## QBM043

Q1. When 36 divide a number, it leaves a remainder of 19. What will be the remainder when 12 divide the number? A.10
B.7
C.11
D.None of these Q2.An isosceles triangle with equal angles = 75o is cut from a cardboard. How many such triangles need to be joined together to form a regular polygon? 1)10
2) 12
3)6
4) A regular polygon cannot be formed Q3.Find a number such that if 5, 15 and 35 are added to it, the product of the first and third results may be equal to the square of the second. a)10
b)7
c)6
d) 5 Q4.What is the ten's digit of 436? a)4
b) 1
c) 9
d) none of these Q5. A can do a piece of work in 36 days, B in 54 days and C in 72 days. All of them began together but A left 8 days and B left 12 days before the completion of the work. How many days in all did C put in till the entire work was finished? (1)48 days
(2)24 days
(3)12 days
(4) None Q6. The remainder obtained when a prime number greater than 6 is divided by 6 is: (1)1 or 3
(2) 1 or 5
(3) 3 or 5
(4) 4 or 5 Q7. The length of a ladder is exactly equal to the height of the wall it is resting against. If lower end of the ladder is kept on a stool of height 3 m and the stool is kept 9 m away from the wall, the upper end of the ladder coincides with the top of the wall. Then, the height of the wall is: (1)12m
(2)15m
(3)18m
(4)11m Q8-Q9 Pinky enters a shop to buy almonds, biscuits and chocolates. She has to buy at least 7 units of each. She buys more biscuits than she does almonds and more chocolates than she does biscuits. She picks up a total of 26 items. Q8. How many almonds does she buy? (1)7
(2)8
(3)9
(4) Cannot be determined Q9.Which of the following is not a valid value for number of chocolates bought? (1)9 (2)10 (3)11 (4) All are valid Q10. Four bells begin to toll together and then at intervals of 6, 7, 8 and 9 seconds. The number of times they will toll together in 2 hours and the intervals at which they will are (a) 14 times, 504 sec
(b) 15 times, 600 sec
(c) 13 times, 650 sec
(d) 11 times, 720 sec Q11. Ram purchased a flat at Rs. 1 lakh and Prem purchased a plot of land worth Rs. 1.1 lakh. The respective annual rates at which the prices of the flat and the plot increased were 10% and 5%. After two years they exchanged their belongings and one paid the other the difference. Then: (1) Ram paid Rs. 275 to Prem
(2) Ram paid Rs. 475 to Prem
(3) Ram paid Rs. 2750 to Prem
(4) Prem paid Rs. 475 to Ram Q12. Mr. Akshay stays in a triangular colony. He stays at one vertex, with a bank and a market at the other two vertices. The roads meeting at the market are at 90. Akshay goes to the bank from his home and then to the market totally covering 160 m. He then walks straight back home from the market. If distance from home to bank is 40 m more then what he covered from bank to market, find the distance he walked from market to home. (a) 80 m
(b) 120 m
(c) 100 m
(d) 155 m ANS: Q13. If you walk for 30 minutes at a rate of 4 miles per hour and then run for 15 minutes at a rate of 10 miles per hour, how many miles have you gone at the end of 45 minutes? a. 5 miles
b.6 miles
c. 5.5 miles
d. 4.5 miles
e. None of these Q14. How many zeros contained in 100!? A. 100
B.24
C.97
D.Cannot be determined Q15. Divide 183 into 3 parts in GP such that the sum of first and third terms is 2 1/20 times the second. What is the middle term? a)84
b)75
c)60
d) 48

Q1. The number is of the form 36N + 19 and when it is divided by 12 we get 7 as the reminder.

Q3. (N + 5) (N + 35) = (N + 15)2

=> 10 N  = 50 => N = 5

Q4. Reminder of  436/100  = Reminder of  576/100  = Reminder of  76/100 [Binomial (50 + 7)6= 76 + 100K  ]

= 49

So unit digit =9 and Tenth digit =4

## Q6

Any prime no. other than 2 &3 can be represented as 6k(+/-)1. Thus remainder is always 1 or 5.

## Q5

Say total d days. Then d/72 + (d-12)(1/36) + (d-8)(1/54) = 1. => (13d/216) – (13/27) = 1. => d = (216*40)(13*27) = 320/13.

## Q2

Here the other angle is 30 deg. when we are constructing a regular polygon equal sides has to be joined together. The angle at the centre has to be 360deg. For which n must be = (360/30)=12.

## Q14

I think it cannot be determined. But zeros at last are easily determinable. Its, 100/5 + 100/(5^2) = 24.

## Q10

LCM(6,7,8,9)= 504. they will toll together after every 504 seconds. In 2 hrs. they'll toll together: [7200/504]= 14 times.

## EXPLAIN

can you plz explain which rule had u applied ..... for determining zero at the end...

## solutions

soln.1  the no. is 36m+19

when divided by 12,

i.e.  36m/12 +19/12

therefore, the remainder will be, 7

soln.2   each internal angle of the polygon will be of, 150 deg

let, there are n sides of the polygon

some of the internal angle in a plygon = (n - 2)180 deg

here, (n - 2) 180= 150n

i.e. n = 12

soln.3   (5+n)(35+n)=(15+n)^2

n = 5

soln.5       work strength for A,B,andC are  x/36, x/54, x/72   respectivaly for one day

in 8 days A does 8x/36= 2x/9 work

in 12 days B works  12x/54=2x/9 work

total wor completed by A and B= 4x/9

work left for C = 5x/9

C have to work for ,    72/x * 5x/9 =40 days

soln.10     L C M for 6, 7, 8, 9 = 540 sec

secs. in 2 hrs = 7200 sec

rings rang togather, 7200/540 - remainder = 14 times

therefore the ans is a)

soln.14.  no. of zeros in 100! is the power of  5 in its factorization ( because 5 * 2 gives zero to a no.)

there are 24 5s in it ,

therefore the ans is = 24

## Soln. 8,9

Pinki has to buy 7 unit each for almond , biscuit and chocolate.

given,   A> B> C

there are only 2 combinations are possible to satisfy the given condition,

A = 7, B = 9, C = 10

and A = 7, B = 8, C = 11

Therefore, Ans-8)  is, 7    and ans-9) is 9

## soln, 4

(43)^6 = (3 + 40)^6 = 6c0 (3)^6 + 6C1 3^5 (40) + 6C2 3^4 (40)^2+----- = 729 + 9720 + ----(after 2 terms there will be zero on tens due to 40^2 40^3 onwards) therefore (43)^6 = ------49 so the ans will be 4

## soln, 4

(43)^6 = (3 + 40)^6 = 6C0 3^6 + 6C1 3^5 (40)+ 6C2 3^4 (40)^2+ 6C3 3^3 (40)^3 + ---- = 729 + 9720 + ---( after 2 terms there will be 0 on tens place due to 40^2 40^3 onwards) = ------49 threfore the ans will be 4.