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These type of questions can occur in both quant or DI depending on length and difficulty of the questions.
I have a presentation made about Venn Diagrams, but I am a little under the weather and am unable to record narration right now.
The slides are pretty self explanatory so I don’t think anyone will have a problem in understanding them.
Here you have the presentation in .ppt format. It is only 88.5 Kb.
Here you go a screenshot of the presentation.
Hope you like the tutorial!
Exercise:
The exercise for similar problems such as the ones solved in the presentation are here.
The file is in .doc format and is of 37 Kb.
Hope you like the post!
Do come back for more!! 😀
Filed under: Data Interpretation, quant | Tagged: CAT, CAT 2009, CAT preparation, Data Interpretation, IIM, Logical Reasoning, quant, Quantitative Aptitude, Venn Diagrams | Leave a comment »
Ruchi asked me a doubt in Number Theory :
Hey thnx nicky
cud u pls temme the soln of the foll ques m nt able 2 solve it .
1234^1235^1236^1237 find the unit digit of this expression .
Here is the solution to her problem:
Solution :
Method 1 –
1234^1235^1236^1237 = (((1234)^1235)^1236)^1237
Now let’s consider the inner most terms -> (1234)^1235
Using our method given in Number Systems Thoery , we get
1235/4 gives us Rem = 3
So, last digit of (1234)^1235 = last digit of 4^3 which is 4
Now,
last digit of
(((1234)^1235)^1236)^1237 is the same as last digit of (4^1236)^1237
Now, consider 4^1236 . Last digit of this can be obtained again by using the same technique
remainder of 1236/4 is 0 , so last digit is last digit of 4^4 which is 6.
Now, similarly, we get
that last digit of (((1234)^1235)^1236)^1237 is the same as last digit of (6^1237)
Again, we get remainder of 1237/6 as 1.
So, last digit of(((1234)^1235)^1236)^1237 is last digit of 6^1 which is 6 .
The last digit of(((1234)^1235)^1236)^1237 is 6.
Method 2 –
If we observe the following
4*4 = 16
4*4*4 = 64
4*4*4*4 = XX6
4*4*4*4*4 = XX4
Therefore, we infer that
– 4 to power of even number gives last digit as 6.
– 4 to power of odd number gives last digit as 4.
Now, we can find out last digit of
1234^1235^1236^1237 = 1234^(1235*1236*1237)
if we know whether 1235*1236*1237 is odd or even.
As we know that odd * even = even , and 1236 is even, we get that 1234 is raised to even power.
So, last digit of 1234 ^ even is 6 (from the observation above)
Last digit of 1234^1235^1236^1237 is 6.
Thank you for the problem Ruchi – I enjoyed solving it!
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I hope you liked the way I solved Ruchi’s problem. If you have any easier method to solve it, do let me know.
Filed under: quant | Tagged: Arithmetic, CAT, CAT 2009, CAT preparation, IIM, Number Systems, Number Theory, quant, Quantitative Aptitude | 4 Comments »