Questions With Tricks

8/13/2019 Questions With Tricks

1/43

Find the number of zeroes at the end of 57!.

Answer: Correct Option is: "a"

Solution:

If n = 30., what is the value of

Answer: Correct Optionis: "b"

logxn

x= 1/n


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3/43

If each interior angle of a regular polygon is 11 times its exterior angle, then the number of sides of the

polygon is

The ratio of the area of the square inscribed in a semicircle to the area of the square inscribed in the

entire circle of the same radius is

In


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the following figure, it is given that PT = 12 cm, CD = 7 cm. Find the value of PC.

Question: A is having Rs. 255 all in Re. 1 denominations, in how many minimumnumber of bags can he distribute this amount so that he can give any

denomination from Re. 1 to Rs. 255 without opening any bag?


Solution: The numbers of coins in a bag should be in the power of 2

20

, 21

, 22

, 23

, 24

, 25

, 26

, 27


5/43

In the figure below, ABCDEFGH is a regular octagon and PQRSDC is a regular hexagon.

Points T, U, V and W are the midpoints of the sides BC, PQ, RS and DE respectively. Find

the ratio of the length of TW to that of UV.

Correct Option is: "a"

Solution:


6/43

What will be the remainder when 45! is

divided by 47?

Answer: Correct Option is: "b"

Solution:

Given that f(x) = ax2+ bx + c and f(4) = 100. If a, b, c are distinct positive integers, then the maximum

possible value of a + b + c is


7/43

How many real ns are there such that n! is a perfect square?

Answer: Correct Option is: "c"

For n > 3, n! > n2. For n = 2 and 3, n! < n

2. For n = 0 and 1, n! is a perfect square (which is 1). Otherwise

n! is never a perfect square.

What is the highest power

of 3 in 87!60!?


Solution: 87!60! = 60! [(87 86 ... 61)1] = 60! (3k1)Highest power of 3 is highest power of 3 in 60!, i.e.

[60/3] + [20/3] + [6/3] = 20 + 6 + 2 = 28

(here [x] denotes greatest integer less than or equal to x)

For logical reasoning questions

When X then Y. So, when not Y, hence not X.


8/43

Reading Comprehension

Step 1Identifying the Argument:

The argument goes something like this:

1. Fullerenes synthesised in laboratory requires distinctive pressure and temperature

2. Fullerenes are now found in nature

3. Therefore, it is possible to evaluate the state of Earths crust at the time naturally occurring

fullerenes were formed.

Options:-

4) Of the older adults who contract influenza, relatively few contract it from children with influenza.

What this option is addressing is the premiseChildren is more likely to contract and spread

influenza. When it tries to attack this premise, it CANNOT strengthen the argument. Hence,

INCORRECT.


9/43

Question: If 2p is the square of a natural number, then which of the following is false?

(Given : p is a natural number greater than 1)

In every square, we have even powers of all prime numbers. Now since 2p is a perfect square, p has to

be an even number, this rules out option (b).

Which also means that p2is divisible by 4. Thus, ruling out option (a).

Now the square root of 2p will have a factor of 2 in it. Thus, it will also be even. Hence, (e).

he center of the square is the same point as the center of the circle

Draw lines! Depending on what the stimulus asks for, draw in lines that create simple shapes. (Squares can

be turned into triangles, for example.)

Shared angles will normally not be explicitly stated, unless necessary.

Trust the pictures, but not too much. Inferences must be drawn from fact. Just because it looks like 90-

degrees doesnt mean it is! (Many of these common inferences will be detailed in this series.) Lengths cannot be negative. Be careful in DS questions that pose equations in the context of quadratic

equations with two solutions. If one solution is negative and the other is positive, only the positive solution

remains and the information is sufficient.

For circles:

d=2r and all lines from the center to the exterior equal r.

C = 2r = d A = r NEVER use 2r unless you are adding the areas of identical circles! Tangent lines create right angles with the radius that meets that tangent.

If you know r, you know everything about the circle!

Use = 22/7 with caution. Remember 22/7 > .

For squares:

The diagonal equals s2, since it creates 45-degree angles. The intersection of the diagonals creates a right angle.

When a circle is inscribed inside a square, the side equals the diameter.


10/43

Perpendiculars drawn from the incentre of the triangle to each side are equal in length.

What will be the last digit of ?

Further explanation of the concepts involved :

If you analyze the powers of 2, which means 2, 22, 23etc. you'll get their numerical values as 2, 4, 8,

16, 32, 64 and so on.

Here, you can see that the last digit of these numbers repeat after every four numbers (this is called

cyclicity).

