subject
stringclasses 1
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|---|---|---|---|---|
mathematics
|
A can do a piece of work in 15 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work?
|
[
"11 6/7days",
"12 6/7days",
"13 6/7days",
"14 6/7days",
"15 6/7days"
] |
8/15 + 6/x = 1
X = 12 6/7days
ANSWER:B
The answer is: B
|
B
|
mathematics
|
Find the no.of ways of arranging the boy and 6 guests at a circular table so that the boy always sits in a particular seat?
|
[
"3!",
"6!",
"7!",
"9!",
"11!"
] |
Ans.(B)
Sol. Total number of persons = 7 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 6 places in 6P6 = 6! Ways ... The number of required arrangements = 6! x 1= 6! = 6! ways
The answer is: B
|
B
|
mathematics
|
A box contains 4 blue marbles, 3 red, 6 green marbles and two yellow marbles. If two marbles are picked at random, what is the probability that they are either blue or yellow?
|
[
"5/10",
"4/10",
"1/10",
"2/10",
"3/10"
] |
Given that there are 4 blue marbles, 3 red marbles, 6 green marbles and 2 yellow marbles. Probability that both marbles are blue = 4Câ‚‚/¹âµCâ‚‚ = (3 * 2)/(15 * 14) = 2/35
Probability that both are yellow = ²Câ‚‚/¹âµCâ‚‚ = (1)/(15 * 14) = 1/210
Probability that one blue and other is yellow = (4Câ‚ * ²Câ‚)/¹âµCâ‚‚ = (4*2)/(15 * 14) = 4/105
Required probability = 2/35 + 1/210 + 4/105
= 1/10
Answer:C
The answer is: C
|
C
|
mathematics
|
In a kilometer race, A beats B by 50 meters or 10 seconds. What time does A take to complete the race?
|
[
"187 sec",
"190 sec",
"168 sec",
"197 sec",
"191 sec"
] |
Time taken by B run 1000 meters
= (1000 * 10)/50 = 200 sec.
Time taken by A = 200 - 10
= 190 sec.
Answer: B
The answer is: B
|
B
|
mathematics
|
A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :
|
[
"7/14",
"7/15",
"7",
"8/15",
"8"
] |
A's 1 day's work = 1/15
B's 1 day's work = 1 /20
(A + B)'s 1 day's work = ( 1/15 + 1/20 ) = 7 /60
(A + B)'s 4 day's work = (4*7)/60 = 7/15
Therefore, Remaining work = ( 1 - 7/15) = 8/15
So correct answer is D
The answer is: D
|
D
|
mathematics
|
From the given equation find the value of z: z² + 5z + 6
|
[
"2",
"1",
"-1",
"-3",
"3"
] |
(z + 2)(z + 3)
Z = -2 or -3
Answer is D
The answer is: D
|
D
|
mathematics
|
A dog takes 3 leaps for every 5 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is :
|
[
"9:5",
"2:3",
"4:7",
"5:6",
"None of these"
] |
Explanation:
Dog : Hare = (3*3) leaps of hare : 5 leaps of hare = 9 : 5.
Answer: A
The answer is: A
|
A
|
mathematics
|
A lawn is in the form of a rectangle having its sides in the ratio 2: 3. The
area of the lawn is (1/6) hectares. Find breadth of the lawn.
|
[
"15 m",
"20 m",
"25 m",
"35 m",
"50 m"
] |
Let length = 2x metres and breadth = 3x metre.
Now, area = (1/6 )x 1000 m2 = 5000/3m2
So, 2x * 3x = 5000/3 <=>x2= 2500/9 <=>x = 50/3
therefore Breadth = 3x = 3(50/3) m
= 50m.
ANSWER E 50 m
The answer is: E
|
E
|
mathematics
|
A basketball coach will select the members of a five-player team from among 12 players, including John and Peter. If the five players are chosen at random, what is the probability that the coach chooses a team that includes both John and Peter?
|
[
"1/9",
"1/6",
"2/9",
"5/33",
"1/3"
] |
you can but that will require more cases and will be time consuming.
straight forward way is to group J and P as always present on the team and as order does not matter so we just need to find the total number of ways to select rest three players = 10c3
total number of ways of selecting 5 players out of 12 = 12c5
probability = 10c3/12c5 = 5/33
D
The answer is: D
|
D
|
mathematics
|
Henry solved a certain number of algebra problems in an hour, his older brother Frank solved
four times as many. Together they solved 80. How many were solved by each?
|
[
"H-12 F-49",
"H-30 F-83",
"H-20 F-90",
"H-16 F-64",
"H-40 F-100"
] |
I am looking for the number of problems solved by Henry (H) and Frank (F).
Who solved the least number of problems? Hopefully, you said Henry.
So let H = x
Frank solved four times as many, therefore
F = 4x
Read the problem again to find a relationship. Together they solved 80. That means that
H + F = 80 Substituting
x + 4x = 80 Solving for x
5x = 80
x = 16
Therefore Henry solved 16 and Frank solved 4 times 16 of 64 problems.
correct answer D
The answer is: D
|
D
|
mathematics
|
Machines A and B produce bottles at their respective constant rates. Machine A produces k bottles in 2 hours and machine B produces k bottles in 4 hours. How many hours does it take machines A and B, working simultaneously, to produce 15k bottles?
|
[
"10",
"15",
"12",
"20",
"18"
] |
A's rate = k/2
B's rate = k/4
k/2 + k/4 = 3k/4
15k / (3k/4) = 20 hours
The answer is D.
The answer is: D
|
D
|
mathematics
|
If A is thrice as fast as B and together can do a work in 15 days. In how many days A alone can do the work?
|
[
"36",
"20",
"28",
"54",
"45"
] |
A’s one day’s work= 1/X
B’s one day’s work= 1/3x
A + B’s one day’s work= 1/x + 1/3x = 1/15
= 3+1/3x = 4/3x = 1/15
x = 15*4/3 = 20
ANSWER:B
The answer is: B
|
B
|
mathematics
|
If x > 3 and y < -3, then which of the following must be true ?
|
[
"x/y > 1",
"x/y < -1",
"x/y < 0",
"x + y > 0",
"xy > 0"
] |
Pick x=3, y = -3
A) x/y > 1 - Incorrect as x/y = -1
B) x/y < -1 - Incorrect as x/y = -1
C) x/y < 0 -Correct. It will hold for all values x > 2 and y < -2 as x/y = -1 < 0
D) x + y > 0 - Incorrect. x + y = 0
E) xy > 0 - Incorrect. XY = -9 which is less than zero.
