IIFT 2015 Question Paper

Given that p, q and r are in A.P., 

2q = p + r

p = 2q - r                                   Eq -1

Given that p, r-q and q-p are in G.P.,

Let us assume the common ratio of k in G.P.

r-q = k(p)                                   Eq -2

q-p = k(r-q)                               Eq -3

q-p = $$k^{2}$$(p)                               Eq -4

Substitute Eq-1 in Eq-3,

q-(2q-r) = k(r-q)

r-q = k(r-q)

So, k=1

From Eq -4, we get q=2p

Now substitute q=2p in Eq-1 we get r=3p

Hence, ratio of p:q:r = p:2p:3p = 1:2:3 

$$log_{25}{5}$$ = a 

=> a=1/2

$$log_{25}{15}$$ = $$log_{25}{3}+log_{25}{5}$$ = b

$$\frac{1}{2} \log_{5}{3} + \frac{1}{2}$$ = b

$$\log_{5}{3}$$ = 2(b -  $$\frac{1}{2})$$.............(i)

$$log_{25}{27}$$ = $$\frac{3}{2} \log_{5}{3}$$.........(ii)

Replacing $$\log_{5}{3}$$ = 2(b -  $$\frac{1}{2})$$ in (ii) we get

$$log_{25}{27}$$ = 3(b -  $$\frac{1}{2}$$)

We can write -$$\frac{1}{2}$$ as (- 1 + $$\frac{1}{2}$$) or (-1 + a)

So, $$log_{25}{27}$$ = 3(b + a - 1)

Hence, option C is the correct answer.

Consider the case where batchmates are sitting together and then subtract those cases from total no. of cases.

When 10 students are arranged in a line, total arrangements possible are 10!

Now considering batchmates sitting together, 

B1 B2  _ _ _ _ _ _ _ _

Then total arrangements possible are 9!*2!

Total ways = 10! - 9!*2!

9!*8 =  2903040

Let the value of pre-paid recharge of Vodafone be 100.

Then the value of pre-paid recharge of Airtel is 79.

Airtel gives 12% more to post-paid, so post-paid value is 79 x 1.12 = 88.48

Vodafone gives 15% less to post-paid than its pre-paid so its value is 85.

Clearly Airtel gives more to its post-paid customers.

Percentage = $$\frac{3.48}{85}$$ x 100 = 4.09%
Therefore, option A is the right answer. 

Let the original service charge be Rs. 1000
1st service charge = Rs. 1000
2nd service charge @ 10% discount = Rs. 900
3rd service charge @ 11% discount = Rs. 801
4th service charge @ 12% discount = Rs. 704.88
5th service charge @ 45% = Rs. 450
Total service charge for Rohan = Rs. 1000 + Rs. 900 + Rs. 801 + Rs. 704.88 + Rs. 450 = Rs. 3855.887
Discount % = 22.88%
Hence, option B is the correct answer.

Let the number of inlet pipes be x, then the number of outlet pipes will be 11-x.

The rate of emptying the tank is more than filling the tank if all the pipes are kept opened.

$$\frac{11-x}{5}$$ - $$\frac{x}{7}$$ = $$\frac{1}{7}$$

Solving, 12x =72,Hence x = 6

Therefore, the number of inlet pipes is 6.

22% of the families own agricultural land, 18% own a mobile phone, 1600 families own both and 68% families own none.

P(A $$\cup$$ B) = P(A) + P(B) - P(A $$\cap$$ B)

32 = 22 + 18 - x

x=8. Hence, there will be 8% families who own both.

8% =1600 (Given in question)

Total families in a village =>100% = 20000

Total handshakes are given by: N$$C_2$$

N$$C_2$$ = 78

$$\frac{N*(N-1)}{2}$$ = 78

N=13

Hence, option D is the correct answer.

We have to find for how many pages, the cost of printing including the price of the printer, will be same for both the printers.

Let the number of pages be n

For inkjet printer, the cost is 5000 + 1.80*n

For laser printer, the cost is 8000 + 1.50*n

Equating: 5000 + 1.80*n = 8000 + 1.50*n

n=10000

For n>10000, the per page printing cost is lesser for laser printer than inkjet printer.

So, firm should purchase laser printer if number of pages printed are more than 10000.

Hence, option B is the correct answer.

Length of arc XZ is the perimeter of quarter circle.

$$\frac{\pi r}{2}$$ = 10$$\pi$$

r=20

Area of sector XYZ = Area of quarter circle = $$\frac{\pi r^{2}}{4}$$ 

Area = 100$$\pi$$