subject stringclasses 1
value | question stringlengths 3 1.14k | options listlengths 5 5 | solution stringlengths 18 3.7k | answer stringclasses 5
values |
|---|---|---|---|---|
mathematics | A man bought a computer at 30% discount on its original price. He sold it at a 520% increase on the price he bought it. What percent of profit did he make on the original price? | [
"1%",
"2%",
"3%",
"4%",
"5%"
] | Original price = 100
CP = 70
S = 70*(150/100) = 105
105 - 100 = 5%
Answer: E
The answer is: E | E |
mathematics | In a certain sequence, the first term is 7, and each successive term is 1 more than the reciprocal of the term that immediately precedes it. What is the fifth term in this sequence? | [
"13/8",
"39/24",
"8/5",
"5/8",
"8/13"
] | let five terms in the sequence be a,b,c,d,e
a=7
b= 1+1/7=8/7
c=1+7/8= 15/8
d= 1+8/15 = 24/15
e= 1+15/24 = 39/24
hence answer should be B.
The answer is: B | B |
mathematics | A man spends 10% of his income in house rent, 20% of the rest on his children’s education, 25% of the rest miscellaneous causes. If he now posses Rs. 1944 then his income is? | [
"Rs.3600",
"Rs.4000",
"Rs.4500",
"Rs.3000",
"Rs.5000"
] | X * (90/100) * (80/100) * (75/100) = 1944
X * 0.9 * 0.8 * 0.75
X = 1944/0.54
X = 3600
ANSWER:A
The answer is: A | A |
mathematics | What is the sum of all the multiples of 10 between 0 and 99? | [
"500",
"620",
"450",
"340",
"440"
] | The multiples of 10 between 0 and 99 are 10, 20, 30, 40, 50, 60, 70, 80, and 90. If these are all added together, the result is 450.
Final Answer:
C
The answer is: C | C |
mathematics | In what ratio must tea at Rs.62 per Kg be mixed with tea at Rs. 72 per Kg so that the mixture must be
worth Rs. 64.50 per Kg? | [
"1 : 2",
"2 : 1",
"3 : 1",
"1 : 3",
"None of these"
] | Explanation :
By the rule of alligation, we have
Cost of 1 kg of 1st kind tea Cost of 1 kg tea of 2nd kind tea
62 72
Mean Price
64.5
72-64.5=7.5 64.5-62=2.5
Required Ratio = 7.5 : 2.5 = 3 : 1
Answer : Option C
The answer is: C | C |
mathematics | The product A of the first 10 prime numbers is closest to which of the following? | [
"6.5 x 10^7",
"6.5 x 10^8",
"6.5 x 10^9",
"6.5 x 10^10",
"6.5 x 10^11"
] | The first 10 primes are: 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.
So, we need to find approximate value of 2*3*5*7*11*13*17*19*23*29.
# of different approximations are possible. For example:
2*5=10
3*17=~50 (actually more than 50);
7*13=~100 (actually less than 100);
11*19=~200 (actually more than 200)
23*29=667=A
2*3*5... | C |
mathematics | A driver of auto rickshaw makes a profit of 20% on every trip when he carries 3 passengers and the price of petrol is Rs. 30 a litre. Find the % profit for the same journey if he goes for 4 passengers per trip and the price of petrol reduces to Rs. 24 litres? (revenue per passenger is same) | [
"20%",
"33.33%",
"100%",
"65.66%",
"Data inadequate"
] | Solution: Assume the cost price = 100 and selling price = 120.
Then, when price of petrol is reduced;
Cost price become 60 and selling price = 160;
Profit increased = 100%.
Answer: Option C
The answer is: C | C |
mathematics | How many positive numbers not greater than 4300 can be formed using the digits 0,1,2,3,4 where repeatation is allowed? | [
"576",
"575",
"620",
"640",
"660"
] | 1 digit = 5
2 digits = 4* 5 = 20
3 digits = 4*5*5= 100
Now,4 digit number till 4000 can have digits 1,2,3 in thousands place ( total choices = 3 )
0,1,2,3,4 in hundreds ,tens and ones place
I.e 3*5*5*5 = 375
Now From 4000 to 4299 = 1*3*5*5 =75
Total = 5+20+100+375+75+1 =576 (1 for 4300)
ANSWER:A
The answer is: A | A |
mathematics | Two trains 160 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is? | [
"10.52 sec",
"18.8 sec",
"14.52 sec",
"10.8 sec",
"11.52 sec"
] | Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 160 + 160 = 320 m.
