Directions: Study the following information carefully and answer the given questions.
Eight friends A, B, C, D, E, F, G and H are sitting around a square table in such a way that four of them sit at four corners of the square while four sit in the middle of each of the four sides. The ones who sit at the four corners face the centre while those who sit in the middle of the sides face outside. A, who faces the centre, sits third to the right of F. E who faces the centre, is not an immediate neighbour of F. Only one person sits between F and G. D sits second to the right of B. B faces the centre. C is not an immediate neighbour of A.
Q1. Who sits third to the left of D?
G
H
F
C
Cannot be determined
Q2. What is the position of C with respect to G?
Fourth to the right
Fourth to the left
Both (a) & (b)
Second to the right
Second to the left
Q3. Which of the following will come in place of the question mark based upon the given seating arrangement? GA EC BG CD (?)
HE
FH
FB
AH
BF
Q4. Which of the following is true regarding C?
C faces the centre
C is second to the left of F.
C sits exactly between A and B
B sits third to the left of C
Cannot be determined
Q5. Four of the following five are alike in a certain way and so form a group. Which is the one that does not belong to that group?
C
G
F
H
D
ANSWERS
Q1. A
Q2. C
Q3. A
Q4. B
Q5. E
Showing posts with label Maths. Show all posts
Showing posts with label Maths. Show all posts
Tips and Tricks - Finding number of Positive Roots
If an equation (i:e f(x)=0 ) contains all positive co-efficient of any powers of x , it has no positive roots then.
Eg: x^4+3x^2+2x+6=0 has no positive roots
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Tips and Tricks - Finding number of Imaginary Roots
For an equation f(x)=0 , the maximum number of positive roots it can have is the number of sign changes in f(x) ; and the maximum number of negative roots it can have is the number of sign changes in f(-x) .
Hence the remaining are the minimum number of imaginary roots of the equation(Since we also know that the index of the maximum power of x is the number of roots of an equation.)
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Tips and Tricks - Reciprocal Roots
The equation whose roots are the reciprocal of the roots of the equation ax^2+bx+c is cx^2+bx+a
Roots
Roots of x^2+x+1=0 are 1,w,w^2 where 1+w+w^2=0 and w^3=1
Finding Sum of the rootsFor a cubic equation ax^3+bx^2+cx+d=o sum of the roots = - b/a sum of the product of the roots taken two at a time = c/a product of the roots = -d/a
For a biquadratic equation ax^4+bx^3+cx^2+dx+e = 0 sum of the roots = - b/a sum of the product of the roots taken three at a time = c/a sum of the product of the roots taken two at a time = -d/a product of the roots = e/a
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Tips and Tricks - Maximum/Minimum problems
-> If for two numbers x+y=k(=constant), then their PRODUCT is MAXIMUM if x=y(=k/2). The maximum product is then (k^2)/4
-> If for two numbers x*y=k(=constant), then their SUM is MINIMUM if x=y(=root(k)). The minimum sum is then 2*root(k) .
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Tips and Tricks - AM GM HM (Means)
For any 2 numbers a>b a>AM>GM>HM>b (where AM, GM ,HM stand for arithmetic, geometric , harmonic menasa respectively) (GM)^2 = AM * HM
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Tips and Tricks - Sum of Exterior Angles
For any regular polygon , the sum of the exterior angles is equal to 360 degrees hence measure of any external angle is equal to 360/n. ( where n is the number of sides)
For any regular polygon , the sum of interior angles =(n-2)180 degrees
So measure of one angle in
Square-----=90
Pentagon--=108
Hexagon---=120
Heptagon--=128.5
Octagon---=135
Nonagon--=140
Decagon--=144
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Tips and Tricks - Problems on clocks
Problems on clocks can be tackled as assuming two runners going round a circle , one 12 times as fast as the other . That is , the minute hand describes 6 degrees /minute the hour hand describes 1/2 degrees /minute . Thus the minute hand describes 5(1/2) degrees more than the hour hand per minute .
The hour and the minute hand meet each other after every 65(5/11) minutes after being together at midnight. (This can be derived from the above) .
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Tips and Tricks - Finding Co-ordinates
Given the coordinates (a,b) (c,d) (e,f) (g,h) of a parallelogram , the coordinates of the meeting point of the diagonals can be found out by solving for [(a+e)/2,(b+f)/2] =[ (c+g)/2 , (d+h)/2]
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Tips and Tricks - Finding Ratio
If a1/b1 = a2/b2 = a3/b3 = .............. , then each ratio is equal to (k1*a1+ k2*a2+k3*a3+..............) / (k1*b1+ k2*b2+k3*b3+..............) , which is also equal to (a1+a2+a3+............./b1+b2+b3+..........)
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Tips and Tricks - Finding multiples
x^n -a^n = (x-a)(x^(n-1) + x^(n-2) + .......+ a^(n-1) ) ......Very useful for finding multiples .For example (17-14=3 will be a multiple of 17^3 - 14^3)
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Tips and Tricks - Exponents
e^x = 1 + (x)/1! + (x^2)/2! + (x^3)/3! + ........to infinity 2 <>GP
-> In a GP the product of any two terms equidistant from a term is always constant .
