XAT - 2008

1

Four digits of the number 29138576 are omitted so that the result is as large as possible. The largest omitted digit is

Directions for questions 2 and 3: A statement is followed by three conclusions. Select the answer from the following options.

1. Using the given statement, only conclusion I can be derived.
2. Using the given statement, only conclusion II can be derived.
3. Using the given statement, only conclusion III can be derived.
4. Using the given statement, all conclusions can be derived.
5. Using the given statement, none of the three conclusions I, II and III can be derived.

2

An operation "#" is defined by:

a # b = 1 - (b/a)

Conclusion I. (2 # 1) # (4 # 3) = −1
Conclusion II. (3 # 1) # (4 # 2) = −2
Conclusion III. (2 # 3) # (1 # 3) = 0

3

A, B, C and D are whole numbers such that

A + B + C = 118
B + C + D = 156
C + D + A = 166
D + A + B = 178

Conclusion I. A is the smallest number and A = 21.
Conclusion II. D is the largest number and D = 88.
Conclusion III. B is the largest number and B = 56.

4

If [X] denotes the greatest integer less than or equal to X, then

$$[{1\over 3}]+[{1\over 3} +{1\over 99}]+[{1\over 3} +{2\over 99}]+.....+[{1\over 3} +{98\over 99}]$$

5

ABCD is a square. P is the midpoint of AB. The line passing through A and perpendicular to DP intersects the diagonal at Q and BC at R. If AB = 2 then PR = ______?