D should be the answer.
The answer is: D
|
D
|
mathematics
|
Train G and H, 455 miles apart, are traveling toward each other at constant rates and in the same time zone. If train G left at 4 pm traveling at a speed of 60 miles per hour, and train H left at 5:45 pm and traveling at 45 miles per hour, then at what time would they pass each other?
|
[
"9.05Am",
"9.11pm",
"8.05pm",
"7.05pm",
"9.05pm"
] |
First, since G has a headstart then in that 1hr45min or 1.75hrs he travels 105 miles
Then remaining distance to be traveled will be 455 - 105 = 350 miles
Now, using relative rates (105)(t) = 350
This gives 10/3 hours
Now 5.45pm + 10/3 hours gives us 9.05pm
Hence answer is D
The answer is: D
|
D
|
mathematics
|
When divided by 5, x has a remainder of 3 and y has a remainder of 1. Which of the following could be the remainder when x + y is divided by 10?
|
[
"6",
"7",
"8",
"9",
"0"
] |
x = 5k+3 and y = 5j+1
x+y = 5(j+k) + 4
When divided by 10, the remainder is either 4 or 9.
The answer is D.
The answer is: D
|
D
|
mathematics
|
If 2x + y = 5 and 3x-2y = 7, then what is the value of 5x - y?
|
[
"1/7",
"3",
"15",
"52/7",
"12"
] |
2x+y=5 ...equation 1
3x-2y=7 ...equation 2
adding both the equations
5x-y=12
correct answer option E
The answer is: E
|
E
|
mathematics
|
A computer is programmed to multiply consecutive even integers 2*4*6*8*…*n until the product is divisible by 1881, What is the value of n?
|
[
"22",
"38",
"114",
"122",
"672"
] |
Factorise 1881.. 3*11*57..
So n has to be a multiple of largest prime number,61..
So n=2*57=114..
Ans :C
The answer is: C
|
C
|
mathematics
|
Three cubes of iron whose edges are 6cm, 8cm and 10cm respectively are melted and formed into a single cube. The edge of the new cube formed is
|
[
"10 cm",
"12 cm",
"16 cm",
"18 cm",
"None"
] |
Sol.
Volume of the new cube
= (63 + 83 + 103) cm3
= 1728cm3.
Let the edge of the new cube be a cm.
∴ a3 = 1728
⇒ a = 12.
Answer B
The answer is: B
|
B
|
mathematics
|
A man can row upstream at 10kmph and downstream at 28 kmph. The speed of the stream is
|
[
"2 km/hr",
"4 km/hr",
"5 km/hr",
"10.5 km/hr",
"None"
] |
Sol.
Speed of stream = 1/2(28-10) kmph = 4 kmph.
Answer B
The answer is: B
|
B
|
mathematics
|
Tough and Tricky questions: Word Problems.
It takes Sarah 12 minutes to do one oil change, and it takes Alice 8 minutes. If Sarah and Alice both begin doing oil changes at exactly 9:00 a.m. without pausing, when is the first time at which they will finish changing the oil of a car simultaneously?
|
[
"09:24 a.m.",
"10:42 a.m.",
"12:00 a.m.",
"1:00 p.m.",
"2:00 p.m."
] |
LCM of 812
8 = 2 * 2 * 2
12 = 2 * 2 * 3
LCM = 2 * 2 * 2 * 3 = 24 minutes
924AM
A
The answer is: A
|
A
|
mathematics
|
How long will a boy take to run round a square field of side 50 meters, if he runs at the rate of 12km/hr?
|
[
"52sec",
"45sec",
"60sec",
"25sec",
"39sec"
] |
Speed = 12 km/hr = 12*5/18 = 10/3 m/sec
Distance = 50*4 = 200m
Time taken = 200*3/10 = 60sec
Answer is C
The answer is: C
|
C
|
mathematics
|
A train passes a station platform in 36 sec and a man standing on the platform in 22 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
|
[
"288",
"210",
"881",
"1277",
"121"
] |
Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 22 = 330 m.
Let the length of the platform be x m . Then,
(x + 330)/36 = 15 => x = 210 m.
Answer: B
The answer is: B
|
B
|
mathematics
|
A train travelling at a speed of 75 mph enters a tunnel miles long. The train is mile long. How long does it take for the train to pass through the tunnel from the moment the front enters to the moment the rear emerges?
|
[
"2",
"3",
"5",
"7",
"8"
] |
Explanation:
Total distance covered =miles
=miles
Time taken = hrs
= hrs
= min
= 3 min
Answer: B) 3 min
The answer is: B
|
B
|
mathematics
|
In how many ways can the letters in mmmnnnppqq can be arranged with two n's together?
|
[
"15120 ways",
"16120 ways",
"14120 ways",
"13120 ways",
"12120 ways"
] |
MMMN(NN)PPQQ so taking two N's together we can get =9!/(3!*2!*2!) arrangements
bow this NN can be arranged in =2!/2!=1 ways
so total arrangements=9!/(3!*2!*2!)=15120 ways
ANSWER:A
The answer is: A
|
A
|
mathematics
|
QUANT 4-PACK SERIES Problem Solving Pack 4 Question 2 For every positive integer n...
For every positive integer n that is greater than 1, the function s(n) is defined to be the sum of all of the odd integers from 1 to n, inclusive. The s(n) could have any of the following units digits except…?
|
[
"1",
"2",
"4",
"6",
"9"
] |
For every positive integer n that is greater than 1, the function s(n) is defined to be the sum of all of the odd integers from 1 to n, inclusive. The s(n) could have any of the following units digits except…?
Used brute force on this one to calculate. Not sure if there is a quicker way.
