We have two unknown positive integers m and n, whose product is less than 100. There are two additional statement of facts available:
1) mn is divisible by six consecutive integers { j, j + 1,...,j + 5 }
2) m + n is a perfect suare.
Which of the two statements above, alone or in combination shall be sufficient to determine the numbers m and n?
Question 2
Direction: Two statements labelled as I and II. Decide if these statements are sufficient to conclusively answer the questions. Choose the appropriate answer from the options given below.
What is the area of the triangle whose two vertices are (1, 2) and (4, 6) and the third vertex lies on the line 4x – 3y = –10?
I. The third vertex lies in the second quadrant.
II. The x-coordinate of the third vertex is –4
Question 3
Direction: Two statements labelled as I and II. Decide if these statements are sufficient to conclusively answer the questions. Choose the appropriate answer from the options given below.
The integers a, b, c, d and e are in geometric progression and c < d. Is a < e?
I. Alternate terms are positive and negative.
II. All terms are positive.
Question 4
If A and B run a race, then A wins by 60 seconds. If B and C run the same race, then B wins by 30 seconds. Assuming that C maintains a uniform speed, what is the time taken by C to finish the race? A) A and C run the same race and A wins by 375 metres. B) The length of the race is 1 km.
Question 5
AB is a chord of a circle. AB = 5 cm. A tangent parallel to AB touches the minor arc AB at E. What is the radius of the circle? A) AB is not a diameter of the circle B) The distance between AB and the tangent at E is 5 cm
Question 6
There is a circle with centre C at the origin and radius r cm. Two tangents are drawn from an external point D at a distance d cm from the centre. What are the angles between each tangent and the X-axis. I. The coordinates of D are given. II. The X-axis bisects one of the tangents.
Question 7
Zakib spends 30% of his income on his children’s education, 20% on recreation and 10% on healthcare. The corresponding percentages for Supriyo are 40%, 25% and 13%. Who spends more on children’s education? A) Zakib spends more on recreation than Supriyo. B) Supriyo spend more on healthcare than Zakib.
Question 8
Direction: The question below is followed by two statements marked I and II. Mark as your answer.
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 9
Direction: The question below is followed by two statements marked I and II. Mark as your answer.
Harry and Sunny have randomly pricked 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.
Question 10
A bag contains marbles of three colours-red, blue and green. There are 8 blue marbles in the bag. There are two additional statement of facts available:
1) If we pull out marbles from the bag at random, to guarantee that we have at least 3 green marbles, we need to extract 17 marbles.
2) If we pull out marbles from the bag at random, to guarantee that we have at least 2 red marbles, we need to extract 19 marbles.
Which of the two statements above, alone or in combination shall be sufficient to answer the question "how many green marbles are there in the bag"?
