What is the last 2 digits of 65*29*37*63*71*87*62 ?

Question

What is the last 2 digits of  65*29*37*63*71*87*62  ?

A. 90
B. 80
C. 70
D. 30
E. 10

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chetan2u · Accepted Answer

We are to find the last two digits of  65*29*37*63*71*87*62 ?

65*29*37*63*71*87*62  
 =13*5*29*37*63*71*87*31*2 
 =13*29*37*63*71*87*31*10

Now,  the last digit will be 0, and the second last would depend on the units digit of the product of all other numbers.  
  13*29*37*63*71*87*31

3*9*7*3*1*7*1.........(3*7)*(3*7)*9.....1*1*9......9

So the number  13*29*37*63*71*87*31*10=...abc9*10=...abc90

The last two digits are 90

A

sujoykrdatta · Answer

65*29*37*63*71*87*62
= 5*13*29*37*63*71*87*2*31
= 5*2*(13*29*37*63*71*87*31)
= 10*(13*29*37*63*71*87*31)

Thus, units digit is 10
The tens digit is obtained as the units digit from

13*29*37*63*71*87*31
= 3*9*7*3*1*7*1
= 9

So the last 2 digits = 90

Answer A

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sujoykrdatta · Answer

The solution is perfect. However, you missed 63!

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chetan2u · Answer

Hi Sujoy I too realised it after posting and edited it. Thanks a ton

TarunKumar1234 · Answer

Given, 65∗29∗37∗63∗71∗87∗62 = 13*5*29*37*63*71*87*31*2 = 10*(13*29*31*37*63*71*87) = xyz90 So, I think A.

MBAAD21 · Answer

Hi Sir,
Why did we segregate 10 (5*2) from the list of numbers? What is the concept behind it? Can you please guide.

TarunKumar1234 · Answer

MBAAD21 !

Let me try to respond.

The question asked last 2 digits. And, we can see 5 and 2 as one of multiples. so, if we take out 10 then 1st digit of remaining numbers multiplications will be the second digit, we are searching for.

I hope, it is clear.

MBAAD21 · Answer

Hi Tarun,
Thankyou so much for the explanation. Appreciate it.

bumpbot · Answer

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What is the last 2 digits of 65293763718762 ?

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