1+3=4 C is out
1+3+....15= 81 A is out
1+3+5+7=16 D is out
1+3+5=9 E i out
Answer: B
The answer is: B
|
B
|
mathematics
|
What is the probability of getting sum 10 with the help of three dice?
|
[
"1/4",
"1/8",
"1/16",
"1/24",
"1/32"
] |
(1,3,6) 3!=6 (2,2,6) =3!/2=3
(1,4,5) 3!=6 (2,4,4)=3
(2,3,5) 3!=6 (3,3,4)=3
prob. of getting sum 10 =(6+6+6+3+3+3)/216 =1/8 Ans
ANSWER:B
The answer is: B
|
B
|
mathematics
|
An elephant fell into a wall of depth 20mts.Everyday it climbs 4mts but at the end falls by 2mts.Find the number of days it would take for the elephant to get out of the wall
|
[
"7 days",
"9 days",
"8 days",
"10 days",
"11 days"
] |
4-2=2
2*8=16
16(8 days)+4(9th day)=20
8+1 =9 days
ANSWER:B
The answer is: B
|
B
|
mathematics
|
Two trains move in the same direction at speeds 50 kmph and 32 kmph respectively. A man in the slower train observes that 15 seconds elapse before the faster train completely passes by him. What is the length of faster train?
|
[
"100m",
"75m",
"120m",
"50m",
"40m"
] |
As both trains move in same direction, the relative velocity is (50-32)Km/hr
=> Velocity = 18Km/hr = 18*(5/18) m/s = 5m/s
As 15seconds is the total time taken by the train,
=> Length of train = 5*15 = 75m
ANSWER:B
The answer is: B
|
B
|
mathematics
|
Kim is taking a math class, and the teacher gives a multiple choice test consisting of 8 questions. If each question has 4 answer choices, and Kim answers every question, in how many different ways can she complete the test?
|
[
"a 4^8",
"b 400",
"c 5^8",
"d 8^5",
"e 40^40"
] |
different ways to solve each question is 4.
So, 4*4*4*4.. 8 times ----> 4^8
Answer will be A
The answer is: A
|
A
|
mathematics
|
David was born 5 years after his father's marriage. His mother is 4 years younger than his father but 20 years older than David who is 8 years old. At what age did the father get married ?
|
[
"19 years",
"20 years",
"21 years",
"18 years",
"17 years"
] |
Explanation:
David's present age = 8 years.
His mother's present age = (20 + 8) years = 28 years.
His father's present age = (28 + 4) years = 32 years.
His father's age at the time of David's birth = (32 - 8) years = 24 years.
Therefore David's father's age at the time of marriage = (24 - 5) years = 19 years.
Answer: A
The answer is: A
|
A
|
mathematics
|
If the sum of the 4th term and the 12th term of an arithmetic progression is 10, what is the sum of the first 15 terms of the progression?
|
[
"65",
"75",
"60",
"55",
"50"
] |
4th term + 12th term = 10
i.e., (a+3d)+(a+11d) = 10
Now, Sum of first 15 terms = (15/2) * [2a + (15-1)d]
= (15/2) * [2a + 14d]
= (15/2) * 10 --------------- From (1)
=75
Answer : B
The answer is: B
|
B
|
mathematics
|
When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 86.12, what is the value of y?
|
[
"96",
"87",
"75",
"25",
"12"
] |
by the definition of a remainder, the remainder here is equal to 9/y. the remainder in decimal form is given as .12
therefore, 9/y = .12
solve for y and get 75.
C
The answer is: C
|
C
|
mathematics
|
If the sample interest on a sum of money 10% per annum for 2 years is $1200, find the compound interest on the same sum for the same period at the same rate?
|
[
"$1260",
"$1520",
"$1356",
"$1440",
"$1210"
] |
Rate = 10%
Time = 2years
S.I. = $1200
Principal = 100*1200/10*2 = $6000
Amount = 6000(1+10/100)^2 = $7260
C.I. = 7260-6000 = $1260
Answer is A
The answer is: A
|
A
|
mathematics
|
The G.C.D. of 1.08, 0.36 and 0.9 is:
|
[
"0.03",
"0.9",
"0.18",
"0.108",
"None"
] |
EXPLANATION
Given numbers are 1.08, 0.36 and 0.90. H.C.F. of 108, 36 and 90 is 18,
H.C.F. of given numbers = 0.18.
Answer C
The answer is: C
|
C
|
mathematics
|
Acording to a military code, SYSTEM is SYSMET and NEARER is AENRER. What is the code for FRACTION ?
|
[
"CARFTINO",
"CARFTION",
"ARFCNOIT",
"CARFNOIT",
"SUIIQQWE"
] |
Explanation:
The letter is the first half and the letter half of the word are separately reversed to obtain the code.
Answer: D
The answer is: D
|
D
|
mathematics
|
A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.157. Find the unknown rate of two blankets?
|
[
"420",
"550",
"490",
"450",
"520"
] |
10 * 157 = 1570
3 * 100 + 5 * 150 = 1050
1570 – 1050 = 520
Answer:E
The answer is: E
|
E
|
mathematics
|
Maximum no of unsuccessful attempts, a thief can do in order to break a number locking system of 4 digits.
|
[
"9988",
"9999",
"9799",
"9685",
"6545"
] |
From 0 to 9999 there are 10000 four digit numbers
So maximum number of unsuccessful attempts = 10000 - 1 = 9999
ANSWER:B
The answer is: B
|
B
|
mathematics
|
The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is?
|
[
"65",
"21",
"78",
"67",
"51"
] |
Let the total number of workers be x. Then,
8000x = (12000 * 7) + 6000(x - 7)
= 2000x = 42000
= x = 21.
Answer: B
The answer is: B
|
B
|
mathematics
|
A man’s current age is (2/5) of the age of his father. After 10 years, he will be (1/2) of the age of his father. What is the age of father at now?
|
[
"40",
"45",
"38",
"50",
"39"
] |
Let, father’s current age is A years.
Then, Man’s current age =[ (2/5)A ]years.
Therefore, [ (2/5)A + 10 ]= (1/2)(A + 10)
2(2A + 50) = 5(A + 10)
A = 50
D
The answer is: D
|
D
|
mathematics
|
The sum of the squares of three number is 138,while the sum of their products taken two at a time is 131. their sum is :
|
[
"20",
"30",
"40",
"None of these",
"Cannot be determined"
] |
Solution
Let the numbers be a,b and c then, a 2 + b 2+ c 2 = 138 and (ab + b c + ac) = 131.
(a + b+ c)2 = a 2 + b 2 + c 2 + 2(ab + b c + ca) = 138 + 2 * 131 = 400 .
