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GMAT - Arithmetic Questions And Answers

Published: Saturday, 30 January, 2016 9:00 AM


1. A boy was asked to multiply a certain number by 45. He multiply it by 75 and got his answer more than the correct one by 180 what was the number?
    A. 6
    B. 18
    C. 30
    D. 32
    E. 36

2. Fill in the blank indicated by the * in the number 4 * 56 so as to make it divisible by 33?
    A. 3
    B. 4
    C. 5
    D. 6
    E. 8

3. Three bells ring together at intervals of 12, 15 and 18 sec. respectively, then how many times do they ring together in one hour if they start simultaneously?
    A. 18
    B. 20
    C. 21
    D. 22
    E. 24
    
4. A grey hound pursues a hare and takes 5 leaps for every 6 leaps of the hare, but 4 leaps of the hound are equal to 5 leaps of the hare. Find the ratio of distance travelled by hound and hare.
    A. 24:25
    B. 25:24
    C. 5:6
    D. 6:7
    E. None of these

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5. John, Marty and Fred starts a fast food restaurant, with contributions of $2,500, $3,000 and $1,500 respectively. After six months Marty withdraws $1,000 from the business and after 9 months Fred invests an additional $1,500 in the business. If their profit in one year of operations was $2750, then John’s share of profit is
    A. $1000
    B. $550
    C. $750
    D. $850
    E. $950

6. The average age of a group of p boys is q years. Three new boys join the group. Their ages are q – 1, 2q + 1 and 2. What is the new average age of the group?
    A. (pq + 3q + 2)/p+3
    B. (pq + 2)/q+3
    C. (3pq + p + q)/p+3
    D. (pq + 3q + 2)/p+3 
    E. None of these

7. 3 gallons are drawn from a cask full of wine containing 27 gallons. The cask is then filled with water. 3 gallons of the mixture are again drawn and the cask is again filled with water. What is the ratio of water to wine now?
    A.  27/64
    B.  64/81
    C.  8/9
    D.  9/8
    E. None of these

8. A given sample of 50 litres of glycerin was found to be adulterated to the extent of 20%. How much of pure glycerin should be added to bring down the percentage impurity to 10%?
    A. 50 litres
    B. 37.5 litres
    C. 12.5litres
    D. 15 litres
    E. 18 litres

9. A businessman knows that the price of commodity will increase by Rs. 5 per packet. He bought some packets of this commodity for Rs.4500. If he bought this packet on new price then he gets 10 packets less. What is the number of packets bought by him?
    A. 90
    B. 100
    C. 50
    D. 125
    E. 145

10. 4 men and 6 women finish a job in 8 days, while 3 men and 7 women finish it in 10 days. In how many days will 10 women will take to finish it?
    A. 40 days
    B. 42 days
    C. 44 days
    D. 46 days
    E. 48 days

Solutions

1. A
    Let the number be x.  75x - 45x = 81, x = 6.

2. A
    Taking * = 3, number becomes 4356 which is divisible by 3 as well as by 11.  The number is divisible by 33.

3. C
    If they start together they will again ring together after LCM of 12, 15, 18 = 180 seconds= 3 minutes.   In 1 hour, they will ring together 20 times.

4. B
    Distance = Speed x Time.  The ratio of distance travelled = 25 : 24.

5. A
    Total contribution of John 2500 x 12 = $30000.
    Total contribution of Marty 3000 x 6 + 2000 x 6 = $30000.
    Total contribution of Fred 1500 x 9 + 3000 x 3 = $22500.

Therefore, John’s share of profit = 30,000/(30,000 + 30,000 + 22500) x 2750 = $1000.

6.  A
    Total age of p boys = pq. Total age of all boys after 3b more boys join = pq + q + -1 +2q +1 +2 = pq + 3q + 2.

Therefore, average age of the group = (pq + 3q + 2)/p+3

7. E

Wine left/capacity = (c-d/c)n , where d = mixture drawn out at a time, c = capacity, n = no. of operations.

Wine left/Capacity = (27-3/27)n = 64/81 .cap

Water : Wine = (81 – 64) : 64 = 17 : 64.

8. A
    Amount of pure glycerin in 50 litres = 80 % of 50 = 40 litres.

Required level of impurity = 10 %.

Let x of pure glycerin be added, then the quantity of pure glycerin = (40 + x) and amount of pure glycerin in solution = 90% of (50 + x).

Therefore, 40 + x = 90% of (50 + x), => x = 50 litres.

9. B
    Let the numbers of packets purchased by the businessman be x.

Then, 

Hence no. of packets = 100.

10. A
    If 4 men and 6 women can do it in 8 days the 32 men and 48 women can do it in 1day.

Similarly, 30 men 70 women can do it in a day.

Equating, 32 men + 48 women = 30 men + 70 women.

=> 2 men = 22 women, or 1 man = 11 women.

=> 32 men + 48 women = (32x11 + 48) women 400 women.

=> 1 woman will take 400 days to complete the work.

=> 10 women will take 40 days to complete the work.

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