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ACT Sample Questions : Mathematics

91. Find the sum of all the integers which are multiples of 7 and lie between 200 and 400.
    1. 8729
    2. 8700
    3. 8428
    4. None of these

    Answer: A

92. How many digits will the number 3²⁰⁰ have if the value of log 3 = 0.4771?
    1. 95
    2. 94
    3. 96
    4. None of these

    Answer: C

93. A and B enter in to a partnership and A invests Rs. 10,000 in the partnership. At the end of 4 months he withdraws Rs.2000. At the end of another 5 months, he withdraws another Rs.3000. If B receives Rs.9600 as his share of the total profit of Rs.19,100 for the year, how much did B invest in the company?
    1. 12,000
    2. 96,000
    3. 8000
    4. 6000

    Answer: C

94. The sum of the first and the 9th of an arithmetic progression is 24. What is the sum of the first nine terms of the progression?
    1. 216
    2. 108
    3. 54
    4. None of these

    Answer: B

95. What is the equation of the line that is parallel to the line 3x + 7y = 10 and passes through the point (4, 8)
    1. 7x - 3y = 46
    2. 3x + 7y = 44
    3. 9x + 21y - 184 = 0
    4. 3x + 7y = 68

    Answer: D

96. Ram and Shyam take a vacation at their grandparents' house. During the vacation, they do any activity together. They either played tennis in the evening or practiced Yoga in the morning, ensuring that they do not undertake both the activities on any single day. There were some days when they did nothing. Out of the days that they stayed at their grandparents' house, they involved in one of the two activities on 22 days. However, their grandmother while sending an end of vacation report to their parents stated that they did not do anything on 24 mornings and they did nothing on 12 evenings. How long was their vacation?
    1. 36 days
    2. 14 days
    3. 29 days
    4. Cannot be determined.

    Answer: C

97. Ram buys Rs.100 shares at Rs.112. If he sells the shares after a year at Rs.132 after receiving a dividend of 8% just before selling, what is the net yield on his investment?
    1. 17.85%
    2. 6.06%
    3. 32%
    4. 25%

    Answer: D

98. The sum of 20 terms of the series 12 + 22, 32 + 42, 52 + 62 is:
    1. 210
    2. 519
    3. 190
    4. None of these.

    Answer: A

99. A tank is fitted with 8 pipes, some of them that fill the tank and others that are waste pipe meant to empty the tank. Each of the pipes that fill the tank can fill it in 8 hours, while each of those that empty the tank can empty it in 6 hours. If all the pipes are kept open when the tank is full, it will take exactly 6 hours for the tank to empty. How many of these are fill pipes?
    1. 2
    2. 4
    3. 6
    4. 5

    Answer: B

100. If A and B work together, they will complete a job in 7.5 days. However, if A works alone and completes half the job and then B takes over and completes the remaining half alone, they will be able to complete the job in 20 days. How long will B alone take to do the job if A is more efficient than B?
     1. 20 days
     2. 40 days
     3. 30 days
     4. 24 days

     Answer: C