⇒ (a + b + c) = 400/20= 20
Answer A
The answer is: A
|
A
|
mathematics
|
A man can row a boat at 20 kmph in still water. If the speed of the stream is 5 kmph, what is the time taken to row a distance of 60 km downstream?
|
[
"30/18 hours",
"37/13 hours",
"80/13 hours",
"12/5 hours",
"30/43 hours"
] |
Speed downstream = 20 + 5 = 25 kmph.
Time required to cover 60 km downstream
= d/s = 60/25
= 12/5 hours.
Answer: D
The answer is: D
|
D
|
mathematics
|
28,14,15,22.5,24.5,61.25,64.25,?
|
[
"224.875",
"234.875",
"244.875",
"254.875",
"264.875"
] |
28*0.5=14
15*1.5=22.5
24.5*2.5=61.25
64.25*3.5=224.875
ANSWER:A
The answer is: A
|
A
|
mathematics
|
Find the annual income derived by investing $ 6800 in 30% stock at 136.
|
[
"550",
"1500",
"250",
"1300",
"400"
] |
By investing $ 136, income obtained = $ 30.
By investing $ 6800, income obtained = $ [(30/136)*6800] = $ 1500.
Answer B.
The answer is: B
|
B
|
mathematics
|
A starts a business with a capital of Rs. 85,000. B joins in the business with Rs.42500 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?
|
[
"8 months",
"7 months",
"6 months",
"10 months",
"5 months"
] |
Let B joined for x months. Then
85000×12:42500×x=3:1
⇒850×12:425x=3:1
⇒850×12×1=3×425x
⇒850×4=425x
⇒x=8
Answer is A.
The answer is: A
|
A
|
mathematics
|
Which of the following numbers completes
the sequence 3, 8, 14, 21, 29, ___?
|
[
"35",
"36",
"37",
"38",
"39"
] |
The numbers increase at a somewhat steady rate, so you have to figure out how much
you have to add to each number to produce the next in the sequence: 3 + 5 = 8; 8 + 6 = 14;
14 + 7 = 21; 21 + 8 = 29, and so on. The rule for the sequence is to add successively larger
numbers to each number; therefore, the next number is 29 + 9 = 38.
correct answer D)38
The answer is: D
|
D
|
mathematics
|
The workforce of Company X is 60% female. The company hired 22 additional male workers, and as a result, the percent of female workers dropped to 55%.How many employees did the company have after hiring the additional male workers?
|
[
"160",
"220",
"264",
"360",
"420"
] |
Let's xx be total quantity of employees
0.6x=females before adding men
0.55(x+22)=females after adding men
as quantity of women doesn't change we can make an equation:
0.6x=0.55(x+22)
0.05x=12.1
x=242 - this is quantity of employees before adding 22 men
So after adding it will be 264
Answer is C
The answer is: C
|
C
|
mathematics
|
What is the perimeter of a regular polygon with sides of length 15 cm and internal angles measuring 160° each?
|
[
"96 cm",
"108 cm",
"120 cm",
"132 cm",
"270 cm"
] |
Sum of all interior angles is given by:
180(n-2) = n is number of sides
180(n-2) = 160*n
from here
n = 18
So perimeter becomes 15*18= 270
Answer :E
The answer is: E
|
E
|
mathematics
|
After giving a discount of rs.45 the shopkeeper still gets a profit of 20%,if the cost price is rs.180.find the markup %?
|
[
"0.4",
"0.55",
"0.45",
"0.48",
"0.58"
] |
cost price=180
s.p=180*120/100=216
disc=45
so...mark price=216+45=261......
mark up%=261-180/180=81/180=.45 or 45%
ANSWER:C
The answer is: C
|
C
|
mathematics
|
Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
|
[
"2435",
"1243",
"1509",
"3456",
"5184"
] |
Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
E
The answer is: E
|
E
|
mathematics
|
IN Common Wealth Games an athlete runs 400 meters in 24 seconds. Hisspeed is ?
|
[
"25 km/hr",
"27 km/hr",
"60.60 km/hr",
"32 km/hr",
"None of these"
] |
Explanation :
(400/1000)/(24/3600)=60.60 km/hr
Answer : C
The answer is: C
|
C
|
mathematics
|
Calculate the standard deviation of each data set {10,10,10,10,10}
|
[
"8.05",
"9",
"10",
"15",
"15.5"
] |
Standard Deviation Data set A
= √[ ( (9-10)2+(10-10)2+(11-10)2+(7-10)2+(13-10)2 )/5 ] = 2
Standard Deviation Data set B
= √[ ( (10-10)2+(10-10)2+(10-10)2+(10-10)2+(10-10)2 )/5 ] = 0
Standard Deviation Data set C
= √[ ( (1-10)2+(1-10)2+(10-10)2+(19-10)2+(19-10)2 )/5 ] = 8.05
Option A
The answer is: A
|
A
|
mathematics
|
An egg seller sells his eggs only in the packs of 3 eggs, 6 eggs, 9 eggs, 12 eggs etc., but the rate is not necessarily uniform. One day Raju (which is not the same egg seller) purchased at the rate of 3 eggs for a rupee and the next hour he purchased equal number of eggs at the rate of 6 eggs for a rupee. Next day he sold all the eggs at the rate of 9 eggs for Rs. 2. What is his percentage profit or loss?
|
[
"10% loss",
"11.11% loss",
"3% loss",
"2.5 % profit",
"None of These"
] |
Solution: CP of one egg in first case = 1/3 = 33.33 paise
CP of one egg in second case = 1/6 = 16.66 paise
Average CP = (33.33 +16.66)/2 = 25 paise
Selling price of 9 eggs = Rs. 2
SP of one egg = 200/9
Profit or loss = [(25 - (200/9))*100]/25
Profit or loss = -11.11. (loss)
Answer: Option B
The answer is: B
|
B
|
mathematics
|
The average salary of workers in an industry is Rs.200 the average salary of technicians being Rs.400 and that of non-technicians being Rs.125. What is the total number of workers?
|
[
"277",
"665",
"662",
"552",
"281"
] |
8 * 84 = 672 – 7 = 665
Answer:B
The answer is: B
|
B
|
mathematics
|
Today John is 3 times older than Mark. If in 14 years, John will be one year younger than twice the age of Mark on that day, how old is John today?
|
[
"13",
"33",
"36",
"38",
"39"
] |
Given after 14yrs john will be 1 year younger than twice mark's age
i.e 3M+14 = 2(M+14)-1
M=13
=>John's current age = 3M = 39
Answer is E
The answer is: E
|
E
|
mathematics
|
If the sum of one-half of a number exceeds one-third of that number by 7 1/3, the number is:
|
[
"15",
"18",
"20",
"25",
"30"
] |
Let the number be x. Then,
(1/2 x + 1/5 x) - 1/3 x = 22/3
11/30 x = 22/3
x = 20
ANSWER:C
The answer is: C
|
C
|
mathematics
|
What is the units digit of (6!*4! + 6!*5!)/12?
|
[
"0",
"3",
"2",
"1",
"4"
] |
(6!*4! + 6!*5!)/12
=6!(4! + 5!)/12
=720 ( 24 + 120)/12
=(720 * 144)/12
= 720 * 12
Units digit of the above product will be equal to 0
Answer A
The answer is: A
|
A
|
mathematics
|
What is the 10th term in this sequence?
