Aptitude Question Bank For AIEEE SSC

Sakshi can do a piece of work in 20 days. Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work is? A. 15 B. 16 C. 18 D. 25 Answer: Option B Explanation: Ratio of times taken by Sakshi and Tanys = 125:100 = 5:4 Suppose Tanya takes x days to do the work. 5:4 :: 20:x => x= 16 days. Hence, Tanya takes 16 days to complete the work.

Ronald and Elan are working on an assignment. Ronald takes 6 hrs to type 32 pages on a computer, while Elan takes 5 hrs to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages? A. 7 hrs 30 min B. 8 hrs C. 8 hrs 15 min D. 8 hrs 25 min Answer: Option C Explanation: Number of pages typed by Ronald in 1 hour = 32/6 = 16/3  Number of pages typed by Elan in 1 hour = 40/5 = 8 Number of pages typed by both in 1 hour = (16/3 + 8) = 40/3 Time taken by both to type 110 pages = (110 * 3/40) = 8 1/4 = 8 hrs 15 min

Problem 1 : Least number which when divided by 35,45,55 and leaves remainder 18,28,38; is? Solution : i) In this case we will evaluate l.c.m.                ii) Here the difference between every divisor and remainder is same i.e. 17.                   Therefore, required number = l.c.m. of (35,45,55)-17 = (3465-17)= 3448. Problem 2 : Least number which when divided by 5,6,7,8 and leaves remainder 3, but when divided by 9, leaves no remainder? Solution : l.c.m. of 5,6,7,8 = 840                  Required number = 840 k + 3                  Least value of k for which (840 k + 3) is divided by 9 is 2 Therefore, required number = 840*2 + 3                                             = 1683 Problem 3 : Greater number of 4 digits which is divisible by each one of 12,18,21 and 28 is? Solution : l.c.m. of 12,18,21,28 = 254                Therefore, required number must be divisible by 254.                Greatest four digit number = 9999                On dividing 9999 by 252, remainder = 171

What will be the least number which when doubled will be exactly divisible by 12, 18, 21 and 30 ? A. 196 B. 630 C. 1260 D. 2520 Explanation:  L.C.M. of 12, 18, 21 30                      2 | 12  -  18  -  21  -  30                                         ----------------------------    = 2 x 3 x 2 x 3 x 7 x 5 = 1260.       3 |  6  -   9  -  21  -  15                                                          ----------------------------    Required number = (1260 ÷ 2)            |  2  -   3  -   7  -   5                    = 630.

The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is: A. 15 cm B. 25 cm C. 35 cm D. 42 cm Answer: Option C Explanation: Required length = H.C.F. of 700 cm, 385 cm and 1295 cm = 35 cm.

The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is: A. 276 B. 299 C. 322 D. 345 Answer: Option C Explanation: Clearly, the numbers are (23 x 13) and (23 x 14).  Larger number = (23 x 14) = 322.

Find the greatest number that will divide 43, 91 and 183 so as to leave the same remainder in each case. A. 4 B. 7 C. 9 D. 13 Answer: Option A Explanation: Required number = H.C.F. of (91 - 43), (183 - 91) and (183 - 43)      = H.C.F. of 48, 92 and 140 = 4.

 Find the one which does not belong to that group ? A. 36 B. 49 C. 64 D. 81 E. 100 Answer: Option B Explanation: 36 = 62, 49 = 72, 64 = 82, 81 = 92 and 100 = 102. 36, 64, 81 and 100 are squares of composite numbers, but not 49.

Find the one which does not belong to that group ? A. 16 B. 28 C. 36 D. 64 E. 4 Answer: Option C Explanation: 16, 36, 64 and 4 are perfect squares but not 28.

Find the one which does not belong to that group ? A. 27 B. 37 C. 47 D. 67 E. 17 Answer: Option A Explanation: 37, 47, 67 and 17 are prime numbers but not 27.

Find the one which does not belong to that group ? A. 3 B. 4 C. 5 D. 9 E. 7 Answer: Option B Explanation: 3, 5, 9 and 7 are odd numbers, but not 4.

Using all the letters of the word "THURSDAY", how many different words can be formed? A. 8 B. 8! C. 7! D. 7 E. 6! Answer: Option B Explanation: Total number of letters = 8 Using these letters the number of 8 letters words formed is ⁸P₈ = 8!.

How many three letter words are formed using the letters of the word TIME? A. 12 B. 20 C. 16 D. 24 E. 30 Answer: Option D Explanation: The number of letters in the given word is four.  The number of three letter words that can be formed using these four letters is ⁴P₃ = 4 * 3 * 2 = 24.

 A boy has nine trousers and 12 shirts. In how many different ways can he select a trouser and a shirt? A. 21 B. 12 C. 9 D. 108 E. 101 Answer: Option D Explanation: The boy can select one trouser in nine ways. The boy can select one shirt in 12 ways. The number of ways in which he can select one trouser and one shirt is 9 * 12 = 108 ways.