-> The sum of an infinite GP = a/(1-r) , where a and r are resp. the first term and common ratio of the GP .
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Tips and Tricks - Mixtures
If Q be the volume of a vessel q qty of a mixture of water and wine be removed each time from a mixture n be the number of times this operation be done and A be the final qty of wine in the mixture then ,
A/Q = (1-q/Q)^n
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Tips and Tricks - Function
Any function of the type y=f(x)=(ax-b)/(bx-a) is always of the form x=f(y)
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Tips and Tricks - Rules of Logarithms
-> loga(M)=y if and only if M=ay
-> loga(MN)=loga(M)+loga(N)
-> loga(M/N)=loga(M)-loga(N)
-> loga(Mp)=p*loga(M)
-> loga(1)=0-> loga(ap)=p
-> log(1+x) = x - (x^2)/2 + (x^3)/3 - (x^4)/4 .........to infinity [ Note the alternating sign . .Also note that the logarithm is with respect to base e ]
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PERIMETER :
Shape Area Perimeter
Circle ∏ (Radius)2 2∏(Radius)
Square (side)2 4(side)
Rectangle length*breadth 2(length+breadth)
1. Area of a triangle = 1/2*Base*Height or
2. Area of a triangle = √ (s(s-(s-b)(s-c)) where a,b,c are the lengths of the sides and s = (a+b+c)/2
3. Area of a parallelogram = Base * Height
4. Area of a rhombus = 1/2(Product of diagonals)
5. Area of a trapezium = 1/2(Sum of parallel sides)(distance between the parallel sides)
6. Area of a quadrilateral = 1/2(diagonal)(Sum of sides)
7. Area of a regular hexagon = 6(√3/4)(side)2
8. Area of a ring = ∏(R2-r2) where R and r are the outer and inner radii of the ring.
SURFACE AREA
Cube :
Let a be the length of each edge. Then,
1. Volume of the cube = a3 cubic units
2. Surface Area = 6a2 square units
3. Diagonal = v 3 a units
Cuboid :
Let l be the length, b be the breadth and h be the height of a cuboid. Then
1. Volume = lbh cu units
2. Surface Area = 2(lb+bh+lh) sq units
3. Diagonal = v (l2+b2+h2)
Cylinder :
Let radius of the base be r and height of the cylinder be h. Then,
1. Volume = ?r2h cu units
2. Curved Surface Area = 2?rh sq units
3. Total Surface Area = 2?rh + 2?r2 sq units
Cone :
Let r be the radius of base, h be the height, and l be the slant height of the cone. Then,
1. l2 = h2 + r2
2. Volume = 1/3(?r2h) cu units
3. Curved Surface Area = ?rl sq units
4. Total Surface Area = ?rl + ?r2 sq units
Sphere :
Let r be the radius of the sphere. Then,
1. Volume = (4/3)?r3 cu units
2. Surface Area = 4?r2 sq units
Hemi-sphere :
Let r be the radius of the hemi-sphere. Then,
1. Volume = (2/3)?r3 cu units
2. Curved Surface Area = 2?r2 sq units
3. Total Surface Area = 3?r2 sq units
Prism :
1. Volume = (Area of base)(Height)
Loss - Shortcut Methods
1. Gain = Selling Price(S.P.) - Cost Price(C.P)
2. Loss = C.P. - S.P.
3. Gain % = Gain * 100 / C.P.
4. Loss % = Loss * 100 / C.P.
5. S.P. = (100+Gain%)/100*C.P.
6. S.P. = (100-Loss%)/100*C.P.
Short cut Methods:
1. By selling an article for Rs. X, a man loses l%. At what price should he sell it to gain y%? (or)
A man lost l% by selling an article for Rs. X. What percent shall he gain or lose by selling it for Rs. Y?
(100 – loss%) : 1st S.P. = (100 + gain%) : 2nd S.P.
2. A man sold two articles for Rs. X each. On one he gains y% while on the other he loses y%. How much does he gain or lose in the whole transaction?
In such a question, there is always a lose. The selling price is immaterial.
Formula for loss %=
3. A discount dealer professes to sell his goods at cost price but uses a weight of 960 gms. For a kg weight. Find his gain percent.
Formula: Gain % =
PROPORTIONS
1. The ratio a : b represents a fraction a/b. a is called antecedent and b is called consequent.
2. The equality of two different ratios is called proportion.
3. If a : b = c : d then a, b, c, d are in proportion. This is represented by a : b :: c : d.
4. In a : b = c : d, then we have a* d = b * c.
5. If a/b = c/d then ( a + b ) / ( a – b )= ( d + c ) / ( d – c ).
Tricks -Important Formulae - LOGORITHMS
If am = x , then m = logax.
Properties :
1. log xx = 1
2. log x1 = 0
3. log a(xy) = log ax + log ay
4. log a(x/y) = log ax - log ay
5. log ax = 1/log xa
6. log a(xp) = p(log ax)
7. log ax = log bx/log ba
Note : Logarithms for base 1 does not exist.
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