subject stringclasses 1
value | question stringlengths 3 1.14k | options listlengths 5 5 | solution stringlengths 18 3.7k | answer stringclasses 5
values |
|---|---|---|---|---|
mathematics | Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 2 sec. What is the length of the fast train? | [
"11 1/9 m",
"11 7/4 m",
"11 7/2 m",
"11 7/9 m",
"11 7/7 m"
] | Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 2 = 100/9 = 11 1/9 m.Answer:A
The answer is: A | A |
mathematics | Sunil invested $ 2600 fir 3 years and $ 1200 for 5 years at the same rate of Simple Interest. If the total interest from these investments is $ 930, what is the rate of interest? | [
"2 3/4%",
"5 1/3%",
"5 1/2%",
"6 3/4%",
"3 2/4%"
] | (2600x3xR)/100+(1200x5xR)/100=930
138R=930
R= 6 3/4%
Answer is D
The answer is: D | D |
mathematics | What is the least value of x. So that 23x58 is divisible by 3. | [
"2",
"0",
"1",
"3",
"4"
] | Explanation:
The sum of the digits of the number is divisible by 3, then the number is divisible by3.
2 + 3 + x + 5 + 8 = 18 + x
Least value of x may be 0
Therefore 18 + 0 = 18 is divisible by 3.
Answer: Option B
The answer is: B | B |
mathematics | Linda spent 3/4 of her savings on furniture and the rest on a TV. If the TV cost her $300, what were her original savings? | [
"$1200",
"$1300",
"$1400",
"$1800",
"$1900"
] | If Linda spent 3/4 of her savings on furnitute, the rest
4 / 4 - 3 / 4 = 1 / 4 on a TV
But the TV cost her $300. So 1 / 4 of her savings is $300. So her original savings are 4 times $300 = $1200
correct answer A
The answer is: A | A |
mathematics | A goods train runs at the speed of 72 kmph and crosses a 230 m long platform in 26 seconds. What is the length of the goods train? | [
"230 m",
"270m",
"643m",
"832m",
"290m"
] | Speed = (72 x 5/18)m/sec = 20 m/sec.
Time = 26 sec.
Let the length of the train be x metres.
Then, x + 230/26 = 20
x + 230 = 520
x = 290.
Answer:E
The answer is: E | E |
mathematics | A security guard at a certain store is instructed to check the receipt of one out of every five customers as they are leaving the store. If, on the guard's shift, 12 customers leave the store, how many different samples of customers could have been selected to have their receipts checked? | [
"20",
"66",
"59",
"90",
"100"
] | to choose the sample of 2 customers from 12. it can be done 12C2 possible ways.
So the answer is B. 66
The answer is: B | B |
mathematics | Annie will be half as old as Larry in 3 years. Annie will also be one-third as old as Jerome in 5 years. If Jerome is 10 years older than Larry, how old is Annie? | [
"3",
"8",
"19",
"26",
"34"
] | J = L+10
(1) 2(A+3) = L+3
(2) 3(A+5) = J+5 = L+15
Let's subtract equation (1) from equation (2)
A+9 = 12
A = 3
The answer is A.
The answer is: A | A |
mathematics | The average age of a group of 5 members is 20 years. Two years later, a new member joins the group. The average age of the group becomes 21 years. What is the age of the new member ? | [
"16 years",
"21 years",
"22 years",
"23 years",
"24 years"
] | The average age of the 5 members is 20 years
=> The sum of the ages of the 5 members is 20*5 = 100 years
Once the new member joins, the average age becomes 21 years.
Let the age of the new member be x.
Then (110+x)/6 = 21
=> x = 16 years
Answer A
The answer is: A | A |
mathematics | judith is practicing her dance steps along with her friends. In a particular sequence, all of them form a row. At that point, judithis standing on the 5th position from either end of the row.
Can you find out how many girls are practicing together? | [
"4",
"9",
"7",
"6",
"8"
] | As judith is 5th from either end of the row, it means that 4 girls are on one of her sides and 4 are present on the other.
4 + 4 + 1(judith herself) = 9.
Hence,9 girls are practicing the dance together.
correct answer is B)9
The answer is: B | B |
mathematics | The speed at which a man can row a boat in still water is 6 km/hr. If he rows downstream, where the speed of current is 3 km/hr, how many seconds will he take to cover 80 meters? | [
"28",
"32",
"36",
"40",
"44"
] | The speed of the boat downstream = 6 + 3 = 9 km/hr
9 km/hr * 5/18 = 2.5 m/s
The time taken to cover 80 meters = 80/2.5 = 32 seconds.
The answer is B.
The answer is: B | B |
mathematics | A childrens identification code consists of a vowel followed by a 3-digit number greater than 200. Exactly 2 of the 3 digits in the code should be identical. How many different codes is it possible to form? | [
"211",
"216",
"1075",
"1080",
"2160"
] | A childrens identification code will be of the type -,-,-,-
first digit can be selected from any of the 5 vowels in 5C1 ways
now for the remaining three digit lets consider the following two cases
case 1: when the number is greater than 200 but less than 300
number will be of the type 2,_,_. now suppose repeating numbe... | C |
mathematics | A shopkeeper buys two articles for Rs.1000 each and then sells them, making 15% profit on the first article and 15% loss on second article. Find the net profit or loss percent? | [
"200",
"150",
"282",
"202",
"270"
] | Profit on first article = 15% of 1000 = 150.
This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.
Answer: B
The answer is: B | B |
mathematics | A bullock cart has to cover a distance of 80km in 10hrs. If it covers half of the journey in 3/5th time. what should be its speed to cover the remaining distance in the time left. | [
"8 km/h",
"10 km/h",
"12 km/h",
"14 km/h",
"16 km/h"
] | Time left = 10 - 3/5*10
= 4 hr 10 km/h
speed =40 km /4 hr
=10 kmph
Answer : B.
