# IIM CAT Preparation Tips

IIM CAT Preparation Tips: August 2013

## Aug 24, 2013

### Profit and Loss Question

Question:
A merchant can buy goods at the rate of Rs. 20 per good. The particular good is part of an overall collection and the value is linked to the number of items that are already on the market. So, the merchant sells the first good for Rs. 2, second one for Rs. 4, third for Rs. 6…and so on. If he wants to make an overall profit of at least 40%, what is the minimum number of goods he should sell?
A.  24
B.  18
C.  27
D.  32

Explanation:
Let us assume he buys n goods.
Total CP = 20n
Total SP = 2 + 4 + 6 + 8 ….n terms
Total SP should be at least 40% more than total CP
2 + 4 + 6 + 8 ….n terms > 1.4 * 20 n
2 (1 + 2 + 3 + ….n terms) > 28n
n(n + 1) > 28n
n2 + n  > 28n
n2 -  27n  > 0
n > 27
He should sell a minimum of 27 goods.

## Aug 21, 2013

### CAT - Percents

Question:

P is x% more than Q. Q is (x - 10)% less than R. If P > R, what is the range of values x can take?
A.  10% to 28%
B.  10% to 25%
C.  10% to 37%
D.  10% to 43%

Explanation:

P = Q

Q = R

R =

P > R

(100 + x) (110 – x) > 100 x 100

11,000 + 110x – 100x – x2 > 10000

1000 + 10x – x2 > 0

x2 – 10x – 1000 < 0

x2 – 10x + 25 < 1000 + 25

(x – 5)2 < 1025

x – 5 < 32

x < 37

x could range from 10% to 37%

Difficulty level II

## Aug 16, 2013

### Number Theory Questions and Solutions

Question:
How many numbers with distinct digits are possible product of whose digits is 28?
A.  6
B.  4
C.  8
D.  12

Explanation:

Two digit numbers; The two digits can be 4 and 7: Two possibilities 47 and 74
Three-digit numbers: The three digits can be 1, 4 and 7: 3! Or 6 possibilities.

We cannot have three digits as (2, 2, 7) as the digits have to be distinct.

We cannot have numbers with 4 digits or more without repeating the digits.

So, there are totally 8 numbers.

Difficulty Level 2

## Aug 12, 2013

### CAT - Logarithms

Question:
If log2X + log4X = log0.25and x > 0, then x is
A.  6-1/6
B.  61/6
C.  3-1/3
D.  61/3

Explanation:

log2x + log4x = log0.25

log2x + = log0.25

log2x * = log0.25

log2x * 3 = 2log0.25

log2x3 = log0.256

log2x3 = -log46

log2x3 =

log2x3 =

2log2x3 = -log26

2log2x3 + log26 = 0

log26x6 = 0

6x6 = 1

x6 =

x =  Choice (A).

Level of difficulty 2