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21 Apr 2021, 03:15
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
58% (01:05) correct
42%
(01:14)
wrong
based on 222
sessions
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Date
Time
Result
Not Attempted Yet
Which one of the following numbers is not a square of any integer?
(A) 17,956
(B) 18,225
(C) 53,361
(D) 63,592
(E) 64,009
(A) 17,956
(B) 18,225
(C) 53,361
(D) 63,592
(E) 64,009
PyjamaScientist
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21 Apr 2021, 03:37
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Option D 63,592 can not be square of any integer because:
Multiplication of no two same digits from 1 to 10 results in a square number that ends with 2.
Series is: 1,4,9,16,25,36,49,64,81,100.
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Multiplication of no two same digits from 1 to 10 results in a square number that ends with 2.
Series is: 1,4,9,16,25,36,49,64,81,100.
Posted from my mobile device
21 Apr 2021, 04:44
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A number is a perfect square if all of its prime factors have even exponents. As the question deals with such large numbers it's probably best to skip prime factorising each and every answer choice and to see if there isn't a pattern within smaller perfect squares that one can work with.
Looking at the first few perfect squares: 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169... one can see that the units digits are a set of numbers which repeat: 1, 4, 6, 9 and 00. This shows that no perfect square will end in 2, 3, 7 or 8.
Looking at our answer choices D ends in 2. Thus, this will most likely be the answer.
To double check
63952/2 = 31796
31796/2 = 15898
15898/2 = 7949
As 7949 is odd, and all other prime numbers besides 2 are odd, it is impossible that there will be another even number to divide by 2 during prime factorisation as odd/odd = odd. Thus 2 will have an exponent of 3 which means that 63952 does not have a perfect square.
Answer D.
Looking at the first few perfect squares: 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169... one can see that the units digits are a set of numbers which repeat: 1, 4, 6, 9 and 00. This shows that no perfect square will end in 2, 3, 7 or 8.
Looking at our answer choices D ends in 2. Thus, this will most likely be the answer.
To double check
63952/2 = 31796
31796/2 = 15898
15898/2 = 7949
As 7949 is odd, and all other prime numbers besides 2 are odd, it is impossible that there will be another even number to divide by 2 during prime factorisation as odd/odd = odd. Thus 2 will have an exponent of 3 which means that 63952 does not have a perfect square.
Answer D.
