Latest CAT Aptitude Question SOLUTION: The sum of four consecutive two-digit odd number,when devided by 10,becomes a perfect square.Which of the one can possibly be one of these four numbers? a)21 b)25 c)41 d)67

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(#M40010434) CAT question Keep an EYE

The sum of four consecutive two-digit odd number,when devided by 10,becomes a perfect square.Which of the one can possibly be one of these four numbers?
a)21 b)25 c)41 d)67 e)73

Asked In CAT skyspy5 (11 years ago)

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prashanthi  (11 years ago)

Let the four 2-digit odd numbers be
n-3 n-1 n+1 n+3

Sum of the 4 numbers ==> 4n

acc to qn, when the sum is divided by 10
we get a perfect square...
perfect squares include==>1,4,9,16,25,36,49,.....

Possible values of 4n/10 ==> 4, 16,36...

If 4n/10=4
n=10
Hence, the corresponding nos are 7,9,11,13(all of which are NOT 2-digit nos)


If 4n/10=16
n=40
Hence the corresponding nos are 37, 39, 41, 43

If 4n/10=36
n=90
Hence the corresponding nos are 87, 89, 91, 93


The answer to the ques therefore is Option C

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skyspy5  (11 years ago)

c)41
sol: (37+39+41+43)/10=16, which is a perfect sqr.

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Jekin   (11 years ago)

suppose two digit consecutive odd nos are is (10*y+x),(10*y+x+2),(10*y+x+4),
(10*y+x+6)

now sum of these no is=(40*y+4*x+12)and when diveded by 10 we have
(40*y+4*x+12)/10

by hit and trial we get 67 where x=7 and y=6(put it in equation

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Akshay  (8 years ago)

Numbers can be

21
22
23
24
ans 90
divided by 10
so answer is a

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