# ECOILER MATH QUESTIONS WITH SOLUTIONS

Problem 1 :

A secret agent wants to crack a six digit code. He knows that the sum of the digits in the even positions is equal to the sum of digits in the odd positions. Which of the following number is the code ?

a)  81**61      b)  7*727*      c)  4*4141    d)  12*9*8

e)  181*2*

Solution :

Option a :

81**61

The sum of the digits in the odd position = 8 + * + 6

= 14 + *

Sum of the digits in the even position = 1 + * + 1

= 2 + *

From this, we understand that sum of the numerals in the odd position and in even position they are not same. So, option a is incorrect.

Option b :

7*727*

The sum of the digits in the odd position = 7 + 7 + 7

= 21

Sum of the digits in the even position = * + 2 + *

= 2 + * + *

To get 21 as the sum of the the above, we should replace the two * by even 9 and 8, we will get 17 + 2 ==> 19. So, option b is incorrect.

Option d :

12*9*8

The sum of the digits in the odd position = 1 + * + *

= 1 + * + *

Sum of the digits in the even position = 2 + 9 + 8

= 19

To get sum as 19 from (1 + * + *), we have to replace * by 9. So, 9 + 9 + 1 ==> 19

Then option d is correct.

Problem 2 :

Meta collects pictures of famous sports people. Each year she collects as many pictures as she did in the previous two years. In 2008 she had 60 photos and this year she has 96. How many did she have in 2006.

a)  20   b)  24   c)  36   d)  40     e) 48

Solution :

Years collected photos :

2006, 2007, 2008, 2009, .......

?, ?, 60, 96, ......

To get 96, we have to add 36 with 60. So, to go back we have to subtract 36 from 60. Then we will get 24.

Number of photos collected in 2007 = 24

The same number of photos she has collected in 2006. So, answer is 24, option b is correct.

Problem 3 :

In a vase there is one red, one blue, one yellow and one white flower. Maja the bee visits each flower exactly once. She begins with the red flower and she never flies directly from the yellow to the white flower. In how many different ways can she visit each flower ?

a) 1      b)  2      c)  3     d)  4        e)  5

Solution :

Let red flower be R, blue flower be B, yellow flower be Y and white flower be W.

Bee is travelling in the order, and it begins with R

• RBWY
• RYBW
• RWYB
• RWBY

We cannot write W after Y, but writing Y after W is possible. So, there are 4 possible ways, option d is correct.

Problem 4 :

In a haunted house the house ghost suddenly disappears. At that moment in time all clocks show 6:15' o clock. However, there is also one strange clock in the house shows that correct time before the event. Starting from the disappearance it stars to count backwards. At 19:30'o clock according to the real time the house ghost disappears. What time does the odd clock show at that time ?

a)  17 : 00     b)  17 : 45     c)  18 : 30    d)  19 : 00

e) 19 : 15

Solution :

At the time of disappearance, all the clock shows 6 : 15. The strange clock shows correct time before the event (not 6:15).

Elapsed time at 19 : 30 = 7 : 30

12 + 7 : 30 = 19 : 30

Incase the clock is going to rotate in clockwise direction, the ghost will disappear at 7: 30. That is,

Time difference between 7 : 30 and 6 : 15

= 1 : 15

= 60 + 15

= 75 minutes

After 75 minutes the time shown in the clock (6 : 15) the ghost will disappear.

We know that, the actual time shown by the clock must be before 7 : 30, but it would be before 6 :15 or after 6 : 15 we are not sure about it.

So, converting 6 hours and 15 minutes to minutes

= 6(60) + 15

= 360 + 15

= 375 minutes.

the time difference between the real time ghost disappears and time shown in the clock = 375-75

= 300 minutes

converting this into hours, we get 300/60

= 5 hours

Elapsed time of 5 ==> 12 + 5

= 17

Option a is the correct answer.

Problem 5 :

In Funny foot land men and women wear the same sort of shoes. Each man has a left foot that is two sizes bigger than the right foot. How ever, shoes are only sold in pairs of same size. To save money some friends decide to buy shoes together. After putting on their new shoes two shoes are left over- one of the size 36 and one of the size is 45. What is the minimum number of people in the group ?

Solution :

 MenLeft foot = x + 2Right foot = x WomenLeft foot = x + 1Right foot x

Size of left over shoes 36 and 45.

• There must be one more shoe with the size 36.
• If that is right foot shoe (36), then the same men will wear the size 38 shoe in his left foot.
• One more shoe with the size of 38 will be their and that must be right foot shoe, then his left foot shoe size will be 40.

36          38

38          40

40          42

42          44

44          45

(one shoe with the size 45 is the left over)

So, there is minimum of 5 persons.

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