| **CAT DOSE 1(SOLUTIONS) - **
May 15th, 2006
NOTE : BETWEEN TWO NUMBERS MEANS THAT THE TWO
NUMBERS ARE EXCLUDED AND "FROM A TO B " MEANS THAT
THE TWO NUMBERS A AND B ARE INCLUDED.
Ans 1. Number of numbers divisible by 5 = Truncate (549/5)= 109
Number of number divisible both 5 and 9 (LCM of 5 and 9 =45)
= truncate (449/45)= 12
So numbers divisible by 5 but not by 9 = 109-12= 97.
Ans 2. Numbers divisible by 8 = Truncate (164/8)= 20
Numbers divisible by 6 = Truncate (164/6)= 27
LCM of 8 and 6 = 24
Numbers divisible by 24= Truncate (164/24)= 6
Numbers divisible by 8 or 6 or both = 20+27-6= 41
Number of number between 1 to 165 ( 1 and 165 not counted) =
165 -2 = 163
So number not divisible by 8 nor by 6 = 163-41= 122
Ans 3. Numbers divisible by 5 = Truncate (1949/5)= 389
Numbers divisible by 11 = Truncate (1949/11)= 177
LCM of 5 and 11= 55
Numbers divisible by both = Truncate (1949/55)= 35
So number divisible either by 5 or 11 = 389+177-35= 531
Ans 4. If 55 numbers are divisible by X then X will be
Truncate (275/55)= 5
Similarly Y = truncate(275/39) = 7
LCM of 7 and 5 = 35.
Numbers divisible by 35 = truncate (275/35) = 7
So 7 numbers will be divisible by both X and Y.
Ans 5. 46*8 = 368. If you add 8 to 368 then there will be 47
numbers divisible by N. So the maximum we can add and still
have 46 numbers divisible by 8 is 7. 368 +7 = 375.
Now 31*12= 372. We can add another 11 to it and still have 31
numbers divisible by 12.
But if we add 11 we will have more numbers divisible by 8.
So the maximum value of N = 375
Ans 6. LCM of 8 and 12 = 24
Numbers divisible by both 8 and 12 = truncate (375/24) = 15
Ans 7. As 75 numbers are divisible by X and 69 numbers are
divisible by X but not by Y , we can say that there are 75-69= 6
numbers divisible by both X and Y.
Since 42 numbers are divisible by Y and not by X and 6 numbers
are divisible by both X and Y, we can say that 42+6= 48 numbers
are divisible by Y.
Ans 8. Numbers not divisible by any of X and Y = Total numbers-
(Divisible by X not Y + Divisible by Y not X + Divisible by both X
and Y)
= 530- (69+42+6)
= 413.
Ans 9. n can take value 2,3,4,5,6,7,8,9 as 2^10 = 1024 which is
greater than 1000.
So 2+3+4+5+6+7+8+9= 44
Ans 10. 10 numbers : 2^4, 2^6, 2^8, 4^2, 6^2, 8^2, 10^2, 12^2, 14^
2, 16^2
Note : 2^2, 4^4 are not possible as the numbers need to be
distinct.
Ans 11. 18 numbers. 3^2, 4^3, 4^2, 5^3, 5^2, 6^3, 6^2, 7^2, 8^2,
9^2, 10^2,11^2, 12^2,13^2,14^2,15^2,16^2,17^2. (Remember x>
y>1)
Ans 12. 7 numbers. 2^3, 2^4, 2^5, 2^6, 2^7, 3^4, 3^5.
Ans 13. We need to find the numbers that are even, less than
500, divisible by 7 and 17 both.
LCM of 7, 17 and 2 = 238.
only 238 and 476 are common elements in the three sets.
So answers = 2 numbers.
Ans 14. There are truncate(459/7) = 65 numbers less than 459
divisible by 7.
Out of these 65 numbers, the 2nd, 4th, 6th......64th number will
be even. so there will be 32 even numbers of these 65 numbers.
The remaining 33 numbers will be odd.
So there are 33 numbers less than 460 that are odd and
divisible by 7.
Ans 15. The number of numbers divisible by any of two numbers
= Numbers divisible by both + number divisible by X and not by Y
+ number divisible by Y but not be X.
= 16+50+34= 100
Ans 16. Number of numbers divisible by X = Numbers divisible
by X and not by Y + numbers divisible by both.
= 16+50 = 66.
Ans 17 and 18.
Before she gave to her sister she had 5+5= 10
Changes when she went to her father: 10 -1 = 9, 9*2= 18
Changes when she went to her mother : 18-1= 17, 17*2= 34
Changes when she went to her brother : 34-4= 30, 30*2= 60.
Ans 17. In end she had 5 and in the beginning she had 60, so
she was 55 short at the end.
Ans 18. She gave 30 to her brother but took back 4 so her brother
has 26 sweets.
Ans 19 and 20:
Starting from the end we get :
When she went to her mother, 49+1= 50, 50/2= 25
When she went to her father , 25+1= 26, 26/2= 13
When she went to her sister , 13+1= 14, 14/2= 7
When she went to her brother, 7+1= 8, 8/2= 4.
Ans 19. She had 4 flowers in the beginning.
Ans 20. She got 7 flowers from her sister.
Ans 21.=C, Ans 22.= F , Ans 23.=A, Ans 24.=G, Ans 25.=D |