3,5,8,15,25,40,67,104,171
|
[
"273",
"278",
"279",
"377",
"277"
] |
3+5 =8 +0 =8
8+5 =13+2 =15
15+8 =23+2 =25
25+15=40+0 =40
40+25=65+2 =67
67+35=102+2 =104
104+67=171+0=171
171+104=275+2=277
so 9th term is 277
ANSWER:E
The answer is: E
|
E
|
mathematics
|
If the cost price of 50 articles is equal to the selling price of 32 articles, then the gain or loss percent is?
|
[
"22",
"56.25",
"78",
"33",
"25"
] |
Given that, cost price of 50 article is equal to selling price of 32 articles.
Let cost price of one article = Rs. 1
Selling price of 32 articles = Rs. 50
But Cost price of 32 articles = Rs. 32
Therefore, the trader made profit.\Percentage of profit = 18/32 * 100 = 56.25%
Answer:B
The answer is: B
|
B
|
mathematics
|
A sphere is inscribed in a cube with an edge of 10. What is the shortest possible distance from one of the vertices of the cube to the surface of the sphere?
|
[
"10(√3-1)",
"5",
"10(√2-1)",
"5(√3-1)",
"5(√2-1)"
] |
As sphere is inscribed in cube then
=>the edge of the cube equals to the diameter of a sphere --> Diameter=10
Diagonal of a cube equals to Diagonal=square_root(10^2+10^2+10^2)=10√3.
half of Diagonal-Diameter is gap between the vertex of a cube and the surface of the sphere = (10√3-10)/2
=5(√3-1)
ANSWER:D
The answer is: D
|
D
|
mathematics
|
In how many different number of ways 1 boys and 2 girls can sit on a bench?
|
[
"700",
"7",
"6",
"8",
"1"
] |
npn = n!
3p3 = 3 × 2 × 1 = 6
C)
The answer is: C
|
C
|
mathematics
|
What approximate value should come in place of question mark (?) in the following equation?
33 1⁄3% of 768.9 + 25% of 161.2 – 64.12 = ?
|
[
"230",
"225",
"235",
"220",
"234"
] |
? = 33 1⁄3% of 768.9 + 25% of 161.2 – 64.12
= 1⁄3 of 768.9 + 1⁄4 of 161.2 – 64.12
= 256.3 + 40.3 – 64.12 ≈ 234
Answer E
The answer is: E
|
E
|
mathematics
|
A man rows his boat 72 km downstream and 30 km upstream, taking 3 hours each time. Find the speed of the stream?
|
[
"6 kmph",
"5 kmph",
"2 kmph",
"8 kmph",
"7 kmph"
] |
Speed downstream = d/t = 72/(3) = 24 kmph
Speed upstream = d/t = 30/(3) = 10 kmph
The speed of the stream = (24 - 10)/2 = 7 kmph
Answer:E
The answer is: E
|
E
|
mathematics
|
It takes Megan 7 minutes to run a mile, and it takes Mike 8 minutes. If Megan and Mike both begin running at exactly 8:00 a.m. without pausing, when is the first time at which they will finish running a mile simultaneously?
|
[
"8:28 am",
"8:35 am",
"8:42 am",
"8:49 am",
"8:56 am"
] |
Since Megan will run s miles after s × 7 minutes and Mike will run c miles after c × 8 minutes, they both will finish running a mile at the same time when s × 7 = c × 8. Since s and c must be integers (they represent the number of miles finished) this question is asking you to find a common multiple of 7 and 8. The question asks for the first time they will finish running a mile simultaneously, so you must find the least common multiple. The least common multiple of 7 and 8 is 56, so in the context of the question, this would be 56 minutes. Therefore, the first time they will finish running a mile at the same time is 8:00 + 56 minutes, or 8:56 a.m. The answer is (E).
The answer is: E
|
E
|
mathematics
|
A trader has 30 kg of rice, a part of which he sells at 14% profit and rest at 6% loss. On the whole his loss is 4% . What is the quantity sold at 14% profit and that at 6% loss?
|
[
"3 and 27 kg",
"10 and 40 kg",
"15 and 27 kg",
"20 and 30 kg",
"40 and 30 kg"
] |
Alligation Method
I PART II PART
14 (x1) -6 (x2)
\ /
x
/ \
(x2-x) (x-x1)
2 18
1 9
Ratio of quantities sold at 14% profit and 6% loss = 1: 9
Quantity sold at 14% profit = 30/1+9 *1 = 3 kg
Quantity sold at 6% loss = 30/1+9 *9 = 27 kg
ANSWER:A
The answer is: A
|
A
|
mathematics
|
The speed of a car is 60 km in the first hour and 30 km in the second hour. What is the average speed of the car?
|
[
"45 kmph",
"65 kmph",
"75 kmph",
"85 kmph",
"90 kmph"
] |
Explanation:
S = (60 + 30)/2 = 45 kmph
A)
The answer is: A
|
A
|
mathematics
|
A person buys an article at Rs.500. At what price should he sell the article so as to make a profit of 20%?
|
[
"600",
"277",
"269",
"261",
"281"
] |
Cost price = Rs.500
profit = 20% of 500 = Rs.100
Selling price = Cost price + Profit
= 500 + 100 = 600.Answer: A
The answer is: A
|
A
|
mathematics
|
Find out the wrong number in the series.
6, 12, 48, 106, 384, 768, 3072
|
[
"768",
"384",
"106",
"488",
"12"
] |
Each even term of the series is obtained by multiplying the previous term by 2.
