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Which of the following numbers is a perfect square?

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Which of the following numbers is a perfect square? [#permalink] New post 22 Mar 2013, 00:04
00:00
A
B
C
D
E

Difficulty:

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Question Stats:

70% (02:09) correct 29% (01:34) wrong based on 58 sessions
Which of the following numbers is a perfect square?

A. 1266
B. 1444
C. 2022
D. 4034
E. 8122
[Reveal] Spoiler: OA

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Last edited by Bunuel on 22 Mar 2013, 02:21, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Which of the following numbers is a perfect square? [#permalink] New post 22 Mar 2013, 02:40
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emmak wrote:
Which of the following numbers is a perfect square?

A. 1266
B. 1444
C. 2022
D. 4034
E. 8122


A perfect square, is an integer that is the square of an integer. For example 16=4^2, is a perfect square.

From above we can deduce that the units digit of a perfect square cannot be 2, 3, or 7. Discard C and E.

Another property: perfect square always has even powers of its prime factors. The reverse is also true: if a number has even powers of its prime factors then it's a perfect square. For example: 36=2^2*3^2, powers of prime factors 2 and 3 are even.

Make prime factorization of the options:

A. 1266 = 2*3*211. Discard. We could discard 1266 after we got that 1266 = 2*633 = 2*odd, so 2 in 1266 has an odd power, which means that 1266 is NOT a prefect square.

B. 1444 = 2^2*19^2 --> so, 1444 IS a perfect square.

D. 4034 = 2*2017. Discard. We could discard 4034 after we got that 4034 = 2*2017 = 2*odd, so 2 in 4034 has an odd power, which means that 4034 is NOT a prefect square.

Answer: B.

Hope it's clear.
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Re: Which of the following numbers is a perfect square? 1266 [#permalink] New post 22 Mar 2013, 00:20
perfect Square never ends with 2, 3, 7 and 8 so straight away you can eliminate 8122 and 2022.
38*38 = 1444
hence B.
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Re: Which of the following numbers is a perfect square? [#permalink] New post 05 Feb 2014, 13:27
emmak wrote:
Which of the following numbers is a perfect square?

A. 1266
B. 1444
C. 2022
D. 4034
E. 8122


Let's begin by eliminating answer choices C and E since a perfect square cannot end in 2,3,7 or 8

Now between A,B and D

Well we can see that all numbers are even for starters. This means that they also must be divisible by 4

Only B fits the bill

Hence B is the correct answer

Hope its clear
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Re: Which of the following numbers is a perfect square? [#permalink] New post 04 Mar 2014, 01:45
Perfect squares cannot end with 2,3,7 or 8, so options C & E are eliminated

A. 1266
B. 1444
E. 8122

Look at the above 3 options. All are divisible by 2, but only 1444 is divisible by 4.
Hence Answer = B

NB - Consider last two digits of any number. If Last two digits of any number are divisible by 4, then the complete number is divisible by 4
Also, If Last digit of any number is divisible by 2, then the complete number is divisible by 3
If Last three digits of any number are divisible by 8, then the complete number is divisible by 8

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Re: Which of the following numbers is a perfect square?   [#permalink] 04 Mar 2014, 01:45
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