The answer is: B | B |
mathematics | A drum contains 4 red balls, 3 blue balls and 2 white balls. Three balls are removed (no replacement) what is the probability that there will be one of each? | [
"22",
"21",
"24",
"25",
"28"
] | 4*3*2 / 9*8*7.
There is a 4/9 chance of taking a red ball first; if you do, ther'es a 3/8 chance of taking a blue ball next, and if you get that far, there's a 2/7 chance of getting a white ball third.
Or you might get white first, blue second and red third: 2/9, followed by 3/8 and then 4/7. No matter what order it mi... | B |
mathematics | Suppose you want to arrange your English, Hindi, Mathematics, History, Geography and Science books on a shelf. In how many ways can you do it? | [
"700",
"710",
"720",
"740",
"750"
] | We have to arrange 6 books.
The number of permutations of n objects isn!=n.(n−1).(n−2)...2.1n!=n.(n−1).(n−2)...2.1
Here n=6n=6 and therefore, number of permutations is 6.5.4.3.2.1=6.5.4.3.2.1= 720
Option is C
The answer is: C | C |
mathematics | A straight pipe 6 yard in length was marked off in fourths and also in thirds. If the pipe was then cut into separate pieces at each of these markings, which of the following gives all the different lengths of the pieces, in fractions of a yard? | [
"1/6 and 1/4 only",
"1/4 and 1/3 only",
"1/6, 1/4, and 1/3",
"1/12, 1/6 and 1/4",
"1/12, 1/6, and 1/3"
] | Since we want to find the fractions, we can assume some other length of the pipe which will make calculation easier. Take the length of the pipe to be 12-meter long (the least common multiple of 3 and 4.
In this case the branch would be cut at3,4, 6,8, and 9meters (in black are given fourths of the length and in red th... | B |
mathematics | How many multiples of 2 are there between 10 and 52, 10 and 52 inclusive? | [
"27",
"25",
"24",
"21",
"22"
] | 2 multiples are ...10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,...,
the answer is =22
Answer is E
The answer is: E | E |
mathematics | There are two concentric circles with radii 8 and 6. If the radius of the outer circle is increased by 25% and the radius of the inner circle decreased by 50%, by what percent does the area between the circles increase? | [
"225",
"250",
"275",
"300",
"325"
] | The area of a circle is piR^2, where R is the radius.
The area of the big circle is 64pi.
The area of the small circle is 36pi.
The area A1 between the circles is 28pi.
When the big circle's radius increases, the new area is 100pi.
When the small circle's radius decreases, the new area is 9pi.
The area A2 between the c... | A |
mathematics | 0.99999999/1.0001−0.99999991/1.0003 | [
"10^(-8",
"3*10^(-8)",
"3*10^(-4)",
"2*10^(-4)",
"10^(-4)"
] | look at the options closely
A. 0.00000001
B. 0.00000003
C. 0.0003
D. 0.0002
E. 0.0001
Only one option is an even number, the rest odd (an esoteric sort of even/odd number)
both fractions in the question are odds
odd minus odd is always even.
So answer must be even.
Only D is even.
The answer is: D | D |
mathematics | A train can travel 50% faster than a car. Both start from point A at the same time and reach point B at 75 kms away from A at the same time. On the way, however, the train lost about 12.5 minutes while stopping at the stations. The speed of the car is? | [
"110 km/hr",
"145 km/hr",
"151 km/hr",
"180 km/hr",
"120 km/hr"
] | E
Let speed of the car be x km/hr.
Then, speed of the train = 150/100 x = 3/2 x km/hr.
75/x - 75/(3/2 x) = 125/(10 * 60)
75/x - 50/x = 5/24 = 120 km/hr.
The answer is: E | E |
mathematics | In a school having roll strength 286, the ratio of boys and girls is 8:5. If 22 more girls get admitted into the school, the ratio of boys and girls becomes | [
"12:7",
"10:7",
"8:7",
"4:3",
"none"
] | Solution: Boys: girls = 8:5; (let the boys = 8x; girl = 5x)
Total strength = 286;
8x+5x = 286;
13x = 286;
Or, x = 286/13 = 22;
Boys = 176 and girls = 110;
22 more girls get admitted then number of girls become,
(5x+22) = 110+22 = 132;
Now, new ratio of boys and girls = 176:132 = 4:3.
Answer: Option D
The answer is: D | D |
mathematics | Mr. Srinivas saves one coin of 5 on first day of the
week, three coins of 5 on the second day of the week.
Five coins of 5 on third day and so on. How much money will he has at the end of the week? | [
"238",
"245",
"2867",
"987",
"111"
] | Number of
5 coins with him at the end of week = 5 × (1 + 3 + 5 + 7 + 9 + 11 + 13) = 5 × (sum of first 7 odd numbers) (By using the formula discussed earlier). ∴ Sum of all numbers = 5 × 72 = 245.
Answer:B
The answer is: B | B |
mathematics | A certain company reported that the revenue on sales increased 30 % from 2000 to 2003, and increased 80 % from 2000 to 2005. What was the approximate percent increase in revenue for this store from 2003 to 2005? | [
"50 %",
"40 %",
"35 %",
"32 %",
"39 %"
] | Assume the revenue in 2000 to be 100. Then in 2003 it would be 130 and and in 2005 180, so from 2003 to 2005 it increased by (180-130)/130=50/130= 39%
Answer: E.
