In this article certain questions have been randomly taken from different topics of the quantitative section of CAT. Each question has been selected keeping in mind certain challenges you need to manage as a test taker. These challenges may range from concept basics to application orientation and test taking strategies.

1. 0

2. 1

3.n/2

4. (n+1)/2n

Further the integers are all consecutive numbers. Hence the difference of the average of the odd and even integers will be one.

Alternatively,

Sum of odd integers in S = X=n/2(2*3 + (n-1)*2)= n+2

Sum of even integers in S= Y=n/2(2*2+(n-1)*2)= n+1

Thus X-Y= (n+2)-(n+1) = 1

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1. 6

2. 4

3. 7

4. 3

Rearranging, 1/m = 1/12 – 4/n

Solving, m= 12n/(n-48)

For m to be an integer, (n-48) has to be a factor of 12n

Thus n take only three values– 49, 51 and 57.

Hence there are three pairs of (m,n) which satisfy the given conditions.

1. 17

2. 16

3. 18

4. 15

Thus x + 10y + 50z = 107

Now the possible values of z could be 0, 1 and 2

For z=0, the equation will be x+10y= 107

Number of integer pairs of values of x and y that satisfy the equation will be (7,10), (17,9), (27,8)…..(107,0)- a total of 11 values

For z=1, the equation will be x+10y+50=107 or x+10y=57

Number of integer pairs of values of x and y that satisfy the equation will be (7,5), (17,4), (27,3)…..(57,0)- a total of 6 values

For z=2, the equation will be x+10y+100=107 or x+10y=7

There is only one integer value of x and y that satisfies the equation and that is (7,0)

The total number of values is 11+6+1= 18.

Mark (1) if the questions can be answered using A alone but not using B alone

Mark (2) if the questions can be answered using B alone but not using A alone

Mark (3) if the questions can be answered using A and B together but not using A or B alone

Mark (4) if the questions cannot be answered even using A and B together

Consider integers x,y,z. What is the minimum possible value of x

A. x+y+z = 89

B. Among x, y, z, two are equal

If the sum is fixed, the numbers have to be as close to each other as possible, for minimum value of the sum of their squares

Using B, nothing specific can be derived about the relation between x, y and z.

Free Master Classes:

A. The inner diameter of the tank is atleast 8 metres.

B. The tank weighs 30,000 kg when empty, and is made of material with density of 3 gm/cc.

So, volume = 4/3 π r

Using B: The given data gives the volume of the material of the tank, which can be expressed as

4/3 π (5