Required time = 320 * 9/250 = 288/25 = 11.52 sec.
Answer: E
The answer is: E | E |
mathematics | A certain club has 10 members, including Parry. One of the 10 members is chosen at random to be the president, one of the remaining 9 members is to be chosen at random to be the secretary, and one of the remaining 8 members is to be chosen at random to be the treasurer. What is the probability that parry will be either... | [
"1/720",
"1/80",
"1/10",
"1/9",
"1/5"
] | In order to become a secretary the person cannot be chosen as a president. This can be done in 9/10 ways. Then to become a secretary this person's probability is 1/9
Probability to become a secretary = (9/10 * 1/9) = 1/10
Similar concept for treasurer. Probability of not president = 9/10, Probability of not secretary =... | E |
mathematics | Jake remembers only the last three letters of his four-letter Klingon name. If he is sure that the first letter is neither "N" nor "X", and assuming that there are only 15 letters in the Klingon alphabet, what is the probability that he will give the correct name when asked for it by the space attendant? | [
"A)8/100",
"B)9/100",
"C)1/8",
"D)1/13",
"E)9/10"
] | Total letters 15, out of which the first letter is anything of 10 but N or X...
So there are 13 possible letters for first place..
And only one of them is correct..
So 1/13
Answer: D
The answer is: D | D |
mathematics | Anand and Deepak started a business investing Rs. 3500 and Rs. 7000 respectively. Out of a total profit of Rs. 2000, Deepak's share is: | [
"1333.3",
"2687.1",
"1200.6",
"1580.2",
"2671"
] | Ratio of their shares = 3500 : 7000 = 1:2
Deepak's share = 2000* 2/3 = Rs. 1333.3.
Answer: A
The answer is: A | A |
mathematics | In an election a candidate who gets 60% of the votes is elected by a majority of 900 votes. What is the total number of votes polled? | [
"A)4500",
"B)5200",
"C)6900",
"D)7520",
"E)6000"
] | Let the total number of votes polled be x
Then, votes polled by other candidate = (100-60)% of x = 40% of x
60% of x - 40% of x = 900
20x/100 = 900
x = 900*100/20 = 4500
Answer is A
The answer is: A | A |
mathematics | If a/b = 1/3, b/c = 2, c/d = 1/2, d/e = 3 and e/f = 1/2, then what is the value of abc/def ? | [
"27/4",
"27/8",
"3/4",
"3/8",
"1/4"
] | Say a = 3. Then:
a/b = 1/3 --> b = 9;
b/c = 2 --> c = 9/2;
c/d = 1/2 --> d = 9;
d/e = 3 --> e = 3;
e/f = 1/2 --> f = 6.
abc/def = (3*9*9/2)/(9*3*6) = 3/4.
Answer: C.
The answer is: C | C |
mathematics | In the table above, what is the least number of table entries that are needed to show the mileage between each city and each of the other five cities? | [
"15",
"21",
"25",
"30",
"36"
] | Total number of entries 6*6(6rows*6columns) =36
Now 6 entries are representing mileage with the city itself so subtract that => 36-6
Minimum entries required = half the Total = 30/2 = 15
ANSWER: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 $200, what were her original savings? | [
"$500",
"$600",
"$700",
"$800",
"$900"
] | 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 $200. So 1 / 4 of her savings is $200. So her original savings are 4 times $200 = $800
correct answer D
The answer is: D | D |
mathematics | The H.C.F. of two numbers is 12 and their L.C.M. is 600. If one of the number is 12, find the other? | [
"100",
"600",
"120",
"200",
"150"
] | Other number = 12*600/12= 600
Answer is B
The answer is: B | B |
mathematics | Lindsay can paint 1/x of a certain room in one hour. If Lindsay and Joseph, working together at their respective rates, can paint the room in two hours, what fraction of the room can Joseph paint in 20 minutes? | [
"1/6x",
"x/(x-6)",
"(x-2)/6x",
"x/(x-2)",
"(x-2)/x"
] | Let J be Joseph's rate per hour.