2nd term = (1st term) x 2 = 6 x 2 = 12
4th term = (3rd term) x 2 = 48 x 2 = 96.
6th term = (5th term) x 2 = 384 x 2 =768.
4th term should be 96 instead of 106.
ANSWER:C
The answer is: C
|
C
|
mathematics
|
The graph of a quadratic function and the graph of a linear function in the xy plane can intersect in at most how many points
|
[
"one",
"Two",
"Three",
"Four",
"More than four"
] |
i also thought 2 but i think we need to consider linear function like y=|X| then it could intersect at 6 points.
E
The answer is: E
|
E
|
mathematics
|
The number of arrangements that can be made with the letters of the word MEADOWS so that the vowels occupy the even places?
|
[
"122",
"134",
"144",
"156",
"176"
] |
Explanation:
The word MEADOWS has 7 letters of which 3 are vowels.
-V-V-V-
As the vowels have to occupy even places, they can be arranged in the 3 even places in 3! i.e., 6 ways. While the consonants can be arranged among themselves in the remaining 4 places in 4! i.e., 24 ways.
Hence the total ways are 24 * 6 = 144.
C)
The answer is: C
|
C
|
mathematics
|
If a card is randomly drawn from a well shuffled pack of cards, what is the probability of drawing a club, or a red jack, or a red queen?
|
[
"19/26",
"15/52",
"17/52",
"8/13",
"5/13"
] |
There are 13 clubs and 2 red jacks and 2 red queens.
P(club or red jack or red queen) = 17/52
The answer is C.
The answer is: C
|
C
|
mathematics
|
Jake can dig a well in 16 days. Paul can dig the same well in 24 days. Jake, Paul and Hari together dig the well in 8 days. Hari alone can dig the well in
|
[
"48",
"99",
"22",
"27",
"92"
] |
Explanation: Simple one. Let the total work to be done is 48 meters. Now Jake can dig 3 mts, Paul can dig 2 mts a day. Now all of them combined dug in 8 days so per day they dug 48/8 = 6 mts. So Of these 8 mts, Hari capacity is 1 mt.
So he takes 48 /1 = 48 days to complete the digging job.
Answer:A
The answer is: A
|
A
|
mathematics
|
Ross is looking at Rachel, but Rachel is looking at Joey. Ross is married, but Joey is not. Is married person looking at the unmarried person?
|
[
"Yes",
"No",
"Insufficient information",
"data irrelevant",
"none of the above"
] |
Explanation:
If Rachel is married, Joey who is unmarried is looking ar Rachel who is married.
If Rachel is unmarried, then Ross who is married is looking at Rachel who is unmarried.
Answer is A
The answer is: A
|
A
|
mathematics
|
If p and q are positive integers each greater than 1, and 17(p+1)=25(q+1), what is the least possible value of p+q?
|
[
"36",
"42",
"40",
"46",
"none"
] |
17(p+1)=29(q+1) --> (p+1)/(q+1) = 29/17 --> the least positive value of p+1 is 25, so the least value of p is 24 and the least positive value of q+1 is 17, so the least value of q is 16 --> the least value of p+q is 24+16=40.
Answer: C.
The answer is: C
|
C
|
mathematics
|
Two numbers are in the ratio of 1 : 2. If 9 be added to both, their ratio changes to 3 : 5. The greater number is
|
[
"20",
"24",
"28",
"32",
"36"
] |
Let the ratio be X : Y,
Given X/Y = 1/2 ,
(X + 9)/(Y + 9) = 3/5
=> X = 18
And Y = 36
ANSWER:E
The answer is: E
|
E
|
mathematics
|
A train 120 m long passes a man,running at 6 kmph in the direction opposite to that of the train,in 6 seconds.The speed of the train is
|
[
"54 kmph",
"60 kmph",
"66 kmph",
"72 kmph",
"82 kmph"
] |
speed of train relative to man: 120/6 * 18/5 km/hr
= 72 km/hr
let speed of train= x
therefore x+6 = 72
x= 72-6
x=66 km/hr
ANSWER:C
The answer is: C
|
C
|
mathematics
|
Find the number of ways in which 4 letters may be selected from the word "Examination"?
|
[
"66",
"70",
"136",
"330",
"4264"
] |
EXAMINATION has 11 letters, and in which 'A', 'I' and 'N', all occur twice. 11C4, would have been fine if all letters were distinct.
So, we have E, X, M, T, O, (AA), (II), (NN). 8 distinct letters.
1. 4 letters selected, which are all distinct: 8C4 = 70
2. 2 letters alike, and 2 distinct (eg: AAEX) = 3C1 x 7C2 = 63
3. 2 letters alike, and 2 letters alike (eg: AAII) = 3C2 = 3
So answer is, 70 + 63 + 3 = 136.
ANSWER:C
The answer is: C
|
C
|
mathematics
|
Winson leaves home everyday at 4 p.m to pick his son from school and returns home at 6 p.m. One day, the school was over at 4 p.m and the son started walking home from school. Winson, unaware of this, starts from home as usual and meets his son on the way and returns home with him 15 minutes early. If the speed of Winson is 30 km\hr, find the speed of his son.
|
[
"15km/hr",
"6 km/hr",
"4.28 km/hr",
"9 km/hr",
"4.12 km/hr"
] |
Winson leaves home everyday at 4 p.m to pick his son from school and returns home at 6 p.m. One day, the school was over at 4 p.m and the son started walking home from school. Winson, unaware of this, starts from home as usual and meets his son on the way and returns home with him 15 minutes early. If the speed of Winson is 30 km\hr, find the speed of his son.
The distance from home to school is 30 km. The round trip distance = 60 km. Because he returns home 15 minutes early, I thought it might be easier to break his trip up into 8 identical 15 minute blocks, each of which he traveled at 7.5 km/hour.
Because we are dealing with a round trip here, Winson would have stopped 7.5 minutes short of the school. This means he traveled Distance=rate* time .5Km/hour*52.5 minutes or 26.25 KM. His son therefore traveled 3.75km/hour by the time he met his dad at 4:52.5. It took the son 52.5 minutes to travel 3.75 km. Because we are trying to find the son's rate per hour (i.e. 60 minutes) and we have his speed for 52.5 minutes it's best to convert to km/minute then multiply by 60 to get km/hour
3.75km/52.5 = .07 km/minute
.07km/minute*60 minutes = 4.28 km/hour.
