Number System questions

[vikram4689]

1. find last 2 digits of the expression
a) 101 x 102 x 103 x 197 x 198 x 199
b) 65 x 29 x 37 x 73 x 81 x 87

2. If u form a subset if integers chosen from between 1 to 3000 such that no two integers add up to a multiple of nine , what can be
maximum no. of elements in the subset [P40Q65]

a)1668 b) 1332 c) 1333 d)1334

DOUBT.....I'm getting different answere

3. the series of numbers(1, 1/2, 1/3 , ...1/1972) is taken .
now two numbers are taken from this series ( the first two) say x,y.
Then the operation x+y+x.y is performed to get a consolidated number.
The process is repeated. What will be the value of the set after all
the numbers are consolidated into one number. [P40Q66]

a) 1970 b) 1971 c ) 1972 d)none

DOUBT....couldn't understand the question

[NikolayZ]

I have never seen questions like that on GMAT , except for the first one i think, it is quite similar to the "units digit of the integer question". So i could help only with the first question.
1)
It is pretty simple. All you have to do is to multiply all units digits, last two digits of this product will be your answer.
in case a) 1*2*3*4*7*8*9=3024. (24)

[vikram4689]

yeah that works well for finding the last digit but it dose not work for 2 digits as can be seen that answere to 1 b) cannot be obtained through this method.
For 1 a) it is luck that we get the result but we need to look for the right method

[NikolayZ]

Hm... my bad. Then we have to multiply last 2 digits of every factor i think. It would be 100% right answer.
By long multiplication we get 64 as the last two digits. ( it took me about 1 min also) so i think it is not very time consuming if you don't know the shortcut.