# Arithmetic (Test 3)

## Cat Entrance Exams : Mathematics Or Quantitative Aptitude

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Arithmetic
| Arithmetic |
Q.1
There are 3 Indians and 3 Chinese in a group of 6 people. How many subgroups of this group can we choose so that every subgroup has at least one Indian?
A. 56
B. 52
C. 48
D. 44
Explaination / Solution:

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Q.2
If  then the value of x is
A. 343/125
B. 125/343
C. -25/49
D. -49/25
Explaination / Solution:

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Q.3
A cube of side 3 units is formed using a set of smaller cubes of side 1 unit. Find the proportion of the number of faces of the smaller cubes visible to those which are NOT visible.
A. 1 : 4
B. 1 : 3
C. 1 : 2
D. 2 : 3
Explaination / Solution:

Consider the cube of side 1 unit shown below.

Now, a set of similar cubes as shown above is joint to form a cube of side 3 units, we have to determine the ratio of faces of smaller cubes visible to those which are not visible . Complete surface area of the cube of side 3 units determined as
A = 6 × (3)2
=54
Again, the area of one face of cube of side 1 unit is
A(1)2 = 1
So, the total number of visible faces is
Nvisible = (A/A1)= 54
Again, total number of smaller cubes required to form the big cube is
Number of smaller cubes = volume of cube of side unit/volume of cube of side unit
= (3)3/(1)3 = 27
So, the total number of faces of smaller cubes is given as
Ntotal = 6 × (number of smaller cubes)
= 6 × 27 = 162
Therefore number of invisible faces is
Ninvisible = Ntotal - Nvisible
= 162 - 54 = 108
Hence, the desired ratio is
(Nvisible /Ninvisible) = 54/108 = 1/2

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Q.4
In a 2 × 4 rectangle grid shown below, each cell is a rectangle. How many rectangles can be observed in the grid?

A. 21
B. 27
C. 30
D. 36
Explaination / Solution:

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Topic: Arithmetic Tag: ME GATE 2011
Q.5
A transporter receives the same number of orders each day. Currently, he has some pending orders (backlog) to be shipped. If he uses 7 trucks, then at the end of the 4th day he can clear all the orders. Alternatively, if he uses only 3 trucks, then all the orders are cleared at the end of the 10th day. What is the minimum number of trucks required so that there will be no pending order at the end of the 5th day?
A. 4
B. 5
C. 6
D. 7
Explaination / Solution:
No Explaination.

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Q.6
If |9y−6| = 3, then y2 −4y/3 is ________ .
A. 0
B. +1/3
C. −1/3
D. undefined
Explaination / Solution:

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Q.7
A product made in two factories p and Q, is transported to two destinations, R and S. The per unit costs of transportation (in Rupees) from factories to destinations are as per the following matrix:

Factory P produces 7 units and factory Q produces 9 units of the product. Each destination requires 8 units. If the north-west corner method provides the total transportation cost as X (in Rupees) and the optimized (the minimum) total transportation cost Y (in Rupees), then (X-Y), in Rupees, is
A. 0
B. 15
C. 28
D. 105
Explaination / Solution:

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Topic: Arithmetic Tag: ME GATE 2009
Q.8
Consider the following PERT network:

The optimistic time, most likely time and pessimistic time of all the activities are given in the table below.
The standard deviation of the critical path is
A. 0.33
B. 0.55
C. 0.77
D. 1.66
Explaination / Solution:
No Explaination.

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Q.9
A cube is built using 64 cubic blocks of side one unit. After it is built, one cubic block is removed from every corner of the cube. The resulting surface area of the body (in square units) after the removal is.
A. 56
B. 64
C. 72
D. 96
Explaination / Solution:

Four blocks are needed for each direction(totally 3 directions) to build a bigger cube containing 64 blocks. So area of one side of the bigger cube = 4 ×4 = 16units There are 6 faces so total area = 6 × 16 = 96units When cubes at the corners are removed they introduce new surfaces equal to exposes surfaces so the area of the bigger cube does not change from 96

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Topic: Arithmetic Tag: EE GATE 2012
Q.10
R aju has 14 currency notes in his pocket consisting of only Rs. 20 notes and Rs. 10 notes. The total money value of the notes is Rs. 230. The number of Rs. 10 notes that Raju has is
A. 5
B. 6
C. 9
D. 10