Answer: C. 4.28 km/hr
The answer is: C
|
C
|
mathematics
|
The ratio between the number of sheep and the number of horses at the Stewart farm is 3 to 7, If each horse is fed 230 ounces of horse food per day and the farm needs a total 12,880 ounces of horse food per day, what is the number of sheep in the farm?
|
[
"24",
"28",
"32",
"56",
"60"
] |
Let the number of sheeps and horses be 3x and 7x.
Now total number of horses = total consumption of horse food/consumption per horse = 12880/230 = 56, which is equal to 7x. => x = 8
Sheeps = 3x = 3*8 = 24. Hence A
The answer is: A
|
A
|
mathematics
|
The remainder when 1!+2!+3!...+50! divided by 5! will be
|
[
"21",
"33",
"77",
"927",
"19"
] |
The remainder when the terms greater than 5! are divided by 5! becomes 0 so we need to consider the terms upto 4!.
So remainder will be whatever is obtained by dividing 1!+2!+3!+4! with 5!.
So remainder is obtained by dividing (1+2+6+24)= 33 with 5! ( 120)
So remainder is 33.
Answer:B
The answer is: B
|
B
|
mathematics
|
The average (arithmetic mean) of 14, 32, and 53 is 3 more than the average of 21, 47, and x. What is x?
|
[
"20",
"21",
"22",
"23",
"24"
] |
The average of 14, 32, and 53 is 33.
The average of 21, 47 and x is 30.
Then 21 + 47 + x = 90.
x = 22.
The answer is C.
The answer is: C
|
C
|
mathematics
|
Pipes A and B can fill a cistern in 8 and 24 minutes respectively. They are opened an alternate minutes. Find how many minutes, the cistern shall be full?
|
[
"11",
"12",
"99",
"75",
"72"
] |
1/8 + 1/24 = 1/6
6 * 2 = 12
Answer: B
The answer is: B
|
B
|
mathematics
|
A mother is planning a party for her child and buys some snacks. She buys 3 bags of chips, 1 bag of pretzels, and 2 packages of cookies. She pays $3.00 per bag of chips, $2.50 per bag of pretzels, and $4.00 per package of cookies. What is the average price per snack the mother paid?
|
[
"$2.25",
"$3.25",
"$2.00",
"$3.50",
"$3.00"
] |
Explanation:
3 1 2
$3.00 $2.50 $4.00
$9.00 + $2.50 + $8.00 = $19.50/6 = $3.25
B
The answer is: B
|
B
|
mathematics
|
In a college, the ratio of the number of boys to girls is 8 : 5. If there are 400 girls, the total number of students in the college is
|
[
"1040",
"920",
"980",
"720",
"820"
] |
Explanation:
Let the boy are 8x and Girls are 5x
=> 5x = 400
=> x = 80
Total students = 8x+5x = 13x = 13(80) = 1040
Option A
The answer is: A
|
A
|
mathematics
|
Integer n is a four digit number such that it is made exactly of 2 distinct digits. If n is divisible by 9, how many possible values does n have?
|
[
"59",
"60",
"61",
"68",
"69"
] |
Then the additional combinations would be, 9000(1), 8883(4), 7776(4), 6669(4), 6660(3), 5553(4), 4446(4), 3339(4), 3330(3), 2221(4), 1116(4), 9990(3).
8*4 = 32
3*3 = 9
1*1 = 1
total = 42
Previous was 27. So total 27+42 = 69.
ANSWER:E
The answer is: E
|
E
|
mathematics
|
The length of one pair of opposite sides of a square is increased by 5 cm on each side the ratio of the length and the breadth of the newly formed rectangle becomes 3 : 2. What is the area of the original square?
|
[
"25 sq.cm",
"81 sq.cm",
"120 sq.cm",
"225 sq.cm",
"None of these"
] |
Let original length of each side = x cm.
Then, its area = (x2)cm2.
Length of rectangle formed = (x + 5) cm
and its breadth = x cm.
∴ x+5/x=3/2 ⇔ 2x + 10 = 3x ⇔ x = 10
∴ Original length of each side = 10 cm and its area = 100 cm2
Answer E
The answer is: E
|
E
|
mathematics
|
A shopkeeper buys two articles for Rs.1000 each and then sells them, making 30% profit on the first article and 30% loss on second article. Find the net profit or loss percent?
|
[
"200",
"278",
"282",
"202",
"300"
] |
Profit on first article = 30% of 1000 = 300.
This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.
Answer: E
The answer is: E
|
E
|
mathematics
|
A man goes from A to B at a speed of 35 kmph and comes back to A at a speed of 28 kmph. Find his average speed for the entire journey?
|
[
"38.9 kmph",
"38.8 kmph",
"38.1 kmph",
"37.1 kmph",
"37.8 kmph"
] |
Distance from A and B be 'd'
Average Speed = total distance/total time
Average Speed = (2d)/[(d/35) + (d/28]
= (2d)/[11d/140) => 38.1 kmph.
Answer:C
The answer is: C
|
C
|
mathematics
|
How many seconds will a 900 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
|
[
"23 sec",
"30 sec",
"49 sec",
"54 sec",
"59 sec"
] |
Speed of train relative to man = 63 - 3
= 60 km/hr.
= 60 * 5/18
= 50/3 m/sec.
Time taken to pass the man = 900 * 3/50
= 54 sec.
Answer:D
The answer is: D
|
D
|
mathematics
|
The number of sailors on a ship is 82% more than the number of officers. The ratio of sailors to officers would be
|
[
"33:25",
"47:20",
"47:25",
"22:25",
"91:50"
] |
Sailor = 1.82 * Officer
Sailor/Officer = 1.82/1 = 182/100 = 91/50
Answer will be E
The answer is: E
|
E
|
mathematics
|
A grocer purchased 80 kg of sugar at 13.50 per kg and mixed it with 120 kg sugar at 16 per kg. At what rate should he sell the mixture to gain 21%?
|
[
"17 per kg",
"18.15 per kg",
"16.5 per kg",
"16 per kg",
"None of these"
] |
C.P. of 200 kg of mixture = (80 × 13.50 + 120 × 16)
= 3000.
S.P. = 121% of 3000 = (121⁄100 × 3000) = 3630
∴ Rate of S.P. of the mixture = (3630⁄200) per kg
= 18.15 per kg.
