Problems To Prepare For IBM Aptitude Tests

Question 1

An exhibition was conducted for 4 weeks. The number of tickets sold in 2nd workweek was increased by 20% and increased by 16% in the 3rd workweek but decreased by 20% in
the 4th workweek. Find the number of tickets sold in the beginning, if 1392 tickets were sold in the last week.

a) 1750 b) 1550 c) 1250 d) 1000

Answer : c) 1250

Solution :

Note that, "If a number A is increased successively by x% followed by y% and then by z%, then the final value of A will be A(1 + x/100)(1 + y/100)(1 + z/100)"

Number of tickets sold in last week = 1392.
i.e.,A(1 + x/100)(1 + y/100)(1 + z/100) = 1392.

We have to find the sale of tickets in 1st week, that is A.
Therefore, A = 1392/(1 + x/100)(1 + y/100)(1 + z/100).
And, x = 20, y = 16 and z = (-20). (Since the sale of ticket decreased by 20% in the last week).
Required number = A = 1392/(1 + 20/100)(1 + 16/100)(1 - 20/100)

Using (a² - b² ) = (a + b)(a - b) for the terms (1 + 20/100)(1 - 20/100).
We have, A = 1392/(1 - (20/100)² )(1 + 16/100)
= 1392 /(1 - 400/10000)(116/100) = 1392/(1 - 400/10000)(116/100)
= 1392 /(9600 / 10000)(116 / 100)
= 1392 x 10000 x 100 / 9600 x 116 = 1250.
Hence, the number of tickets sold in the 1st workweek was 1250.

Question 2

The drink rate from a certain company has ups and downs every year. The rate of 1/2 litre drink increases for two consecutive years consistently by 30% and in the third year decreases by 20%. The same effect repeats for every three years. If we start counting from the year 2008 then what will be the effect on the rate of the drink in 2012?

a) Increases by 75.76% b) Decreases by 70.08% increase c) Increases by 68.69% d) Decreases by 52.52%

Answer : a) Increases by 75.76%

Solution :

From the question, we can infer that for two consecutive years the rate increases by 30%.
Now we have to started counting from the year 2008. For the next two years (i.e., 2009 & 2010) the rate increases by 30%.
In the third year, the rate decreases by 20%. Here the third year is 2011.

Since the effect is repeats for every three years, the next year i.e., 2012 will get an increase by 30% and the process continues.

Let us assume that the rate of drink in 2008 as Rs. 100.
Using the formula, A(1 + x/100)(1 + y/100)(1 + z/100)
Here A = 100.

Rate of the drink in the year 2012 = 100 x (1 + 30/100)(1 + 30/100)(1 - 20/100)(1 + 30/100)
= 100 (130/100) (130/100) (80/100) (130/100)
= 8x13³ / 100 = 175.76
Therefore, the effective percentage increase = Rate of the drink in the year 2012 - Rate of the drink in the year 2008 = 175.76 - 100 = 75.76.
Hence, the answer is 75.76% increase.

Question 3

The cost of two varieties of paint is Rs.3969 per 2 kg and Rs.1369 per 2 kg respectively. After how many years will the value of both paint be the same, if variety1 appreciates at 26% per annum and variety2 depreciates at 26% per annum?

a) 3 b) 4 c) 1 d) 2

Answer : d) 2.

Solution :

Note that, "If the value P depreciates at the rate of R% per annum then after n years it becomes = P x (1 - R/100)ⁿ and if the value of P appreciates at the rate of R% per annum then after n years it becomes = P x (1 + R/100)ⁿ".

Let the required time be n years.
Given that, the cost of variety1 is Rs.3969 and depreciates at the rate of 26% per year.
Therefore, the cost of variety1 after n years = P x (1 - R/100)ⁿ = 3969 x (1- 26/100)ⁿ= 3969 x (74/100)ⁿ...(1)

And, the cost of variety2 is Rs.1369 and appreciates at the rate of 26% per year.
Therefore, the cost of variety2 after n years = P x (1 + R/100)ⁿ = 1369 x (1+ 26/100)ⁿ = 1369 x (126/100)ⁿ...(2)

From the given condition, we have (1) and (2) are equal.
i.e., 3969 x (74/100)ⁿⁿⁿ = 1369 x (126/100)ⁿ

3969/1369 = (126/74)ⁿ(63/37)²= (63/37)ⁿn = 2.

Hence the required answer is 2 years.