What this means is that the digits 2, 4, 8 and 6 (in that order) appear in a cyclic order as the last digit

of numbers which are higher powers of 2.

So, if we know exactly what type of power 2 has, we can find out the last digit of the entire number

itself. Let me explain -

If the number is of type 24k(where k is a natural number) like 24, 28etc. then the last digit of this

number will be 6.

If its 2(4k+1)

then last digit will be 2.

If its 2(4k+2)


If its 2(4k+3)


So, in this question we are trying to figure out the remainder left when the power of , which is

345, is divided by 4.

Now 3 leaves a remainder of -1 when divided by 4.

You can also see that in 345, 3 is multiplied 45times which means some even number of times.

So, the remainder -1 will be multiplied even number of times and hence will give 1.

Hence, 345

when divided by 4, should give a remainder of 1.

So, 345

is of type 4k+1 and 2345

is of type 24k+1

.


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Hence last digit of 2345will be 2 (as explained above)

Similarly we have calculated the last digit for 31535See that the cyclicity of last digit of powers of 3 is 4

again (in the order 3, 9, 7 and 1).

If X is the smallest number that is divisible by both 6 and 5, than find the maximum possible power of 10

that would completely divide the product of the first 20 multiples of X.

Ans- Product of first 20 multiples of 30 can be written as (30)20[20!]. (30)20has 20 zeros and 20! has 4

zeros. Hence total number of zeros is 24.

*If b, c are two sides of triangle and h is the altitude drawn from vertex common

to b and c, then R = bc/2h.

Area of triangle= abc/4R

Remember that for every four side lengths which form a quadrilateral, a cyclic

quadrilateral can be formed.

If D1 and D2 are the two diagonals of a quadrilateral which intersects at angle P, then itsarea is given byD1D2sinP.

a

bc

A

B C

h

R= Radius of

circumcircle


12/43

Funda 1

The ratio of intercepts formed by a transversal intersecting three parallel lines is equal

to the ratio of corresponding intercepts formed by any other transversal.

? a/b = c/d = e/f

Funda 2

The CentroidandIncenterwill always lie inside the triangle. About the other points,

- For an acute angled triangle, the Circumcenterand the Orthocenterwill lie inside the

triangle.

- For an obtuse angled triangle, the Circumcenterand the Orthocenterwill lie outside the

triangle.

- For a right-angled triangle,the Circumcenterwill lie at the midpoint of the hypotenuse

and the Orthocenterwill lie at the vertex at which the angle is 90.


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Funda 3

The orthocenter, centroid, and circumcenteralways lie on the same line known as Euler

Line.

- The orthocenter is twice as far from the centroid as the circumcenter is.

- If the triangle is Isoscelesthen the incenter lies on the same line.

- If the triangle is equilateral, all four are the same point.

Funda 4:Appolonius Theorem {AD is the median}

AB2+ AC2= 2 * (AD2+ BD2)


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Funda 5: For cyclic quadrilaterals

Area = ?((s - a) (s - b) (s - c) (s - d)) where s is the semi perimeters = (a + b + c + d)/2

Also, Sum of product of opposite sides = Product of diagonals

? ac + bd = PR * QS

Funda 6


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If a circle can be inscribed in a quadrilateral, its area is given by = ?(abcd)

Funda 7:Parallelograms

A parallelogram inscribed in a circle is always aRectangle. A parallelogram circumscribed about

a circle is always aRhombus. So, a parallelogram that can be circumscribed about a circle and in

which a circle can be inscribed will be aSquare.

Each diagonal divides a parallelogram in two triangles of equal area.

Sum of squares of diagonals = Sum of squares of four sides,

AC2+ BD

2= AB

2+ BC

2+ CD

2+ DA

2


16/43

ARectangleis formed by intersection of the four angle bisectors of a parallelogram.

From all quadrilaterals with a given area, the square has the least perimeter. For all quadrilaterals

with a given perimeter, the square has the greatest area.

Funda 8:Trapeziums

Sum of the squares of the length of the diagonals = Sum of squares of lateral sides + 2 Product of

bases.

AC2+ BD

2= AD

2+ BC

2+ 2 x AB x CD

If a trapezium is inscribed in a circle, it has to be an isosceles trapezium.

If a circle can be inscribed in a trapezium, Sum of parallel sides = Sum of lateral sides.

Funda 9


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A regular hexagon can be considered as a combination of six equilateral triangles.

All regular polygons can be considered as a combination of n isosceles triangles.

Equal cords of a circle are equi-distant from the centre.


