1. How many four-digit odd integers, greater than 3009 can be formed with the digits 0, 2, 3, 5 and 7, if repetition of digits is not allowed?
(1) 36 (2) 32 (3) 72 (4) 54 (5) 120
The units digit can be filled in 3 ways (3, 5 or 7) and once this is done the thousands digit can be filled in 2 ways.
The hundreds and the tens digit can be filled up with remaining digits in 3 2 = 6 ways.
Total number of ways = 3 2 6 = 36.
Hence, total such four digit number greater than 3009 = 36.
The last three digits of any number is same as the remainder when the number is divided by 1000.
2. What is the digit at the hundredths place of the number N = 45^36 ?
(1) 1 (2) 0 (3) 6 (4) 5 (5) 7
45^36/1000 = 5^33 * 9^36/8
The remainder when 9^36 is divided by 8 will be 1 as 9^36 = (8 + 1)^36
5^33/8 = 5 * (25)^16/8 = 5 * (24+1)^16/8
So, the remainder when 5^33 is divided by 8 will be 5.
So, the remainder when 45^36 is divided by 1000 will be 125 5 1 = 625.
The required digit is 6.
3. The sum of coefficients of the terms which do not contain odd powers of x in the expansion of (x + y)^100 + (x y)^100 isanswer is 2^100. Explanation is too big!
(1) 2^99 (2) 2^100 (3) (2^100 2) (4) (2^100 1)/2 (5) 0
154/125 = 1.232; so Net change is (+23.2%)
4. After three successive changes (two increases and one decrease, not necessarily in that particular order), the price of a watch became (154/125)
of its initial price. If the percentage changes are P, 2P and 4P respectively, then what is the value of 4P?
(1) 20 (2) 8 (3) 200 (4) 40 (5) Either (1) or (4)
Let us check by options:
For 20% : The four successive percentage changes could be one or other of (5, 10, 20), (5, 10, 20), (5, 10, 20) and (5, 10, 20).
None of the above combinations gives a net change of 23.2%.
For 8% : Even if we take all the percentage changes (2, 4, 8 ) as positive, the net percentage change would be less than 14.56%.
For 200% : The three successive absolute percentage changes are (50,100, 200). For any combination of the percentage changes, the net change cannot be equal to 23.2%.
For 40% : The three successive absolute percentage changes are (10, 20, 40)
If we take the successive percentage changes as (10, 20, 40), then the net increase is 23.2%.
root3/2 sq. cm.
5. ABC is an equilateral triangle and D is a point on the side BC. A perpendicular DE is drawn from D on AC and another perpendicular EF is drawn from E on BC. The length of the side BC is 6 cm and the
ratio of the lengths of BD to BC is 1 : 3. Find the area (in square cm) of triangle EFC.
(1) root3 (2) root3/2 (3) root3/4 (4) root2 (5) 3*root3/2