Official Quant thread for CAT 2013

Q1

@The_Loser said:
Out of 100 person surveyed, 78 like Apples and 62 like Bananas.5. At least how many like apples only?6. At most how many like apples only?7. At least how many like exactly one fruit?8. At most how many like exactly two fruits?9. At least how many like at least one fruit?10. At most how many do not like any of the two fruits?
5.16
6.38
7.60
8.40
9.78
10.22

?

@The_Loser

5. At least how many like apples only?

78-62=16


6. At most how many like apples only?
38

7. At least how many like exactly one fruit?
16

8. At most how many like exactly two fruits?
62

9. At least how many like at least one fruit?
84

10. At most how many do not like any of the two fruits?

22

@vbhvgupta said:
Q40 andQ4115 36 20 42
@gs4890 yar can you solve this?
A group of 400 people went to picnic,on returning 240 were perfectly happy & no complains...among the rest 3 complained about delays,food and lack of facility..60 complained about the delay only.11 about food and lack of facility. 7 about delay and lack of facility..and 8 about delay and food.80 people complained about either only lack of food or only lack of facilities.so, the total no.who complained about only food was?
a.27 b.24 c.40 d.46
@gs4890 said:
5.166.387.608.409.7810.22?
7th, 8th - do check dse again. Rest correct

@sirari said:
@The_Loser5. At least how many like apples only?78-62=166. At most how many like apples only?387. At least how many like exactly one fruit?168. At most how many like exactly two fruits?629. At least how many like at least one fruit?8410. At most how many do not like any of the two fruits?22
9th - check that again. Rest correct

"I am seven times as old as you were when I was as old as you are". said a man to his son.Find the present age in years of man and son respectively if sum of their ages is 110.

Guys please explain the eqns being created here....
Having trouble to comprehend the meaning of the statement......

@The_Loser said:
an easy one.a + b + c + d = 90a,b,c,d =how many solutions?
Total ways=93C3

a+46+b+c+d=90

a+b+c+d=44

47C3

93C3-4*47C3

@vbhvgupta

taking natural numbers u can see that for two prog to follow the condition they need to have odd number. value for p =3n + (0,1,2) with 2 reqd condition satisfied .therfore we need 3n+2 for those cases where it have even value as two prog needs odd value for n else, avg is in decimal.

n=8,14,20,26 etc.

p1,p2 satisfies condition for 20 and 26

@bhatkushal said:
"I am seven times as old as you were when I was as old as you are". said a man to his son.Find the present age in years of man and son respectively if sum of their ages is 110.Guys please explain the eqns being created here....Having trouble to comprehend the meaning of the statement......
Let the ages be m and s so m+s=110
Now, Father was 's' years old before m-s
So son was s-(m-s) = 2s-m years old (m-s) years back
Now, s = 7(2s-m) => 7m=15s
Now solve and get m=75 and s=35

@The_Loser

9. 78

@The_Loser said:
Out of 100 person surveyed, 78 like Apples and 62 like Bananas.5. At least how many like apples only?6. At most how many like apples only?7. At least how many like exactly one fruit?8. At most how many like exactly two fruits?9. At least how many like at least one fruit?10. At most how many do not like any of the two fruits?
5.16,6.38,7.16,8.62,9.78,10.22

@ravi.theja

bhai question thik hai? only food + only fac= 80..yeh hi given info sa arraha hai jo baad ma given hai.........

pls explain how to approach....

@TootaHuaDil said:
Find the last two digits of 33^288??Find the last two digits of 78^379??Any one will serve as an example???
3 is showing cyclicity of 20 for two digit
11 is showing cyclicity of 10 for two digit

3^288*11^288
3^8*11^8
61*81=41

2 is showing cyclicity of 20 for two digits
39 is showing cyclicity of 10 for two digits

2^379*39^379
2*2^18*39^9
88*59
92

Q2

@The_Loser said:
Out of 100 person surveyed, 78 like Apples and 62 like Bananas.5. At least how many like apples only?6. At most how many like apples only?7. At least how many like exactly one fruit?8. At most how many like exactly two fruits?9. At least how many like at least one fruit?10. At most how many do not like any of the two fruits?
5->17
6->38
7->18
8->61
9->62
10->21

If 'a' is a factor of x and 'b' is also a factor of x, then is (a*b) also a factor of x? Why/ Why not?


Thanks in advance for answers
@gnehagarg Could you explain please......
@Veknash said:
If 'a' is a factor of x and 'b' is also a factor of x, then is (a*b) also a factor of x? Why/ Why not?Thanks in advance for answers
If a and b are factors of x then x could be a^p.b^q...
Clearly ab is also a factor of x
@Veknash said:
If 'a' is a factor of x and 'b' is also a factor of x, then is (a*b) also a factor of x? Why/ Why not?Thanks in advance for answers
if X = a*b*c*d...
then ofcrs a*b also divides X...