After successfully completing the CAT 2016 sprint series and the SNAP 2016 sprint series, we are back with the XAT 2017 sprint preparation series – Quant 9 to boost your prep. This series will consist of 10 sets of questions from past year XAT papers, leading to XAT 2017 and covered almost all the question types that you needed to know come the 8th of January.
XAT 2017 sprint preparation series – Quant 9
1. In a square PQRS, A and B are two points on PS and SR such that PA = 2AS, and RB = 2BS. If PQ = 6, the area of the triangle ABQ is
A. 6
B. 8
C. 10
D. 12
E. 14
2. How many whole numbers between 100 and 800 contain the digit 2?
A. 200
B. 214
C. 220
D. 240
E. 248
3. p, q and r are three non-negative integers such that p + q + r = 10. The maximum value of pq + qr + pr + pqr is
A. ≥ 40 and < 50
B. ≥ 50 and < 60
C. ≥ 60 and < 70
D. ≥ 70 and < 80
E. ≥ 80 and < 90
4. A number is interesting if on adding the sum of the digits of the number and the product of the digits of the number, the result is equal to the number. What fraction of numbers between 10 and 100 (both 10 and 100 included) is interesting?
A. 0.1
B. 0.11
C. 0.16
D. 0.22
E. None of the above
5. Arun has to go to the country of Ten to work on a series of task for which he must get a permit from the Government of Ten. Once the permit is issued, Arun can enter the country within ten days of the date of Issuance of the permit. Once Arun enters Ten, he can stay for a maximum of ten days. Each of the tasks has a priority, and takes a certain number of days to complete. Arun cannot work on more than one task at a time.
The following table gives the details of the priority and the number of days required for each task.
Task | Priority | Number of Days Required |
T1 | 1 | 3 |
T2 | 2 | 5 |
T3 | 5 | 3 |
T4 | 3 | 4 |
T5 | 4 | 2 |
Arun’s first priority is to complete as many tasks as possible, and then try to complete the higher priority tasks. His last priority is to go back as soon as possible. The tasks that Arun should try to complete are:
A. T1 and T2
B. T1, T2 and T5
C. T1, T4 and T5
D. T1, T2 and T4
E. T1, T3 and T4
6. However, Arun’s manager has told him to do some background research on the tasks before leaving for Ten. At the same time, there is no guarantee that Government of Ten will give the permit to Arun. Background research involves substantial costs, and therefore Arun has decided that he will not start his background research without getting the permit.
The following table gives the details of the priority, the number of days required for each task and the number of days required for background research on each task.
Task |
Priority |
Number of Days Required | No. of Days required for background research |
T1 | 1 | 3 | 3 |
T2 | 2 | 5 | 5 |
T3 | 5 | 3 | 2 |
T4 | 3 | 4 | 2 |
T5 | 4 | 2 | 3 |
Arun’s first priority is to complete as many tasks as possible, and then try to complete the higher priority tasks. His last priority is to go back as soon as possible within ten days.
A. T1, T2 and T3
B. T1, T2 and T5
C. T1, T2 and T4
D. T1, T3 and T4
E. T1, T4 and T5
7.The radius of a circle with centre O is √50 cm. A and C are two points on the circle, and B is a point inside the circle. The length of AB is 6 cm, and the length of BC is 2 cm. The angle ABC is a right angle. Find the square of the distance OB
A. 26
B. 25
C. 24
D. 23
E. 22
8. Six playing cards are lying face down on a table, two of them are kings. Two cards are drawn at random. Let a denote the probability that at least one of the cards drawn is a king, and b denote the probability of not drawing a king. The ratio a/b is:
A. ≥ 0.25 and ≤ 0.5
B. ≥ 0.5 and ≤ 0.75
C. ≥ 0.75 and ≤ 1.0
D. ≥ 1.0 and ≤ 1.25
E. ≥ 1.25
9.Consider the expression: (xxx)_{b} = x^{3} , where b is the base, and x is any digit of base b. Find the value of b.
A. 5
B. 6
C. 7
D. 8
E.None of the above
10.Consider a function f(x) = x^{4} + x^{3} + x^{2} + x + 1, where x is a positive integer greater than 1. What will be the remainder if f(x^{5}) is divided by f(x)?
A. 1
B. 2
C. 5
D. a monomial in x
E. a polynomial in x
Answers –
1. C. Simply take the fractions as 2x and x on both the sides and find the area of the three right angled triangles. The length of the side will be 3x = 6 and so, the area 5x^2 / 2 will be 10.
2. B. 114+100 = 214.
3. C. Put p = q = r = 10/3. So, we get 100/3+1000/27 = 33.33+27 = 60.xx.
4. A. ab + a + b = 10a + b
9a = ab, b = 9. So, there will be 9 such numbers. 9/91 will be approximately 0.1.
5. B.
6. E.
7. A.
8. E. b = 4c2/6c2 = 4/15 and a = 11/15. So, a/b = 11/4.
9. E. xb^2 + bx + x = x^3
(b^3 – 1)/(b – 1) = x^2. None match.
10. C. Simple division should help here.
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You can follow the entire sprint series here: XAT 2017 Sprint Preparation Series by Learningroots