M4maths Previous Puzzles

07 Sep 2018 Find Value of

Find the value of x^2 + 3xyz + 2y^ + 3z^2
where x = Mean , y = Median and z = Mode of following numbers:
83 87 93
97 110 48 114 119
87 118 122

OPtion

1) 2512195
2) 2522195
3) 2532795
4) 2542195
5) 2552195
6) 2532195
7) 2562195
8) 2572195
9) 2582195
10) None of these

Solution

Mean x = Sum of nos. / Count of numbers = 1078/11 = 98
Median y = Middle term when number are arranged in ascending order = 97
Mode z = Number which is present maximum number of times = 87
x^2 + 3xyz + 2y^2 + 3 z*2 = (98)^2 + 3*98*97*87 + 2*(97)^2 + 3*(87)^2 = 2532195


Option 6)

Correct Option: 6 Best Solution (0)

06 Sep 2018 Rank of the word

Find Rank of the word MILLENNIUM in the dictionary of words formed by the letters of the word MILLENNIUM

OPtion

1) 121711
2) 121712
3) 121713
4) 121714
5) 121715
6) 121716
7) 121718
8) 121717
9) 121719
10) None of these

Solution

MILLENNIUM
Lets arrange the letters alphabetically = E II LL MM NN U

Words starting with E = 9!/(2!*2!*2!*2!) = 22680
Words starting with I = 9!/(2!*2!*2!) = 45360
Words starting with L = 9!/(2!*2!*2!) = 45360
Words starting with ME = 8!/(2!*2!*2!) = 5040
Words starting with MIE = 7!/(2!*2!) = 1260
Words starting with MII = 7!/(2!*2!) = 1260
Words starting with MILE = 6!/(2!) = 360
Words starting with MILI = 6!/(2!) = 360
Words starting with MILLEI = 4!/(2!) = 12
Words starting with MILLEM = 4!/(2!) = 12

Words starting with MILLENI = 3! = 6
Words starting with MILLENM = 3! = 6


Words starting with MILLENNIM = 1
and the required word is the next one MILLENNIUM

Sum of all = 121718



Words starting with lm = 8!/(2!*2!) = 10080
Words starting with ln = 8!/(2!) = 20160
Words starting with ls = 8!/(2!*2!) = 10080

Words starting with luc = 7!/(2!*2!) = 1260
Words starting with lue = 7!/(2!) = 2520
Words starting with lui = 7!/(2!*2!) = 1260

Words starting with lumc = 6!/(2!*2!) = 180
Words starting with lume = 6!/(2!) = 360

Words starting with lumic = 5!/(2!*2!) = 30
Words starting with lumie = 5!/(2!) = 60

Words starting with luminc = 4!/(2!) = 12

Words starting with luminec = 3! = 6
Words starting with luminee = 3! = 6
Words starting with luminen = 3! = 6
Words starting with luminescen = 1

Sum of all = 121718

Option 7)

Correct Option: 7 Best Solution (0)

05 Sep 2018 Probability

An Indian State name (excluding union territories) is randomly picked. What is the probability that that name of the picked Indian State starts with a vowel?

OPtion

1) 3/14
2) 7/29
3) 5/29
4) 1/4
5) 4/29
6) 8/29
7) 6/29
8) 1/5
9) 9/29
10) None of these

Solution

Total number of states in India = 29

Number of states whose name starts with a vowel:Andhra Pradesh, Arunachal Pradesh, Assam, Odisha, Uttar Pradesh, Uttarakhand => Count is 6

So required probability = 6/29

Correct Option: 7 Best Solution (6)

G.S.Kantharao   3 Months AGO

Total States =29
Required outcomes=Arunachalam Pradesh, Andhrapradesh,Assam,Orissa,
Uttarpradesh and Uttarakand(6)
Probability=6/29
Right option is 7👈

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Varun   3 Months AGO

There are 29 states
And 6 states' name start from vowels
= 6/29
= Option (7)

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Ravikumar   3 Months AGO

6/29

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Dimple   3 Months AGO

Out of 29 states, names of 6 states start with a vowel.
Assam
Arunachal pradesh
Andhra Pradesh
Orissa
Uttrakhsnd
Uttar pradesh
so probability =6/29

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Kariamal   3 Months AGO

n(E)=6 {andhra Pradesh,Arunachal Pradesh,assam,Odisha,uttarakhand ,utter Pradesh }
n(S)=29
P(E)=6/29

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R.P   3 Months AGO

because there are 6 states started with vowel letter.

