Aptitude and Reasoning Questions

Let the rate be R% p.a.

I  gives, P = Rs. 8000 and T = 4 years.

II gives, S.I = Rs. (8800 - 8000) = Rs. 800.

R = [100 x S.I] / [p x t ]= (100 x 800)/(8000 x 4) = 2 ½ % p.a

Thus, I and II both are needed to get the answer.

fix one person and the brothers B1 P B2 = 2 ways to do so.
other 17 people= 17!

 
Each person out of 18 can be fixed between the two=18, thus, 2 x 17! x 18=2 x 18!

A perfect cube will have prime factors that are in groups of 3; for example 125 has the prime factors 5 x 5 x 5 , and 64 x 125 will also be a cube because its factors will be 4 x 4 x 4 x 5 x 5 x 5

Consider the answer choices in turn.

8 is the cube of 2, and p is a cube, and so the product will also be a cube.

pq will also be a cube as shown above.

pq is a cube and so is 27, but their sum need not be a cube. Consider the case where p =1 and q = 8, the sum of pq and 27 will be 35 which has factors 5 x 7 and is not a cube.

-p will be a cube.

Since the difference between p and q is raised to the power of 6, this expression will be a cube (with cube root = difference squared).

The figure may be labelled as shown

Rectangles :

The simplest rectangles are CVSR, VETS, RSWM and STKW i.e 4 in number.

The rectangles composed of two components each are CETR, VEKW, RTKM and CVWM i.e 4 in number.

The rectangles composed of three components each are ACRP, PRMO, EGHT and THIK i.e 4 in number.

The rectangles composed of four components each are CEKM, AVSP, PSWO,VGHS and SHIW i.e 5 in number.

The rectangles composed of five components each are AETP, PTKO, CGHR and RHIM i.e 4 in number.

The rectangles composed of six components each are ACMO and EGIK i.e 2 in number.

The rectangles composed of eight components each are AGHP, PHIO, AVWO and VGIW i.e 4 in number.

The rectangles composed of ten components each are AEKO and CGIM i.e 2 in number.

AGIO is the only rectangle having sixteen components

Total number of rectangles in the given figure = 4 + 4 + 4 + 5 + 4 + 2 + 4 + 2 + 1 = 30.

Hexagons :

The hexagons in the given figure are CDEKLM, CEUKMQ, CFHJMQ, BEUKNP and BFHJNP. So, there are 5 hexagons in the given figure.

Given that Rs. 1860 will become Rs. 2641.20 at 12%

=> Simple Interest = 2641.20 - 1860 = Rs. 781.20

We know I = PTR/100

=> 781.20 x 100 = 1860 x T x 12

=> T = 78120/1860x12

=> T = 78120/22320

=> T = 3.5 years.

3712 = 752

Required number =  75218 = 75 x 4 = 300