The answer is: E | E |
mathematics | An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.3200, what will be the difference between Q and R's share? | [
"2788",
"4000",
"7282",
"2782",
"2729"
] | 4 --- 3200
5 --- ? => 4000
Answer:B
The answer is: B | B |
mathematics | find the number, difference between number and its 3/5 is 50. | [
"120",
"123",
"124",
"125",
"126"
] | Explanation:
Let the number = x,
Then, x-(3/5)x = 50,
=> (2/5)x = 50 => 2x = 50*5,
=> x = 125
Answer: Option D
The answer is: D | D |
mathematics | Worker A takes 5 hours to do a job. Worker B takes 15 hours to do the same job. How long it take both A & B, working together but independently, to do the same job? | [
"15/4",
"40/9",
"50/9",
"60/9",
"80/9"
] | one day work of A = 1/5
one day work of B = 1/15
so one day work of A and B together = 1/5 + 1/15 = 4/15
so total days required = 15/4
ANSWER:A
The answer is: A | A |
mathematics | The length of a room is 5.5 m and width is 3.75 m. Find the cost of paying the floor by slabs at the rate of Rs. 400 per sq.metre. | [
"Rs. 15,000",
"Rs. 8,250",
"Rs. 15,600",
"Rs. 16,500",
"None"
] | Solution
Area of the floor = (5.5 x 3.75)m²
= 20.635m ²
Cost of paying = Rs. (400 x 20.625)
= Rs.8,250.
Answer B
The answer is: B | B |
mathematics | The area of a circular field is 17.56 hectares. Find the cost of fencing it at the rate of Rs. 6 per metre approximately | [
"4457",
"4567",
"4235",
"4547",
"8915"
] | Explanation:
Area = (17.56 x 10000) m2= 175600 m2.
ΠR2 = 175600 ⇔ (R)2 = (175600 x (7/22)) ⇔ R = 236.37 m.
Circumference = 2ΠR = (2 x (22/7) x 236.37) m =1485.78 m.
Cost of fencing = Rs. (1485.78 x 6) = Rs. 8915.
Answer: Option E
The answer is: E | E |
mathematics | There are 202 lights which are functional and each is controlled by a separate On/Off switch. Two children A and B start playing with the switches. A starts by pressing every third switch till he reaches the end. B, thereafter, presses every fifth switch till he too reaches the end. If all switches were in Off position... | [
"93",
"94",
"92",
"96",
"95"
] | Editing my solution:
Number of switches = 202
Number of switches turned on by A: 3, 6, ... 201 = 67
Number of switches turned on by B: 5, 10, ....200 = 40
Few switches are turned on by A and later turned off by B: LCM(3,5) = 15x = 15, 30,....90 = 6.
Subtract the above 6 switches from both A and B as they are turned off... | E |
mathematics | The mean of 50 observations was 36. It was found later that an observation 48 was wrongly taken as 23. The corrected new mean is ? | [
"33.3",
"36.5",
"26.5",
"16.5",
"86.5"
] | Correct Sum = (36 * 50 + 48 - 23) = 1825.
Correct mean = = 1825/50 = 36.5
Answer: B
The answer is: B | B |
mathematics | If n is an integer and n^4 is divisible by 32, which of the following could be the remainder when n is divided by 32? | [
"2",
"4",
"5",
"6",
"10"
] | Given:
n^4/32 = int
n^4/2^5 = int
1/2(n/2)^4 = int
try n= int = 2,4,6,8... because n/2 must be an integer
n=2 wont work because 1/2(n/2)^4 needs to be an integer.
n=4, result = 1/2 (2)^4 = 8, so the remainder of n/32 = remainder of 8/32 = 8 (not an option)
n=8, result = 1/2(8/2)^4 = 1/2(4)^4 = 1/2x16x16= 16x8, so the r... | B |
mathematics | A sum of money is divided among A, B, C & D in the ratio 3:5:8:9 respectively. If the share of D Rs.1872 more than the share of A, then what is the total amount of money of B & C together? | [
"3000",
"4056",
"5000",
"5400",
"5600"
] | Sol. Share of B + C = -3 x (5 + 8) = Rs. 4056
B
The answer is: B | B |
mathematics | A, B, C hired a car for Rs. 520 and used it for 7, 8 and 11 hours respectively. Hire charges paid by B were? | [
"127",
"160",
"287",
"237",
"111"
] | A : B : C = 7 : 8 : 11.
Hire charges paid by B = Rs. (520 * 8/26) = Rs. 160.
Answer: B
The answer is: B | B |
mathematics | A person travels equal distances with speeds of 3 km/hr, 4 km/hr and 5 km/hr and takes a total time of 54 minutes. The total distance is? | [
"1 km",
"2 km",
"3 km",
"3.4 km",
"5 km"
] | D
3 km
Let the total distance be 3x km.
Then, x/3 + x/4 + x/5 = 54/60
47x/60 = 54/60 => x = 1.14
Total distance = 3 * 1.14 = 3.4 km.
The answer is: D | D |
mathematics | If -3x < 9, which of the following must be true? | [
"x < -3",
"x < -2",
"x > -3",
"x > -2",
"x > 0"
] | -3x < 9
=> -x < 3
=> x > - 3
Answer C
The answer is: C | C |
mathematics | To mail a package, the rate is 10 cents for the first pound and 5 cents for each additional pound. Two packages weighing 3 pounds and 5 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved? | [
"Combined, with a saving of 5 cents",
"Combined, with a saving of 10 cents",
"Combined, with a saving of 15 cents",
"Separately, with a saving of 5 cents",
"Separately, with a saving of 10 cents"
] | 3 pounds cost = 10+2*5 = 20
5 pounds cost = 10+4*5 = 30
Total = 50
8 pounds cost = 10+ 7*5 =45
Answer : A
The answer is: A | A |
mathematics | The population of locusts in a certain swarm doubles every two hours. If 4 hours ago there were 1,000 locusts in the swarm, in approximately how many hours will the swarm population exceed 128,000 locusts? | [
"12",
"8",
"4",
"10",
"16"
] | - 4 hours: 1,000
-2 hours: 2,000
Now: 4,000
+ 2 hours: 8,000
+ 4 hours: 16,000
+ 6 hours: 32,000
+ 8 hours: 64,000
+ 10 hours: 128,000
Answer : D
The answer is: D | D |
mathematics | By selling an umbrella for Rs. 300, a shop keeper gains 20%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is: | [
"7",
"7.5",
"8",
"9",
"10"
] | Explanation:
Marked price = Rs. 300
C.P. = 100/120 * 300 = Rs. 250
Sale price = 90% of Rs. 300 = Rs. 270
Required gain % = 20/250 * 100 = 8%.