18/43

For para-jumbles/ para completion/line exlusion

1. See the tone of the passage.

2. General statement if any will come before the specific statements.

3. See what is being discussed


19/43

For similar regular polygons like equilateral triangle, square, regular pentagon,

hexagon, octagon etc the ratio of area is the square of the ratio of sides.

In a triangle ABC, right angled at B, a median BE and an angle bisector BD are drawn. The lengths of

DE, AD and EC, in the same order, are in Arithmetic Progression. If the length of AC is 10 cm and AB 23 then which of the following numbers would always divide

P 1+ P 2?


27/43

N = 51!+2!+3!+...+12!+13!

The digits of the number N are added to get another number. Then the digits of the

number obtained are added to get yet another number. The process is repeated till a single

digit number is obtained. What is that single digit number?

How many natural numbers less than 25 have a composite number of factors?

Read the question properly. Specially whether it asks for incorrect

sentences or correct sentences.


28/43

No of common factors of two numbers = no of factors of the HCF


29/43

In the figure given below, ABCD is a square and a semicircle is drawn having DC as the diameter. ON is a

tangent to the semicircle at the point F and the line DF is extended to meet BC at E. If the measure of

then what is the measure of ?


30/43

A bag contains 9 blue cards numbered 1, , 9 and 9 yellow cards numbered1, , 9. In how many ways can we choose 9 out of the 18 cards so that thereare exactly 3 jugalbandis, where a jugalbandi means a blue card and a yellow

card with the same number?

Answer: CorrectOption is:

"b"


31/43

The LCM of three positive

integers X, Y and Z is 1192.

Find the total number of

ordered triplets (X, Y and Z).

Answer: Correct Option is: "b"

Solution:


32/43


33/43

V is a 56 digit number. All the digits except the 32nd

from the right are the same. If V is divisible by 13,

then which of the following can never be the units digit of V?


34/43

Let f(x) = ax + bx + c where a,

b and c are constants. If themaximum of f(x) occurs at

then which of thefollowing is necessarily equal

to f(0)?


Solution:


35/43

P and Q are two opposite ends of a straight running track. Ria and Tia start running towards each

other simultaneously from P and Q respectively. As soon as any of them reaches an end, she turns

back and starts running towards the other end. Their first meeting happens at a point 210 m away

from P and the second meeting happens at a point 150 m away from Q. If the speeds (in m/s) of Ria

and Tia are x and y respectively, such that 2x > y > x, then what is the distance between P and Q?


36/43

Four identical bags are distributed

among four boys. If each boy can get

any number of bags then what is the

probability that no boy gets more than

two bags?

Answer: Correct Option is: "c"

Solution:


37/43

The question given below

is followed by twostatements, A and B. Mark

the answer using the

following instructions:Mark (a) if the question

can be answered by one of

the statements alone, but

cannot be answered byusing the other statement

alone.

Mark (b) if the question

can be answered by usingeither statement alone.

Mark (c) if the question

can be answered by using

both the statementstogether, but cannot be

answered by using eitherstatement alone.

Mark (d) if the question

cannot be answered even

by using both statementstogether.

Q.In a knockouttournament, a player is

eliminated with a singleloss. If the number of

players, say n, is even,then n/2 players move on

to the next round while if

n is odd, then (n+1)/2players move on to the

next round. If the numberof players in any round is

odd, then one of them isgiven a bye, that is, he/she

automatically moves on tothe next round. The

process is continued tillthe final round, which

obviously is playedbetween two players. Xis the number of players


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that participated in a

knockout tournament.Byes were necessarily

given in the alternate

rounds. If Y was thetotal number of byes given

in the tournament, then

what is the remainderwhen X is divided byY?A. 40 < X < 100.

B.10 < X < 30.

Answer: Correct Option is: "d"


39/43

Solution:


40/43

Remember all the

formulae of solution oftriangles and sin and

cos.


41/43

Which of the following number(s) is/are

not prime?

(i) 25001

+ 1

(ii) 25002

+ 1

(iii) 25003+ 1


Solution:


42/43

The route taken by a bus from Delhi to Jaipur has

n stops, including the source and the destination.

When m new stops are added on the route of the

bus (where m > 1) the number of different tickets

that can be issued between two stops on the route

increases by 11. What is the value of n?


Solution:


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19. Application of H.C.F.The greatest natural number that will dividex, y and z leaving remainders r1, r2 and r3, respectively,

is the H.C.F. of (x r1), (y r2) and (z r3)

20. Application of L.C.M.The smallest natural number that is divisible byx, y and z leaving the same remainder r in each case

is the L.C.M. of (x, y and z) + r

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