# CAT Questions Week 5

Here are the CAT questions for Week 5.

1. If 5x + 2y + z = 81 where x, y and z are distinct positive integers, then find the difference between the

maximum and the minimum possible value of x + y + z.

a. 44 b. 48 c. 55 d. 60 e. 64

2. The total number of terms in an arithmetic progression (A.P.) is odd. The sum of all the even placed terms is 7 and the sum of all the odd placed terms is 8.75 in this A.P. It is also given that the last term of this A.P. exceeds the first term by 2. Find the total number of terms in the A.P.

a. 5 b. 9 c. 11 d. 21 e. Cannot be determined

3. A circle with radius 2 cm is circumscribed by two triangles ABC and ADE as shown in the following figure. It is given that DE = 7 cm, BC = 5 cm, AC = 13 cm and the measure of ?CBD = 90°. Also it can be concluded that GF = 2BD / BD + k where ‘k’ is a real constant. Find the value of ‘k’.

a. 1 b. 2 c. 3 d. 4 e. 0

4. How many different points in the X-Y plane are at a distance of 5 units from the origin and have

co-ordinates (a, b), where ‘a’ and ‘b’ are integers?

a. 6 b. 8 c. 10 d. 12 e. 16

5. In how many ways can Rs.18.75 be paid in exactly 85 coins consisting of 50 paise, 25 paise and 10 paise coins?

a. One b. Two c. Four d. Eight

6. In Madhubani, 90% of the people drink coffee, 80% drink tea, 70% drink whiskey and 60% drink vodka. If each person drinks exactly three of the four beverages, then what percentage of people drink liquor? Vodka and whiskey are liquors.

a. 70% b. 80% c. 90% d. 100%