ANSWER IS C
The answer is: C | C |
mathematics | A car takes 6 hours to cover a distance of 504 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time? | [
"48 Kmph",
"50 Kmph",
"52 Kmph",
"56 Kmph",
"60 Kmph"
] | Time = 6
Distence = 504
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 504/9 = 56 Kmph
D
The answer is: D | D |
mathematics | Of the families in City X in 1994, 40 percent owned a personal computer. The number of families in City X owning a computer in 1998 was 30 percent greater than it was in 1994, and the total number of families in City X was 4 percent greater in 1998 than it was in 1994. what percent of the families in City X owned a per... | [
"50%",
"52%",
"56%",
"70%",
"74%"
] | Say a 100 families existed in 1994 then the number of families owning a computer in 1994 - 40
Number of families owning computer in 1998 = 40 * 130/100 = 52
Number of families in 1998 = 104
The percentage = 52/104 * 100 = 50%.
ANSWER:A
The answer is: A | A |
mathematics | If x^2 + y^2 = 13 and xy = 3, then (x − y)^2 = | [
"7",
"11",
"14",
"17",
"20"
] | but you cannot take xy+ 3 to mean xy=-3..
only if xy+3=0, it will mean xy=-3..
rest your solution is perfect and you will get your correct answer as 13-2*3=7..
Answer A
The answer is: A | A |
mathematics | A cement mixture is composed of 3 elements. By weight, 1/3 of the mixture is sand, 1/2 of the mixture is water, and the remaining 8 pounds of the mixture is gravel. What is the weight of the entire mixture in pounds? | [
"30",
"36",
"42",
"46",
"48"
] | Let the total weight be x.
Sand content= (1/3)x
Water content= (1/2)x
Gravel=x-(1/3)x-(1/2)x=(1/6)x=8
x=48
Then answer will be E=48
The answer is: E | E |
mathematics | Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many four letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter? | [
"2,145",
"6,435",
"326,040",
"12,870",
"25,740"
] | Since we are given atleast one symmetric letter in the three letter word we can take the following cases
1. All four
2. One symmetry and other three non
3. Two symmetry and other two non
4. Three symmetry and one non
4. All the three letters can be arranged in 24 ways
( 11c4 + 11c1 * 15c3 + 11c2 * 15c2 + 11c3 *15c1 ) *... | C |
mathematics | If n is a positive integer and n^2 is divisible by 36, then the largest positive integer that must divide n is | [
"6",
"12",
"24",
"36",
"48"
] | The question asks aboutthe largest positive integer that MUST divide n, not COULD divide n. Since the least value of n for which n^2 is a multiple of 72 is 12 then the largest positive integer that MUST divide n is 12.
Complete solution of this question is given above. Please ask if anything remains unclear.
I spent a ... | A |
mathematics | In how much time will a train of length 110 m, moving at 36 kmph cross an electric pole? | [
"sec",
"sec",
"sec",
"sec",
"sec"
] | Convert kmph to mps. 36 kmph = 36 * 5/18 = 10 mps.
The distance to be covered is equal to the length of the train.
Required time t = d/s = 110/10 = 11 sec.
Answer:D
The answer is: D | D |
mathematics | In a recent election, Ms. Robinson received 3200 voters cast by independent voters, that is, voters not registered with a specific political party. She also received 10 percent of the votes cast by those voters registered with a political party. IF N is the total number of votes cast in the election and 40 percent of t... | [
"0.06N+3200",
"0.1N+7200",
"0.4N+7200",
"0.1N+8000",
"0.06N+8000"
] | 40% of N are independent voters, hence 60% of N are not independent voters. From this group she received 10% votes so, 0.1*0.6*N plus 3,200 votes from independents: total=0.1*0.6*N+3,200=0.06*N+3,200.
Answer: A.
The answer is: A | A |
mathematics | A women sells 3 different size(in kgs) packs of sugar which are multiples of 1.A person who buys sugar should buy all types of packs.4 different people buys 20,21,23,29 kgs .what will the maximum and minimum amounts a person can buy?? | [
"22",
"33",
"34",
"54",
"85"
] | packet are 11,6 and 7
7+7+6=20
7+7+7=21
6+6+11=23
7+11+11=29
and min 6+6+6=18
and max 11+11+11=33
ANSWER:B
The answer is: B | B |
mathematics | If a - b = 3 and a^2 + b^2 = 29, find the value of ab. | [
"12",
"15",
"10",
"18",
"13"
] | 2ab = (a^2 + b^2) - (a - b)^2
= 29 - 9 = 20
ab = 10.
Answer is C.
The answer is: C | C |
mathematics | A brick measures 20cm*10cm*7.5cm how many bricks will be required
for a wall 25m*2m*0.75m ? | [
"24000",
"23000",
"22000",
"25000",
"27000"
] | 25*2*0.75=20/100*10/100*0.75/100*X
25=1/100*X
X=25000
Answer :D
The answer is: D | D |
mathematics | Tickets numbered from 1 to 20 are mixed and then a ticket is selected randomly. What is the probability that the selected ticket bearsa number which is a multiple of 3? | [
"1/5",
"2/5",
"3/10",
"3/7",
"1/7"
] | Here, S = [1, 2, 3, 4, …., 19, 20]
Let E = event of getting a multiple of 3 = [3, 6, 9, 12, 15, 18]
P (E) = n (E) / n (S) = 6 / 20 = 3/10
C
The answer is: C | C |
mathematics | A shopkeeper loses 15%,if an article is sold for Rs. 102. What should be the selling price of the article to gain 20%? | [
"221",
"144",
"666",
"888",
"212"
] | Given that SP = Rs. 102 and loss = 15%
CP = [100(SP)]/(100 - l%) = (100 * 102)/85 = 20 * 6 = Rs. 120.