Answer B
The answer is: B
|
B
|
mathematics
|
When positive integer X is divided by positive integer Y, the remainder is 11.52. If X/Y = 96.12, what is the value of Y?
|
[
"96",
"75",
"48",
"25",
"12"
] |
When positive integer x is divided by positive integer y, the remainder is 11.52 --> x=qy+11.52;
x/y=96.12 --> x=96y+0.12y (so q above equals to 96);
0.12y=11.52 --> y=96.
Answer: A.
The answer is: A
|
A
|
mathematics
|
Three pipes of same capacity A,B,C can fill a tank in 6 hours. If there are only two pipes B and C of same capacity, the tank can be filled in?
|
[
"2",
"4",
"9",
"12",
"16"
] |
The part of the tank filled by three pipes in one hour
= 1/6
=> The part of the tank filled by two pipes in 1 hour
= 2/3 * 1/6 = 1/9.
The tank can be filled in 9 hours.
Answer:C
The answer is: C
|
C
|
mathematics
|
A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age?
|
[
"228",
"267",
"800",
"297",
"127"
] |
25 = E/(1000 - E) * 100
1000 - E = 4E
1000 = 5E => E = 200
1000 - 200 = 800
Answer: C
The answer is: C
|
C
|
mathematics
|
Positive integer n leaves a remainder of 4 after division by 6 and a remainder of 3 after division by 5. If n is greater than 30, what is the remainder that n leaves after division by 40?
|
[
"3",
"12",
"18",
"22",
"30"
] |
The theory says:
if a # x is devided by y and leave the positive # r as the remainder then it can also leave negative # (r-y) as the remainder.
e.g:
9 when devided by 5 leves the remainder 4 : 9=5*1+4
it can also leave the remainder 4-5 = -1 : 9=5*2 -1
back to the original qtn:
n leaves a remainder of 4 after division by 6 and a remainder of 3 after division by 5
==> n leaves a remainder of -2 (i.e. 4-6) after division by 6 and a remainder of -2 (i.e. 3-5) after division by 5
==> n when devided by 5 and 6 leaves the same remainder -2.
what is n?
LCM (5,6)-2 = 30-2 = 28
CHECK: 28 when devided by 6 leaves the remainder 4 and when devided by 5 leaves the remainder 3
However, the qtn says n > 40
so what is the nex #, > 28, that can give the said remainders when devided by 6 and 5
nothing but 28 + (some multiple of 6 and 5) as thissome multiple of 6 and 5will not give any remainder when devided by 5 or 6 but 28 will give the required remainders.
hence n could be anything that is in the form 28 + (some multiple of 6 and 5)
observe thatsome multiple of 6 and 5is always a multiple of 30 as LCM (5,6) = 30.
hence when n (i.e. 28 + some multiple of 6 and 5) is devided by 30 gives the remainder 28.
E
The answer is: E
|
E
|
mathematics
|
Anand and Deepak started a business investing Rs. 40,000 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is?
|
[
"2777",
"2888",
"6440",
"2882",
"2781"
] |
Ratio of their shares =40000 : 35000 = 8:7
Deepak's share = 13800 * 7/15 = Rs. 6440.
Answer: C
The answer is: C
|
C
|
mathematics
|
John went on a diet 6 months ago when he weighed 224 pounds. If he now weighs 200 pounds and continues to lose at the same average monthly rate, in approximately how many months will he weigh 180 pounds?
|
[
"3",
"3.5",
"4",
"4.5",
"5"
] |
224 - 200 = 24 pounds lost in 6 months
24/6 = 4, so Joe is losing weight at a rate of 4 pounds per month.
...in approximately how many months will he weigh 180 pounds?
A simple approach is to just list the weights.
Now: 200 lbs
In 1 month: 196 lbs
In 2 months: 192 lbs
In 3 months: 188 lbs
In 4 months: 184 lbs
In 5 months: 180 lbs
Answer: E
The answer is: E
|
E
|
mathematics
|
If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time?
|
[
"Rs. 51.25",
"Rs. 52",
"Rs. 54.25",
"Rs. 60",
"Rs. 70"
] |
Sum = (50 * 100) / (2 * 5) = Rs. 500
Amount = [500 * (1 + 5/100)2] = Rs. 551.25
C.I. = (551.25 - 500) = Rs. 51.25.
ANSWER:A
The answer is: A
|
A
|
mathematics
|
In a city, the streets are aligned in a grid, where the east-west roads are called 1st Rd, 2nd Rd, 3rd Rd, etc, increasing in number as one moves northward. The north-south roads are called 1st Ave, 2nd Ave, 3rd Ave, etc, increasing in number as one moves eastward. If Bill needs to walk from the corner of 2nd Rd and 3rd Ave to the corner of 6th Rd and 9th Ave in the shortest possible time, how many different routes could he take?
|
[
"90",
"120",
"150",
"180",
"210"
] |
Bills needs to walk 4 blocks north and 6 blocks east.
One possible solution is NNNNEEEEEE.
There are 10C4 = 210 possible solutions.
The answer is E.
The answer is: E
|
E
|
mathematics
|
Antony, Ben, and Charles each try independently to win a carnival game. If their individual probabilities for success are 2/5, 3/8, and 2/7, respectively, what is the probability that exactly two of the three players will win but one will lose?
|
[
"3/140",
"1/280",
"3/280",
"3/35",
"68/280"
] |
P = P(A wins, B wins, C loses) + P(A wins, B loses, C wins) + P(A loses, B wins, C wins) = 2/5*3/8*5/7 + 2/5*5/8*2/7 + 3/5*3/8*2/7 = 68/280.
Answer: E.
The answer is: E
|
E
|
mathematics
|
In a group of 12 engineers, 4 engineers have a PHD degree; the others have only an MS or BS degree. A team of 4 engineers is to be chosen which must have at least 1 engineer with a PHD, how many different teams can be chosen?
|
[
"495",
"70",
"245",
"425",
"555"
] |
The problem asks for a combination, since order doesn't matter. Now, selecting r items from a set of n gives the Combination Formula: nCr= n!/r!(n-r)!
n = 12
r = 4
So, total teams is 12C4 = 12!/(4!(12 - 4)!) = 495, and
n = 12 - 4 = 8
r = 4
for teams without a PHD is 8C4 = 8!/(4!(8 - 4)!) = 70,
so, teams with at least 1 PHD = 495 - 70 = 425
Answer: D
The answer is: D
|
D
|
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