TANCET 2012 Quant - Qn 43

This question tests your ability to express one variable in terms of the other. Level of difficutly easy.

If x = 2k – 2 and y = 4k^2, then what is y in terms of x?
1. x + 2
2. ((x + 2)^2)/2
3. (x + 2)^2
4.  x^2 + 4
5. (x + 4)^2

TANCET 2008 Quant Qn 9 - Geometry, Mensuration

Question 9 : Geometry - Right Triangles : If the shaded area is one half the area of triangle ABC and angle ABC is right angle, then the length of line segment AD is

1. 
2. c
3. 
4. 
5. 

Profit Loss Question

Profit Loss is a relatively easy topic and quite often gets tested in these kinds of entrance tests.

Question

If the cost price of 12 articles is the same as the selling price of 10 of those articles, what percent profit does the trader make?
1. 16.66%
2. 20%
3. 25%
4. 16.66% loss
5. 20% loss

Correct Answer: Choice (2) - 20% profit.

Explanatory Answer

Let the cost of 12 articles = Rs.x

Hence, the cost of 1 article = x/12

So, the selling price of 10 articles = Rs.x

Hence, the selling price of 1 article = x/10

The quickest way to solve this question is to assume some value for x. Assume x to be a number that is divisible by 12 and 10.

So, x should be a multiple of 12 and 10. Take x to be 120.

So, the cost of 12 articles = 120. Therefore, the cost of 1 article = Rs.10

The selling price of 10 articles = 120. Therefore, the selling price of 1 article = Rs.12.

The profit on 1 article = Selling price - Cost price = 12 - 10 = Rs.2

Percent Profit = (Profit / CP) * 100 = (2/10)*100 = 20%

TANCET Quant : Linear Equations, Word Problems

Here is a word problem that requires you to frame a pair of linear equations, solve the equations to arrive at an answer.

Rajesh is 10 years younger to Baskar. 10 years back, Rajesh's age was two-thirds that of Baskar's. How old is Baskar now?
1. 30
2. 40
3. 20
4. 16
5. 28

Correct Answer is Choice (2). 40 years.

Explanatory Answer

Let the present age of Baskar be 'b' and that of Rajesh be 'r'.
So, r = b - 10 .... eqn (1).

10 years back Rajesh was (r - 10) years old. 10 years back Baskar was (b - 10) years old.
The question states that 10 years back Rajesh was two thirds as old as Baskar was.

i.e., (r - 10) = (2/3)*(b - 10) .... eqn (2).
Cross multiplying, we get 3(r - 10) = 2(b - 10)
or 3r - 30 = 2b - 20 .... eqn (2)

From eqn (1) we can substitute r as (b - 10) in eqn (2)
So, 3(b - 10) - 30 = 2b - 20
or 3b - 30 - 30 = 2b - 20
or b = 40.

The present age of Baskar is 40 years.

TANCET Quant : Progressions

AP, GP (Arithmetic Progressions and Geometric Progressions) are two topics from which you could expect to get at least one question.

An interesting topic and the kind of questions that you can expect in the TANCET quant section from these two topics will be rather elementary.

The AP topic has two formulae to remember.

The first one is to find the nth or the last term 'l' of an AP : l = a + (n - 1)d, where 'a' is the first term, n is the number of terms and 'd' is the common difference.

The second formula is to find the sum of first 'n' terms of an AP. Sn = (n/2)(2a + (n - 1)d)

Here is a question that tests your understanding of these concepts.

If the first term of an AP is 12 and the 7th term is 36, what is the sum of these 7 terms?

1. 240

2. 168

3. 336

4. 84

5. 121

Explanatory Answer

The first term a = 12

The 7th term l = 36.

We know that l = a + (n - 1)d

or 36 = 12 + (7 - 1)d

or 24 = 6d

or d = 4.

Sum of these first 7 terms = (n/2)(a + (n - 1)d), where n = 7, a = 12, d = 4

Substituting we get, (7/2)(2*12 + (7 - 1)4)

= (7/2)(24 + 24)

= 7 * 24

= 168

Choice (2) is the correct answer.