To get 20% profit, New SP = [(100 + p%)CP]/100 = (120 * 120)/100 = Rs. 144
Answer:B
The answer is: B | B |
mathematics | How many positive three-digit integers are divisible by both 5 and 7? | [
"10",
"15",
"18",
"20",
"26"
] | A number to be divisible by both 5 and 7 should be divisible by the least common multiple of 5 and 7 so by 35.
Multiples of 35 between 100 and 999, inclusive is
(last-first)/multiple+1=(980-105)/35+1=25+1=26
Answer: E.
The answer is: E | E |
mathematics | Two boys starts from the same place walking at the rate of 5.5 kmph and 7.5 kmph respectively in the same direction. What time will they take to be 32 km apart? | [
"18",
"16",
"19",
"15",
"34"
] | Explanation:
Relative speed = 7.5 - 5.5 = 2 kmph (because they walk in the same direction)
distance = 32 km
time = distance / speed=32/2=16 hr
Answer :B
The answer is: B | B |
mathematics | A grocer has a sale of Rs. 3435, Rs. 3927, Rs. 3855, Rs. 4230 and Rs. 3562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 3500? | [
"s. 1991",
"s. 2991",
"s. 3991",
"s. 4991",
"s. 5991"
] | Explanation:
Total sale for 5 months = Rs. (3435 + 3927 + 3855 + 4230 + 3562) = Rs. 19009.
Required sale = Rs. [ (3500 x 6) – 19009 ]
= Rs. (21000 – 19009)
= Rs. 1991.
Answer A
The answer is: A | A |
mathematics | A rectangular table seats 3 people on each of two sides, with every person directly facing another person across the table. If six people choose their seats at random, what is probability that any two of them directly face other? | [
"1/5",
"1/8",
"1/7",
"15/56",
"4/7"
] | A B C
------------
| TABLE |
------------
D E F
A to F are 6 people.
Prob to select any 1 person = 1
Prob to select the person opposite to the chosen person = 1/5
For ex. If we select A as the person than prob of choosing D is 1/5.
Hence, answer will be A.
The answer is: A | A |
mathematics | A student is to take her final exams in two subjects. The probability that she will pass the first subject is 3/4 and the probability that she will pass the second subject is 2/3. What is the probability that she will pass one exam or the other exam? | [
"5/12",
"1/2",
"7/12",
"5/7",
"11/12"
] | Let the two subjects be X (probability of passing 3/4) and Y (probability of passing 2/3)
The probability of passing in X only is 3/4 times 1/3 (failing in Y) = 1/4
The probability of passing in Y only is 2/3 times 1/4 (failing in X) = 1/6
Therefore the total probability = 1/4 + 1/6 = 5/12
Hence A
The answer is: A | A |
mathematics | The probability that a number selected at random from the first 50 natural numbers is a composite number is ? | [
"17/29",
"17/25",
"17/27",
"17/29",
"17/89"
] | The number of exhaustive events = ⁵⁰C₁ = 50.
We have 15 primes from 1 to 50.
Number of favourable cases are 34.
Required probability = 34/50 = 17/25
Answer: B
The answer is: B | B |
mathematics | A man has Rs. 720 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? | [
"33",
"38",
"135",
"90",
"28"
] | Let number of notes of each denomination be x.
Then x + 5x + 10x = 720
⇒ 16x = 720
∴ x = 45.
Hence, total number of notes = 3x = 135
Answer:C
The answer is: C | C |
mathematics | Two tables are purchased for the total cost of Rs. 5000. First table is sold at 40% profit and second at 40% loss. If selling price is same for both the tables, what is the cost price of the table that was sold at profit? | [
"Rs. 1500.",
"Rs. 2500.",
"Rs. 3500.",
"Rs. 4500.",
"Rs. 5500."
] | Ans: 140% of cost price of first table = 60% of cost price of second table.
Therefore, Cost price of first table : Cost price of second table
= 60 : 140 = 3 : 7
Therefore, Cost price of first table = 3/10× 5000 = Rs. 1500.
Answer A
The answer is: A | A |
mathematics | A tank is filled by three pipes with uniform flow. The first two pipes operating simultaneously fill the tank in the same during which the tank is filled by the third pipe alone. The second pipe fills the tank 5 hours faster than the first pipe and 4 hours slower than the third pipe. The time required by the first pipe... | [
"17",
"27",
"15",
"19",
"16"
] | Suppose, first pipe alone takes x hours to fill the tank. Then, second and third pipes will take (x - 5) and (x - 9) hours respectively to fill the tank.
1/x + 1/(x - 5) = 1/(x - 9)
(2x - 5)(x - 9) = x(x - 5)
x2 - 18x + 45 = 0
(x- 15)(x - 3) = 0 => x = 15
Answer: C
The answer is: C | C |
mathematics | In a 100 m race, A runs at 8km per hour. If A gives B a start of 4 m and still him by 15 seconds, what is the speed of B ? | [
"5.56 km/hr.",
"5.06 km/hr.",
"5.76 km/hr.",
"6.76 km/hr.",
"5.72 km/hr."
] | Time taken by A to cover 100 m =(60 X 60 / 8000) x 100 sec = 45 sec.
B covers (100 - 4) m = 96 m in (45 + 15) sec = 60 sec.
B's speed = (96 x 60 x 60)/(60 x 1000)km/hr = 5.76 km/hr.
Answer is C
The answer is: C | C |
mathematics | How many four digit numbers can be formed using the digits {1, 3, 4, 5, 7,9}(repetition of digits is not allowed)? | [
"360",
"729",
"365",
"735",
"345"
] | The given digits are six.
The number of four digit numbers that can be formed using six digits is ⁶P₄
= 6 * 5 * 4 * 3 = 360.
