Q1. How many combinations of two-digit numbers having 8 can be made from the following numbers?
8, 5, 2, 1, 7, 6
Sol. The possible two-digit numbers are : 88, 85, 82, 81, 87, 86, 58, 28, 18, 78, 68.
These are 11 in number.
Q2. In the numbers from 100 to 1000, how many times digit 1 comes at the tens place?
Sol. The digit 1 comes at the tens place in numbers from 110 to 119; 210 to 219; 310 to 319; 410 to 419; 510 to 519; 610 to 619; 710 to 719; 810 to 819 and 910 to 919.
∴ Required number = 10 × 9 = 90.
Q3. Rahul ranked sixteenth from the top and twenty-ninth from the bottom among those who passed an examination. Six boys did not participate in the competition and five failed in it. How many boys were there in the class?
Sol. Number of boys who passed = (15 + 1 + 28) = 44.
∴ Total number of boys in the class = (44 + 6 + 5) = 55
Q4. In a class of 60, where girls are twice that of boys, kamal ranked seventeenth from the top. If there are 9 girls ahead of Kamal, how many boys are after him in rank?
Sol. Let the number of boys be x
Then number of girls = 2x
∴ x + 2x = 60 or 3x = 60 or x = 20
So, number of boys = 20 and number of girls = 40
Number of students behind Kamal in rank = (60 – 17) = 43
Number of girls ahead of Kamal in rank = 9
Number of girls behind Kamal in rank = (40 – 9) = 31
∴ Number of boys behind Kamal in rank = (43 – 31) = 12.
Q5 Raju is sixth from the left end and Vinay is tenth from the right end in a row of boys. If there are eight boys between Raju and Vinay, how many boys are there in the row?
Sol. Clearly, number of boys in the row = (6 + 10 + 8) = 24.
Q6. In a row of 21 girls, when Soniya was shifted by four places towards the right, she became 12th from the left end. What was her earlier position from the right end of the row?
Q7. In a row of boys, if A who is tenth from the left and B who is ninth from the right interchange their positions, A becomes fifteenth from the left. How many boys are there in the row?
Sol. Clearly, A’s new position is 15th form the left. But this is the same as B’s earlier position which is 9th from the right.
So number of boys in a row = (15 + 8) = 23
Q8. Students line up in a queue in which Ashish stands fifteenth from the left and Sachin is seventh from the right. If they interchange their places, Sachin would be fifteenth from the right. How many students are there in the queue?
(d) None of these
Sol.Sachin’s new position is 15th from the right as well as the left end of the row.
∴ Number of students in the queue = (14 + 1 + 14) = 29.
Q9. Shankar moved to his North-west side for 2 km. From there he turned 90° clockwise and moved 2 km. from there he turned 90° clockwise and travelled 2 km then he would be in which direction from the original position?
(a) North East Region
(b) South East Region
(c) South West Region
(d) Western Region
Direction :In this question a statement is given followed by four conclusions (a) to (d). You have to consider the statements to be true even if they seem to be at variance from commonly known facts. You have to decide which one of the given conclusions are definitely drawn from the given statement.
Q10. “All the members of the Tennis club are members of the Badminton club too.” “No woman plays Badminton”.
(a) Some women play Tennis
(b) No member of the Tennis club plays Badminton
(c) Some women are members of the Tennis club
(d) No woman is a member of the Tennis club