# Intern Placement Prep

Hello Junta! We’re back with our next issue.

To all the creative minds out there who are curious about us, I’d like to welcome you to InvestmentEtc, a magazine published by the Finance Club at IIT Madras.

Finance is vital in school, college, and where not. Whether it be to extend your Gpay balance or your non-core interns and placements (yes, we’ve seen it happen when the core trial phase tests negative). Nobody tells you what to do or how to prepare. This can be puzzling and stressful. That’s where we attempt to be your one-stop shop and go-to guide.

Find below some of the interesting content from the immeasurable amount of resources to get you going with your journey in finance to crack profiles like Analyst or Quant.

**SECTION 1: Practice Questions**

In this section, you can find six practice questions with answers and explanations asked by companies that hired analysts in past years.

1.**( American Express, Easy)** If a + 1/a = √3, then the value of a^18 + a^12 + a^6 + 1 is

**Soln: **

a^3 + 1/a^3 = (a + 1/a)^3 – 3(a + 1/a)

=> 3 √3 – 3 √3 = 0

So a^3 + 1/a^3 = 0

Thus a^6 + 1 = 0

Then,

a^18 + a^12 + a^6 + 1

a^12(a^6 + 1) + (a^6 + 1)

a^12 x 0 + 0 = 0

2. ** (JPMC, Easy)** A rubber ball rebounds (5/6)th of its height after striking to the ground from which it has fallen. Find the total distance that it travels before coming to rest, if it is gently dropped from a height of 360 meters.

**Soln:**

It becomes an infinite sum of series.

So, use a/(1-r) to calculate the distance

Ball rebounds to 5/6 of its height → 360x (5/6) = 300

[360/1 – (5/6)] + [300/1-(5/6)] [360/(1/6)] + [300/(1/6)]= 2160 + 1800

= 3960

Hence, the total distance traveled by the ball is **3960 meters**.

3. ** (Goldman Sachs, Hard) **The banker’s discount on a sum of money for 1.5 years is Rs.558 and the true discount on the same sum for 2 years is Rs.600. The rate percent is:

**Soln:**

B.D for 1.5 years = Rs 558

B.D for 2 years = Rs 558 x ⅔ x 2 = Rs 744

T.D for 2 years = Rs 600

Therefore, sum = B.D x T.D / (B.D – T.D)

= (744 x 600) /( 744- 600)

= 3100

So Rs 744 is the SI on Rs 3100 for 2 years

Rate = (744 x 100) / (3100 x 2) % = **12%**

4. ** (JPMC, Intermediate)** Pick the odd one out in this sequence : 7, 8, 18, 57, 228, 1165, 6996 :

**Soln:**

The odd one out is **228**

Let the given numbers be A, B, C, D, E, F, G.

Then, A, A x 1 + 1, B x 2 + 2, C x 3 + 3, D x 4 + 4, E x 5 + 5, F x 6 + 6 are the required numbers.

5. ** (Goldman Sachs, Intermediate) **X lies from 121 to 1331 (121<X<1331) and X^2 + 1 when divided by 11, what will not be the remainder?

a) 1 b) 4 c) 6 d) 8

**Soln:**

Since X should be greater than 121, let y be a whole number greater than 0, X^2 + 1 can be written as (121 + y)^2 + 1

Dividing this expression by 11, we get

y^2 / 11 + 121^2 / 11 + 2*y*(121)/11 + 1/11

That is, (y^2 + 1)/11 and y^2 can be 1,4,9,16,25……

So the remainder can be 1,4,6 but not 8.

The answer is **8.**

6. ** (American Express, Hard)** Two containers, A and B have certain quantities of the mixture in them. In container A, three liquids X, Y and Z are mixed in the ratio of 5 : 4 : 3 respectively and in container B two liquids Y and Z are mixed in the ratio of 16 : 15 respectively. Mixtures from both containers A and B are poured into an empty container C. The ratio of the quantities of liquids X, Y and Z in container C becomes 25 : 68 : 60 respectively. Quantity of mixture in container B is how much percent less or more than the quantity of mixture in container A?

**Soln:**

Let in A, the quantity of liquid X, Y and Z is ‘5x’, ‘4x’ and ‘3x’ liters respectively. And in B, quantity of liquid Y and Z is ‘16y’ and ‘15y’ respectively

According to the question:

(5x) : (4x + 16y) : (3x + 15y) = 25:68:60

So, [5x/ (4x+16y)] = 25/68

[5x / (x + 4y)] = 25/1785x = 25x + 100y

60x = 100y

3x = 5y

And, (4x+16y) / (3x+15y) = 68/ 60

(x+4y)/ (x+5y) = 17/20

20x + 80y = 17x + 85y

3x = 5y

So, x=5, y=3

Quantity in container A = 12x = 60 liters

Quantity in container B = 31y = 93 liters

Desired percentage = [ {(93-60)/ 60} * 100] = **55%**

Stay tuned for the next issue!