Answer:A
The answer is: A | A |
mathematics | A and B started a business in partnership investing Rs.20,000 and Rs.15,000 respectively. After 6months, C joined them with Rs.20,000. Whatwill be B's share in total profit of Rs.22,000 earned at the end of 2years from the startingof the business? | [
"s. 5,000",
"s. 5,500",
"s. 5,700",
"s. 6,600",
"s. 7,500"
] | A : B : C = (20,000 x 24) : (15,000 x 24) : (20,000 x 18) = 4 : 3 : 3.
B's share = Rs. 22000 x 3/10 = Rs. 6,600.
D
The answer is: D | D |
mathematics | In a class there are 20 boys and 24 girls. In how many ways can a boy and a girl be selected? | [
"508",
"480",
"800",
"570",
"503"
] | We can select one boy from 20 boys in 20 ways.
We select one girl from 24 girls in 24 ways
We select a boy and girl in 20 * 24 ways i.e., = 480 ways.
Answer:B
The answer is: B | B |
mathematics | Find the cost of fencing around a circular field of diameter 28 m at the rate of Rs.1.50 a meter? | [
"299",
"132",
"269",
"267",
"262"
] | 2 * 22/7 * 14 = 88
88 * 1 1/2
= Rs.132
Answer:B
The answer is: B | B |
mathematics | The average of a set of five distinct integers is 350. If each number is less than 2,000, and the median of the set is the greatest possible value, what is the sum of the two smallest numbers? | [
"-4,244",
"-3,997",
"-3,494",
"-3,194",
"The answer cannot be determined from the information given"
] | Sum of the set = 350*5=1750 Each number is less than 2000 and median of the set is the greatest possible value.
Therefore last 3 numbers can be 1999,1998 and 1997. Their sum=5994.
Therefore sum of two smallest numbers= 1750-5994= -4244
Answer=A
The answer is: A | A |
mathematics | On a certain day, orangeade was made by mixing a certain amount of orange juice with an equal amount of water. On the next day, orangeade was made by mixing the same amount of orange juice with twice the amount of water. On both days, all the orangeade that was made was sold. If the revenue from selling the orangeade w... | [
"$0.15",
"$0.20",
"$0.33",
"$0.40",
"$0.45"
] | On the first day 1 unit of orange juice and 1 unit of water was used to make 2 units of orangeade;
On the second day 1 unit of orange juice and 2 units of water was used to make 3 units of orangeade;
So, the ratio of the amount of orangeade made on the first day to the amount of orangeade made on the second day is 2 to... | C |
mathematics | The price of commodity X increases by 30 cents every year, while the price of commodity Y increases by 20 cents every year. If in 2001, the price of commodity X was $4.20 and the price of commodity Y was $4.50, in which year will commodity X cost 90 cents more than the commodity Y? | [
"2010",
"2011",
"2012",
"2013",
"2014"
] | The cost of commodity X increases by 10 cents per year relative to commodity Y.
The price of X must gain 30 + 90 = $1.20 cents on commodity Y, which will take 12 years.
The answer is D.
The answer is: D | D |
mathematics | The ratio of the volumes of two cubes is 2744 : 1331. What is the ratio of their total surface areas? | [
"196 : 121",
"81 : 127",
"181 : 196",
"81 : 161",
"81 : 182"
] | Explanation:
Ratio of the sides = ³√2744 : ³√1331 = 14 : 11
Ratio of surface areas = 14^2 : 11^2 = 196 : 121
Answer: Option A
The answer is: A | A |
mathematics | What is the next number of the following sequence.
8, 8, 6, 2,.... ? | [
"-4",
"-5",
"-6",
"-7",
"-8"
] | 8-(2*0) = 8
8-(2*1) = 6
6-(2*2) = 2
2-(2*3) = -4
ANSWER:A
The answer is: A | A |
mathematics | If a and b are the two values of t that satisfy
the equation t2 – 6t + 8 = 0, with a > b, what is the value of a – b? | [
"2",
"4",
"6",
"8",
"10"
] | Factor the left side of the equation:
t2 – 6t + 8 = 0
(t – 2)(t – 4) = 0
Split this equation into two equations and solve:
t – 2 = 0 t – 4 = 0
t = 2 t = 4
Thus, a = 4 and b = 2. So a – b = 4 – 2 = 2.
correct answer A)2
The answer is: A | A |
mathematics | 30 men can do a work in 40 days. When should 16 men leave the work so that the entire work is completed in 40 days after they leave the work? | [
"87 days",
"14 days",
"55 days",
"44 days",
"22 days"
] | Total work to be done = 30 * 40 = 1200
Let 16 men leave the work after 'P' days, so that the remaining work is completed in 40 days after they leave the work.
40P + (16 * 40) = 1200
40P = 560 => P = 14 days
Answer:B
The answer is: B | B |
mathematics | When 242 is divided by a certain divisor the remainder obtained is 4. When 698 is divided by the same divisor the remainder obtained is 8. However, when the sum of the two numbers 242 and 698 is divided by the divisor, the remainder obtained is 7. What is the value of the divisor? | [
"5",
"17",
"13",
"23",
"None of these"
] | let that divisor be x
since remainder is 4 or 8 it means divisor is greater than 8.
now 242-4=238 =kx (k is an integer and 234 is divisble by x)
similarly 698-8=690 = lx (l is an integer and 689 is divisible by x)
adding both 698 and 242
= (238+690)+4+8
=x(k+l) + 12
when we divide this number by x then remainder will b... | A |
mathematics | Convert 700 miles into meters? | [
"784596",
"1126538",
"804670",
"784596",
"864520"
] | 1 mile = 1609.34 meters
700mile = 700*1609.34 = 1126538 meters
Answer is B
The answer is: B | B |
mathematics | Pipe A can fill a tank in 6 hours, pipe B in 8 hours, and pipe C in 24 hours. If all the pipes are open, in how many hours will the tank be filled? | [
"2.5",
"3",
"3.5",
"4",
"4.5"
] | The part filled by A + B + C in 1 hour
= 1/6 + 1/8 + 1/24
= 8/24 = 1/3
All the three pipes together will fill the tank in 3 hours.