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04 Sep 2018 Work & Time

If 10 men and 15 women can do a piece of work in 8 days and 9 men and 12 women can do it in 9 days,

how many days will 5 men and 15 women take to do it?

OPtion

1) 14.75
2) 14.50
3) 14.33
4) 14.66
5) 14.20
6) 13.20
7) 13.33
8) 13.75
9) 14.40
10) None of these

Solution

Let a man's daily work is x units and that of a woman is y units.
So total amount of work, W = 8(10x + 15y) = 9(9x + 12y)

Solving we get, 80x - 81x = 108y - 120y
=> x = 12y



Now, 10 x + 15 y can do work in 8 days.
So, 120y + 15 y can do work in 8 days.
So, 135 y can do work in 8 days.

Now, 5x + 15y = 60y + 15y = 75y

Hence, if 135y can do work in 8 days, 75y can do work in (135*8)/75 = 14.4 days.

Option 9)

Correct Option: 9 Best Solution (10)

G.S.Kantharao   3 Months AGO

10m+15w=8d
80m+120w=1d
9m+12w=9d
81m+108w=1d
81m+108w=80m+120w
1m=12w
10m+15w=120w+15w=135w =8d
5m+15w=5*12w+15w=xd
x=8*135/75=8*9/5=72/5=14.4d
Hence my option is 9👈

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anupama   3 Months AGO

One day work
10M+15W=1/8---(1)
9M+12W=1/9----(2)
(1)-(2)--->M+3W=1/72
on multiplying by 5,we get
5M+15W=5/72
entire work=72/5=14.4

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ruby   3 Months AGO

Given,
10m+15w=8days
9m+12w=9days
Total Work
8(10m+15w)=9(9m+12w)
1m=12w
Apply in 1st 10*12w+15w=1/8
135w=1/8 -----> 1w=1080
Question
5*1w+15w=75w=1080/75=14.40
Hence Option 9

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Vishnu Prakash   3 Months AGO

10m+15w=1/8
9m+12w=1/9
On solving these two equations,
5m+15w=5/72
So, work is done in 72/5 = 14.4 days

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Kariamal   3 Months AGO

10m+15w=1/8...(1)
9m+12w=1/9.....(2)
From eq 1 and 2
w=1/1080
m=1/90
5m+15w=5/72=14.40

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Ravikumar   3 Months AGO

14.4

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Shafigheh   3 Months AGO

let m=1 man-day
let w= 1 woman-day
1st equation:10(8)m+15(8)w=80m+120w=work done
2st equation: 9(9)m+12(9)w=81m+108w=work done
from 1 and 2 equation =>1m=12 w
so work done=80(12)w + 120w = 1080w
let' put the results in question:
5m[day]+15w[day]=5(12)w[day]+15w[day]=75w[day]=1080w
so the Answer is: day=1080/75=14.40

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Prateek Mishra   3 Months AGO

Because a MAN can do work equal to 12WOMEN.

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SAYANTAN PATRA   3 Months AGO

let the total work=lcm(8 and 9)=72
now 10 men 15 women can do 72/8=9 unit/day
and 9 men 12 women can do 72/9=8 unit /day
by substructing we can get 1 men 3 women can do 1 unit/day
now multiplying with 5 we can get
5 men and 15 women can do 5unit/day
so they complete 5 unit in 1 day
then 72 unit(whole work) in 72/5=14.40 days

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Kaustubh S.   3 Months AGO

work done by men and women per day is 1/x and 1/y
so
10/x+15/y=1/8
9/x+12/y=1/9
solving these two equation we get
X=90 , Y=1080
so substituting z and y in the required equation i.e
5/x+15/y=z
we get Z =14.40

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03 Sep 2018 Probability

A 2 digit number between 11 to 50 (both inclusive) is randomly picked.
What is the probability that the picked number is such a prime number whose sum of digits is an odd number?

OPtion

1) 3/40
2) 9/40
3) 11/40
4) 1/8
5) 6/40
6) 1/5
7) 7/40
8) 5/39
9) 2/13
10) None of these

Solution

Total numbers between 11 to 50 = 40
List of prime numbers between 11 to 50= 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47

List of prime numbers between where sum of digit is an odd number = 23, 29, 41, 43, 47

Count of Prime number where sum of digit is an odd number = 5

Required probability = 5/40 = 1/8

Correct Option: 4 Best Solution (1)

G.S.Kantharao   3 Months AGO

Two figured Primes whose sum of its digits is odd=23,29,41,43,47=(5)
Total out comes=40
Probability=5/40=1/8
My option is 4👈

Like? Yes (1) | No   

31 Aug 2018 Average

The average of 7 consecutive numbers is 16. What is the largest number?

