Ques 1.Let K be a positive number such that K + 4 is divisible by 7, Then the smallest positive integer n, greater than 2, such that K + n2 is divisible y 7 equals
Ans 1. K + 4 is divisible by 7
. . K is of the form 7h + 3
k + n2 or 7h + 3 + n2 is divisible by 7.
i.e. 3 + n2 is divisible by 7.
=> the smallest value of n (> 2) possible is 5.
Ques 2.If x is a positive integer such that x2 + 12 is perfectly divisible by x, then the number of possible values of x is
Ques 3.The rate of increase of the price of sugar is observed to be two per cent more than the inflation rate expressed in percentage. The Price of Sugar on January 1, 1994 is Rs 20 per kg. The inflation rates for the years 1994 and 1995 are expected to be 8% each. The expected price of sugar on Juanuary 1, 1996 would be
(a) Rs 23.60
(b) Rs 24.00
(c) Rs 24.20
(d) Rs 24.60
Ques 4.Sheila has scored 65,90, 75, 70 and 85 marks in the preliminary tests.If the final test has twice as much weightage as the preliminary tests, what must be her mark in the final test to raise her average to 80 per cent ?
Ans 4. Let the mark in the final test be x.
Ques 5.The least number which must be subtracted from 6708 to make it exactly divisible by 9 is
Ans 5. 6 + 7 + 0 + 8 = 21
To make 6708 divisible by 9, 3 must be subtracted from 21 . Hence, 3 must be subtracted from 6708 to make it exactly divisible by 9.
Ques 6.The average temperature from 9th to 16th of a month was 32C and that o f from 10th to 17th of the same month was 30C. The temperature on 9th was 35C what was the temperature on 17th ?
(d) None of these
Ans 6. Sum of temperature from 9th to 16th = 32 x 8 = 256oC
Sum of the temperature from 10th to 17th = 30 x 9 = 240oC
Temperature on 17th = ( 240 - 256 + 35)oC
Ques 7.How much 3% stock at 84 1/4 be sold to realise Rs 12600 ?
(a) Rs 12600
(b) Rs 15000
(c) Rs 14750
(d) Rs 13700
Ques 8.A tank 25 m long, 20 m broad and 15 m deep is dug in a field 400 m long and 20 m wide . By how much will the level of the field rise if the earth dug out of the tank is evenly spread over the field ?
(a) 1 m
(b) 0.5 m
(c) 2.5 m
(d) 0. 25 m
Ans 8. Volume of the earth dug out
= 25 x 20 x 15 m3 = 7500 m3
evenly spread = 400 x 20 - 25 x 20 m2
= 7500 m2
. . Rise in the level of the field = 7500/7500 m
Ques 9.If 24 men working 8 hours a day can do a piece of work in 18 days, in hoe many days will be men working 12 hours a day finish the same work ?
(a) 6 days
(b) 8 days
(c) 10 days
(d) 12 days
Ques 10.The average of five consecutive prime numbers starting from 3 is