 6 and this square number is less than 5*6 = 30 meaning X is 6. sqrt root of 36 is 6

can anyone explain why I think so :)
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The square of an even number equals 6 less than 5 times the number. Wh  [#permalink]

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New post 21 Jan 2018, 08:18
dave13 wrote:
fc2262a wrote:
The square of an even number equals 6 less than 5 times the number. Which of the following is the square of the number?

A) 2

B) 3

C) 4

D) 6

E) 9




6 less than 5 times the number. shoudnt it be like this \(x^2= 6-5x\) rather than \(x^2= 5x - 6\)

can anyone explain why I think so :)
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Re: The square of an even number equals 6 less than 5 times the number. Wh  [#permalink]

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New post 21 Jan 2018, 09:10
This question is simple if you read it carefully. But the trap is "square of the number" which people may fail to notice. Good one though
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Re: The square of an even number equals 6 less than 5 times the number. Wh  [#permalink]

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New post 21 Jan 2018, 09:29
fc2262a wrote:
The square of an even number equals 6 less than 5 times the number. Which of the following is the square of the number?

A) 2

B) 3

C) 4

D) 6

E) 9


Check using options, from the highlighted part we can eliminate options (A) , (B) and (D)...

Plug in and check 4 , the original number must be 2

So, \(4 = 2*5 - 6\)

Answer will be (C)


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Re: The square of an even number equals 6 less than 5 times the number. Wh  [#permalink]

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New post 20 Apr 2018, 03:03
Solve using the options and keep in mind that only the square of the number is asked. Hence option C.
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Re: The square of an even number equals 6 less than 5 times the number. Wh  [#permalink]

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New post 22 Apr 2018, 02:33
chetan2u wrote:
fc2262a wrote:
The square of an even number equals 6 less than 5 times the number. Which of the following is the square of the number?

A) 2 B) 3 C) 4 D) 6 E) 9



Follow rules as applicable here..

As for your question, choices itself give out answer..
You are looking for square of even number as ANSWER
Only 4 fits in
D

Algebraically..
Number=n
\(n^2=5n-6.....n^2-5n+6=0....n^2-3n-2n+6=0.....(n-2)(n-3)=0\)
So n can be 2 or 3, but it is even so 2
Square of 2=4
D


Dear chetan2u,

in a different post I got the tip to always rephrase an "even number" with 2n.

Hence I got stuck at \(2n^2 - 5n + 3 = 0\)

Can you explain when to rephrase an "even number" as 2n and when as simply n?
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Re: The square of an even number equals 6 less than 5 times the number. Wh  [#permalink]

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New post 23 Apr 2018, 17:35
fc2262a wrote:
The square of an even number equals 6 less than 5 times the number. Which of the following is the square of the number?

A) 2

B) 3

C) 4

D) 6

E) 9


We can let n = the number, and thus:

n^2 = 5n - 6

n^2 - 5n + 6 = 0

(n - 3)(n - 2) = 0

n = 3 or n = 2

Since n is even, n must be 2. The square of 2 is 4.

Answer: C
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Re: The square of an even number equals 6 less than 5 times the number. Wh  [#permalink]

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New post 25 Apr 2018, 21:33
paddy41 wrote:
chetan2u wrote:
fc2262a wrote:
The square of an even number equals 6 less than 5 times the number. Which of the following is the square of the number?

A) 2 B) 3 C) 4 D) 6 E) 9



Follow rules as applicable here..

As for your question, choices itself give out answer..
You are looking for square of even number as ANSWER
Only 4 fits in
D

Algebraically..
Number=n
\(n^2=5n-6.....n^2-5n+6=0....n^2-3n-2n+6=0.....(n-2)(n-3)=0\)
So n can be 2 or 3, but it is even so 2
Square of 2=4
D


Dear chetan2u,

in a different post I got the tip to always rephrase an "even number" with 2n.

Hence I got stuck at \(2n^2 - 5n + 3 = 0\)

Can you explain when to rephrase an "even number" as 2n and when as simply n?


Hey,

You could have taken the number as "2n" also and solved the question. :)

However, the equation written by you incorrect! :(

According to the question:

The square of an even number: \((2n)^2\)

Equals 6 less than 5 times the number : \(5*(2n) - 6\)

Thus, we will write

\((2n)^2 = 5*(2n) - 6\)

\(4n^2 - 10n + 6 = 0\)

\(2n^2 - 5n + 3 = 0\)

\(2n^2 - 2n - 3n + 3 = 0\)

\(2n (n -1) -3 ( n-1) = 0\)

\((n-1) (2n -3) = 0\)

Since n needs to be an integer, the value of n will be 1

And the even number will be \(2n = 2*1 = 2\) and the square of this number will be \(2^2 = 4\)

I hope this clears your doubt. :)


Regards,
Saquib
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Re: The square of an even number equals 6 less than 5 times the number. Wh &nbs [#permalink] 25 Apr 2018, 21:33
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