OPtion

1) 11
2) 12
3) 14
4) 15
5) 13
6) 16
7) 17
8) 19
9) 18
10) None of these

Solution

Let the numbers be x, x + 1, x + 2, x + 3, x + 4, x + 5 and x + 6,

Then (x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6)) / 7 = 16.

=> 7x + 21 = 112
=> x = 13

Largest number = x + 6 = 13+6 = 19.

Correct Option: 8 Best Solution (8)

sruthi pujari   3 Months AGO

Middle num will be the average of consecutive numbers. So 4th term is 16
7th term > 19

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amit   3 Months AGO

if the find the average of consecutive no. and the total numbers are odd then the average always be the middle among those numbers i.e
13 14 15 16 17 18 19
so the largest is 19.

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Ravikumar   3 Months AGO

13,14,15,16,17,18,19
average=16
large number=19

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G.S.Kantharao   3 Months AGO

Consecutives are 13,14,15,16,17,18,19
Biggest is 19.
My option is 8👈

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Kariamal   3 Months AGO

x+x+1+x+2+x+3+x+4+x+5+x+6=7*16
7x+21=112
x=13
Largest number=x+6=19

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swathi katakam   3 Months AGO

let 7 consecutive no's be --x,x+1,x+2,x+3,x+4,x+5,x+6.
avg=(sum/no)
(x+x+1+x+2+x+3+x+4+x+5+x+6)/7=16
7x+21=112
x=13
hence,largest no=x+6=13+6
=19

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ruby   3 Months AGO

Numbers are x, x+1, x+2,x+3,x+4,x+5,x+6
7x+21/7=16
x=13,
Largest number =13+6 = 19

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bhavani veesam   3 Months AGO

7 consecutive numbers are x,x+1,x+2,x+3,x+4,x+5,x+6
average of 7 consecutive numbers are x+x+1+x+2+x+3+x+4+x+5+x+6/7=16
7x+21=16*7=112
7x=112-21=91
x=91/7
x=13
hece ,largest nuumber is x+6=13+6=19

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30 Aug 2018 Statistics

Run Scored by Murali, Shikhar, Rahul, Virat, Ajinkya, Hardik, Dinesh, Ashwin, Shami, Ishant and Umesh in 1st Match are:
33 24 19 21 41 39 37 47 38 29 and 26 respectively.

Run Scored by Murali, Shikhar, Rahul, Virat, Ajinkya, Hardik, Dinesh, Ashwin, Shami, Ishant and Umesh in 2nd Match are:
13 44 19 93 41 76 33 44 29 11 and 7 respectively



What is the difference between population standard deviation between second match and first match?

OPtion

1) 25.807
2) 18.791
3) 17.589
4) 16.981
5) 18.183
6) 17.197
7) 16.817
8) 17.961
9) 8.610
10)None of these

Solution

1st Match
Mean of 11 scores = 354/11 = 32.18
Sum of squared difference from mean for each number = (33-32.18)^2 + (24-32.18)^2 + ......+ (26-32.18)^2 = 815.6364

Average of Squared difference (Variance) = 815.6364/11 = 74.1487
Population Standard Deviation = Square root of variance = 74.1487^1/2 = ~8.610


2ns Match
Mean of 11 scores = 410/11 = 37.27273
Sum of squared difference from mean for each number = (13-37.27)^2 + (44-37.27)^2 + ......+ (7-37.27)^2 = 7326.18

Average of Squared difference (Variance) = 7326.18/11 = 666.016
Population Standard Deviation = Square root of variance = 666.016^1/2 = ~25.807

Difference between Population standard deviation of 2nd match and 1st match = 25.807 - 8.610 = ~17.197

Option 6)

Correct Option: 6 Best Solution (3)

Shanjay Sundar . D   3 Months AGO

sq rt(1109.81-1035.55)
=8.61
sq rt(2055.27-1389.25)
=25.80
25.80-8.61=17.197

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vaishali more   3 Months AGO

.

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Irfana fathima   3 Months AGO

Standard deviation follows the below rule
Find AVG of the runs scored
Subtract AVG from the scores
Find square of the above subtracted scores and take AVG of that
Take square root of the AVG we obtain the Standard Deviation
Match 1 standard deviation 8.610967
Match 2 Standard deviation 25.8074
We get, 17.19645
Approximately the answer will be 17.197

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29 Aug 2018 Even Number

How many factors of 45434373264 are even numbers?