The answer is B.
The answer is: B | B |
mathematics | If, in a baseball game, a single picher can decide to throw either a 100mph fastball or 60 mph knuckleball on any pitch, how much less time, in seconds, does the batter have from when the ball is released as a fastball than when the ball is released as a knuckle ball? (Assume where the batter's point of contact is exac... | [
"6/22s",
"7/22s",
"8/22s",
"9/22s",
"15/22s"
] | One conversion to know is = 1 mile = 5280 ft
Time taken for fastball = (60 / (100 * 5280)) * 60 * 60 = 9/22
Time taken for knuckle ball = (60 / (60 * 5280)) * 60 * 60 = 15/22
Qn is the difference between the time taken by the two balls => 15/22 - 9/22 = 6/22
Option A
The answer is: A | A |
mathematics | Points A, B, and C lie, in that order, on a straight railroad track. The distance from point A to point B is twice the distance from point B to point C. A train traveled from point A to point C without stopping. The train's average speed when traveling from point A to point B was 150 miles per hour and the train's aver... | [
"22.5",
"21.43",
"25.5",
"26.5",
"27.5"
] | Average speed = distance/time
Because we are looking for average speed we can pick a distance for the variable d.
Speed A-B = 150
Speed B-C = 100
Average Speed = total distance/total rate
rate = distance/time
A====================B==========C
If A-B is twice the length of B-C then let A-B = 2d and let B-C = d
Average s... | B |
mathematics | If a fair coin is tossed five times, what is the probability of getting exactly four heads in a row? | [
"1/64",
"1/32",
"1/16",
"1/8",
"1/4"
] | P(HHHHT) = 1/32
P(THHHH) = 1/32
The sum of these probabilities is 2/32 = 1/16
The answer is C.
The answer is: C | C |
mathematics | The traffic lights at 3 different roads change after every 14 sec, 72 sec, 108 sec respectively. If they all change simultaneously at 9:15 AM then at what time will they again change simultaneously. | [
"9:22:12",
"9:42:15",
"10:15:24",
"9:40:12",
"10:01:20"
] | LCM of 14,72,108 = 1512 = 25mnts 12sec
The lines will change every 25m 12sec
The light will change again after 9:15 AM is = 9:15+0:25:12 = 9:40:12
Answer is D
The answer is: D | D |
mathematics | A box contains 22 electric bulbs, out of which 4 are defective. Two bulbs are chosen at random from this box. The probability that at least one of these is defective is | [
"4/19",
"7/19",
"12/19",
"21/99",
"26/77"
] | Solution
P( None is defective)
= 18C2 / 22C2
= 51/77
P( at least one is defective)
= (1- 51/77)
= 26/77.
Answer E
The answer is: E | E |
mathematics | AA is two digit number then m times its cube of AA has 1 in its tens place then what is m. | [
"3",
"4",
"5",
"6",
"7"
] | when AA=11
7*(11)^3= 7*1331= 9317
m=7
ANSWER:E
The answer is: E | E |
mathematics | The L.C.M of two numbers is 2310 and their H.C.F is 30. If one number is 210 the Other is | [
"330",
"300",
"270",
"250",
"350"
] | The other number
= L.C.M * H.C.F/given number
= 2310*30/210 = 330
Answer is A.
The answer is: A | A |
mathematics | In a theater, the first row has 17 seats and each row has 3 more seats than previous row. If the last row has 44 seats, what is the total number of seats in the theater? | [
"265",
"275",
"285",
"295",
"305"
] | The number of seats in the theater is
17 + (17+3) + ...+ (17+27)=
10(17) + 3(1+2+...+9)=
10(17) + 3(9)(10)/2= 170 + 135 = 305
The answer is E.
The answer is: E | E |
mathematics | Four extra-large sandwiches of exactly the same size were ordered for m students, where m > 7. Three of the sandwiches were evenly divided among the students. Since 4 students did not want any of the fourth sandwich, it was evenly divided among the remaining students. If Carol ate one piece from each of the four sandwi... | [
"(6m-21)/[m(m-7)]",
"(4m-21)/[m(m-7)]",
"(8m-21)/[m(m-5)]",
"(10m-21)/[m(m-5)]",
"(4m-15)/[m(m-5)]"
] | Three of the sandwiches were evenly divided among the students
i.e. Amount of Sandwiches with each students = 3/m
Amount of 4th Sandwich with remaining (m-7) students = 1/(m-7)
The amount of Sandwich that carol ate = 3/m + 1/(m-7) = (3m-21+m)/[m(m-7)] = (4m-21)/[m(m-7)]
Answer: B
The answer is: B | B |
mathematics | One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 38 minutes, then the slower pipe alone will be able to fill the tank in | [
"144 mins",
"140 mins",
"136 mins",
"152 minw",
"None of these"
] | Explanation:
Let the slower pipe alone fill the tank in x minutes
then faster will fill in x/3 minutes.
Part filled by slower pipe in 1 minute = 1/x
Part filled by faster pipe in 1 minute = 3/x
Part filled by both in 1 minute =
1/x+3/x=1/38
=>4/x=1/38
x=38∗4=152mins
Option D
The answer is: D | D |
mathematics | 4 buses runs between Chennai and Mysore. If a man goes from Chennai to Mysore by a bus and comes back to Mysore by another bus, then the total possible ways are | [
"4",
"8",
"12",
"16",
"None of these"
] | Since the man can go in 4 ways and can back in 3 ways. Therefore total number of ways are 4 x3 = 12ways.
Answer C
The answer is: C | C |
mathematics | A diet contains 400 grams of a mixture of two foods, food X and food Y. Food X contains 10 percent protein and food Y contains 15 percent protein. If a diet provides exactly 50 grams of protein daily, how many grams of food X are in the mixture? | [
"120",
"140",
"150",
"160",
"200"
] | Let x be the number of grams of food X in the mixture.
