Instructions

For the following questions answer them individually

Question 61

In the final semester, an engineering college offers three elective courses and one mandatory course. A student has to register for exactly three courses: two electives and the mandatory course. The registration in three of the four courses is: 45, 55 and 70. What will be the number of students in the elective with the lowest registration?

Question 62

X and Y are the digits at the unit's place of the numbers (408X) and (789Y) where X â‰ Y. However, the digits at the unit's place of the numbers $$(408X)^{63}$$ and $$(789Y)^{85}$$ are the same. What will be the possible value(s) of (X + Y)?

Question 63

If 2 â‰¤ |x - 1| Ã— |y + 3| â‰¤ 5 and both x and y are negative integers, find the number of possible combinations of x and y.

Question 64

David has an interesting habit of spending money. He spends exactly Â£X on the Xth day of a month. For example, he spends exactly Â£5 on the 5th of any month. On a few days in a year, David noticed that his cumulative spending during the last 'four consecutive days' can be expressed as $$2^N$$ where N is a natural number. What can be the possible value(s) of N?

Question 65

A cone of radius 4 cm with a slant height of 12 cm was sliced horizontally, resulting into a smaller cone (upper portion) and a frustum (lower portion). If the ratio of the curved surface area of the upper smaller cone and the lower frustum is 1:2, what will be the slant height of the frustum?

Question 66

Two circles with radius 2R and $$\sqrt{2R}$$ intersect each other at points A and B. The centers of both the circles are on the same side of AB. O is the center of the bigger circle and âˆ AOB is 60Â°. Find the area of the common region between two circles.

Question 67

These statements provide data that may help answer the respective questions. Read the questions and the statements and determine if the data provided by the statements is sufficient or insufficient, on their own or together, to answer the questions. Accordingly, choose the appropriate option given below the questions.

A group of six friends noticed that the sum of their ages is the square of a prime number. What is the average age of the group?

Statement I: All members are between 50 and 85 years of age.

Statement II: The standard deviation of their ages is 4.6.

Question 68

These statements provide data that may help answer the respective questions. Read the questions and the statements and determine if the data provided by the statements is sufficient or insufficient, on their own or together, to answer the questions. Accordingly, choose the appropriate option given below the questions.

Harry and Sunny have randomly picked 5 cards each from a pack of 10 cards, numbered from 1 to 10. Who has randomly picked the card with number 2 written on it?

Statement I: Sum of the numbers on the cards picked by Harry is 5 more than that of Sunny.

Statement II: One has exactly four even numbered cards while the other has exactly four odd numbered cards.

Instructions

Six teams are playing in a hockey tournament where each team is playing against every other team exactly once. At an intermediate stage, the status is as follows:

Notes:

â€¢ The team that scores more goals than it concedes wins the match, while if both the teams score the same no. of goals, the match is declared drawn.

â€¢ Ina match played between Team X and Team Y, if team X scores 1 and concedes none. then the score line would read: Team X â€” Team Y (1-0)