OPtion

1) 288
2) 360
3) 420
4) 432
5) 384
6) 360
7) 192
8) 240
9) 396
10) None of these

Solution

45434373264 = 89^1* 31^3 * 17^1 * 7^1 * 3^2 * 2^4

Any factor of this number should be of the form 31^a * 17^b * 7^c * 3^d * 2^e * 89 ^f

For the factors of this number to be an even number e should be non 0

a can take values 0, 1, 2, 3
b can take values 0, 1
c can take values 0, 1
d can take values 0, 1, 2
e can take values 1, 2, 3, 4
f can take values 0, 1

Total number of even factors = 4*2*2*3*4*2= 384

Option 5)

Correct Option: 5 Best Solution (1)

Varun   3 Months AGO

Significant factors are 2 2 2 2 2
So, it contributes to even factors along with 3 3 7 17 31 31 31 and 89
So total 384
= Option (5)

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28 Aug 2018 Boats and Streams

A man goes down stream with a boat to some destination and returns upstream to his original place in 15 hours. If the speed of the boat in still water and downstream are 10km/hr and 14km/hr respectively, the distance of the destination from the starting place in KMs is

OPtion

1) 48
2) 51
3) 45
4) 66
5) 67
6) 68
7) 69
8) 70
9) 63
10) None of these

Solution

Let the distance be D

Speed of boat in still water = 10
Speed of boat in down stream = 14
Speed of Stream = 14=10 = 4
Speed of boat in upstream = 10-4 = 6

Time Downstream + Time upstream = 15
=> D/14 + D/6 = 15
=> 10D = 630
=> D = 63
Option 9)

Correct Option: 9 Best Solution (7)

ruby   3 Months AGO

Boat = 10
Downstream (B+W)=14
Water speed = 14-10 4
X/14+X/6=15
20X=15*14*6
X=63

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G.S.Kantharao   3 Months AGO

Still water,Streek=10kmph,4kmph
Distance=x
X/14+x/6=15
x=630/10=63
Right option is 9👈

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SAYAN CHATTERJEE   3 Months AGO

Speed of boat is 10 and current is (14-10)= 4
So, S(1/14+1/6)= 15
S= 63.
OPTION 9.

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Azhagar.S   3 Months AGO

Let us assume the distance as D.
Time = 15hours
Then ,
D/(10+4) + D/(10-4) = 15
10D/42 = 15
10D = 42*15
D = 63
So the distance of the destination from the starting place is 63kms.
So my option is 9

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ARINJOY GHOSH   3 Months AGO

let the distance=d
now,d/14+d/6=15
d=15*21*2/10=63

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APURBA CHATTOPADHYAY   3 Months AGO

speed of boat=10
downstream=14
downstream=speed of boat+speed of stream
so speed of stream=4
thus upstream=10-4=6
now let distance=d.
so d/14+d/6=15
so d=63

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VIJAYAKUMAR S   3 Months AGO

Let the distance be 'x'.
The speed of boat in still water is 10 Km/hr and the speed of the current is (Speed of boat in downstream-speed of boat in still water) 4 Km/hr.
(Distance/speed)=time.
Therefore,
(x/6)+(x/14)=15 hrs.

on solving we get x=63 KM

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27 Aug 2018 Simple Interest

At what simple interest rate percent per annum will a sum of money double in 14 years.

OPtion

1) 14.28
2) 7.00
3) 7.33
4) 13.50
5) 7.25
6) 7.14
7) 7.75
8) 6.75
9) 6.66
10) None of these

Solution

SI = PRT/100

SI = P

So P = P*R*14/100
= R= 100/14 = 7.14
Option 6)

Correct Option: 6 Best Solution (5)

Devendra Marghade   3 Months AGO

When the sum doubles, the interest is equal to sum.
Let the sum be x and interest be r, then
x*r*14/100 = x
=> r=100/14=7.14
Option 6)

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G.S.Kantharao   3 Months AGO

P=P*T*R%=P*14*R/100
R=100/14=7.14%
My option is 6 👈

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sruthi pujari   3 Months AGO

100/14 = 7.14% to get simple interest which is equal to Principle amount

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ruby   3 Months AGO

Amount Doubles in 14 years, ie = 2P
P*14*R/100 = P
14R=1010
R=7.142
Hence option 6

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SAYAN CHATTERJEE   3 Months AGO

Pr*14/100= p
So, r= 7.14.
Option 6.

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