0.1x + 0.15(400-x) = 50
0.05x = 10
x = 200
The answer is E.
The answer is: E | E |
mathematics | A and B start a business with Rs.6000 and Rs.8000 respectively. Hoe should they share their profits at the end of one year? | [
"3:8",
"3:4",
"3:5",
"3:2",
"3:1"
] | They should share the profits in the ratio of their investments.
The ratio of the investments made by A and B
=6000 : 8000 => 3:4
Answer:B
The answer is: B | B |
mathematics | How many times digit 6 is used while writing numbers from 150 to 1000? | [
"648",
"300",
"252",
"225",
"26"
] | There are 100 numbers which begin with 600
Next, In every 10 numbers such as 100 to 110, 110 to 120, 120 to 130 6 comes at least once. Number of such intervals = End limit - First no. / interval. Our range of numbers is 100 - 1000
1000 - 100 = 900/10 = 90
Number of 10s interval in this is 90. So 90 '6s'
So far we have ... | C |
mathematics | The distance between Delhi and Mathura is 110 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet? | [
"11 a.m",
"10 a.m",
"77 a.m",
"55 a.m",
"65 a.m"
] | D = 110 – 20 = 90
RS = 20 + 25 = 45
T = 90/45 = 2 hours
8 a.m. + 2 = 10 a.m.
Answer: B
The answer is: B | B |
mathematics | A train covers a distance of 12 km in 10 min. If it takes 6 sec to pass a telegraph post, then the length of the train is? | [
"100",
"110",
"120",
"121",
"123"
] | Speed = (12/10 * 60) km/hr = (72 * 5/18) m/sec = 20 m/sec.
Length of the train = 20 * 6 = 120 m.
Answer: Option C
The answer is: C | C |
mathematics | At what approximate time between 4 and 5 am will the hands of a clock be at right angle? | [
"4 : 40 am",
"4 : 38 am",
"4 : 35 am",
"4 : 39 am",
"None of these"
] | Here H × 30 = 4 × 30 = 120°.
(Since initially the hour hand is at 4. ∴ H = 4).
Required angle A = 90° and since, H × 30 > A° so, there will be two timings.
Required time T = 2⁄11(H × 30 ± A) minutes past H.
∴ One timing = 2⁄11(4 × 30 + 90) minutes past 4
= 382⁄11 minutes past 4.
Or 4 : 38 approx.
Answer B
The answer is... | B |
mathematics | A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good? | [
"125/167",
"125/118",
"125/126",
"125/128",
"125/129"
] | Required probability
= 1 - 1/126 = 125/126
Answer: C
The answer is: C | C |
mathematics | Difference of 2 numbers is 1660. If 7.5% of one number is 12.5% of the other number, find the 2 numbers? | [
"125,150",
"5124,4515",
"4150,2490",
"3250,4510",
"1254,3210"
] | Let the numbers be x and y
7.5% of x = 12.5% of y
x = 125y/75 = 5y/3
x-y = 1660
5y/3 - y = 1660
y = 2490
x = 5y/3 = 4150
Answer is C
The answer is: C | C |
mathematics | A person got Rs.48 more when he invested a certain sum at compound interest instead of simple interest for two years at 8% p.a. Find the sum? | [
"7500",
"2776",
"2877",
"2667",
"2671"
] | P = (d * 1002) / R2
=> (48 * 100 * 100) / 8 * 8 = Rs.7500
Answer:A
The answer is: A | A |
mathematics | The organizers of a week-long fair have hired exactly eight security guards to patrol the fairgrounds at night for the duration of the event. Exactly three guards are assigned to patrol the grounds every night, with no guard assigned consecutive nights. If the fair begins on a Monday, how many different groups of 3 gua... | [
"6",
"8",
"10",
"12",
"14"
] | For any given day, only the guards patrolling on the previous day won't be available. So, 3 guards who patrolled on Friday won't be available. We are thus left with 5 guards.
To choose 3 out of 5, we will have 5C3 = 10 different groups.
The answer is C.
The answer is: C | C |
mathematics | A can do a work in 60 days. He works for 15 days and later B alone completes the work in 30 days. In what time will they together complete the work? | [
"24 days",
"25 days",
"30 days",
"32 days",
"None of these"
] | let A can do a work in = 1/60 days
he does 15 days so work done by A in 15 days= (15) * (1/60) = 1/4
remaining work is = 1- 1/4= 3/4
B's one day work is =1/30
so 3/4 work is done by B in=(3/4) * (1/30) = 1/40 days
time require to complete the work is= 1/60 + 1/40 = 5/120
5/120 = 1/24
so 24 days require to complete the ... | A |
mathematics | X Y
+Y X
________
The sum of the two digit numbers above is a three digit number PQ6, where each letter X, Y, P, and Q represents a different non zero digit. Which of the following can be the value of X?
I) 7
II) 8
III) 9 | [
"I only",
"II only",
"III only",
"I , II and III",
"I and II only"
] | it can be a combination of 9,7 or 8,8
I choose D as an answer.
The answer is: D | D |
mathematics | A bat is bought for Rs.400 and sold at a gain of 20% find its selling price? | [
"Rs.460/-",
"Rs.480/-",
"Rs.500/-",
"Rs.520/-",
"Rs.540/-"
] | 100 % ------> 400 (100 * 4 = 400)
120 % ------> 480 (120 * 4 = 480)
Selling price = Rs.480/-
Option 'B'
The answer is: B | B |
mathematics | Look at this series: 0.6, 0.3, ____, 0.075, 0.0375, ... What number should fill the blank? | [
"0.015",
"1.15",
"0.15",
"0.25",
"0.35"
] | This is a simple multiplication series. Each number is multiple by 1/2.
Answer: C
The answer is: C | C |
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