1/x + J = 1/2 of a room per hour
J = 1/2 - 1/x, of a room per hour
In 20 minutes Joseph can paint 1/3*(1/2-1/x) = 1/6-1/3x = (x-2)/6x
The answer is C.
The answer is: C | C |
mathematics | If one root of the equation 2x^2 + 3x – k = 0 is 5, what is the value of k? | [
"65",
"79",
"68",
"87",
"90"
] | We just enter this root into the equation in order to recieve an equation to find the answer!
2*5^2+3*5-k=0
k=50+15=65
The answer is A
The answer is: A | A |
mathematics | Matt is touring a nation in which coins are issued in two amounts, 2¢ and 5¢, which are made of iron and copper, respectively. If Matt has twuenty iron coins and thuenty copper coins, how many different sums from 1¢ to 140¢ can he make with a combination of his coins? | [
"137",
"140",
"166",
"136",
"2"
] | The total sum is 20*2 + 20*5 = 140¢. If you can make each sum from 1 to 140 (1¢, 2¢, 3¢, ..., 140¢), then the answer would be 140 (maximum possible).
Now, with 2¢ and 5¢ we cannot make 1¢ and 3¢. We also cannot make 139¢ and 137¢ (since total sum is 140¢ we cannot remove 1¢ or 3¢ to get 139¢ or 137¢).
So, out of 140 su... | D |
mathematics | Evaluate: 1234562- 12*3*2 = ? | [
"32435453",
"1234554",
"76768786",
"97979797",
"75868656"
] | According to order of operations, 12?3?2 (division and multiplication) is done first from left to right
12**2 = 4* 2 = 8
Hence
1234562 - 12*3*2 = 1234562 - 8 = 1234554
correct answer B
The answer is: B | B |
mathematics | Bill bought 100 packets of candy. He was able to sell 1/2 of them at a 20% profit, another 1/4 of them at zero profit and the remainder was sold at a 5% loss. Find the total profit or loss made by Bill after selling those 100 packets. A packet sold at a loss had a price of $9.
Please provide an intuitive answer if poss... | [
"0",
"Profit of $87.5",
"Loss of $25",
"Profit of $80",
"Profit of $85"
] | A packet sold at a 10% loss had a price of $9, thus the cost of a packet is $10.
50 packets was sold at a 20% profit --> gives profit of 10*0.2*50 = $100.
25 packets was sold at a 5% loss --> gives loss of 10*0.05*25 = $12.5.
The overall Profit is $100 - $12.5 = $87.5.
Answer: B.
The answer is: B | B |
mathematics | A shopkeeper sold an article at $100 with 10% profit. Then find its cost price? | [
"$120",
"$100",
"$91",
"$72",
"$69"
] | cost price = selling price *100/(100+profit)
C.P. = 100*100/110 = $91(approximately)
Answer is C
The answer is: C | C |
mathematics | John has 6 people in his group of friends. How many different ways can he invite one or more of them to his house? | [
"56",
"97",
"63",
"65",
"71"
] | John can select one or more of his group of 6
=> Required number of ways = 2^6 – 1= 63.
C
The answer is: C | C |
mathematics | Three partners A,B,C invested 360000rs.,378000rs. and 414000rs.in a business.at the end of one year,there is profit of 64000rs.then calculate the profit share of C. | [
"24000",
"23000",
"28000",
"2750",
"2880"
] | ratio of A,B,C investment=360000:378000:414000=20:21:23.
total profit=64000 rs.
share of C=[64000×23/64]=23000 rs.
answer B
The answer is: B | B |
mathematics | If z is a multiple of 9702, what is the remainder when z^2 is divided by 4? | [
"0",
"1",
"2",
"3",
"It depends on z."
] | 2 is a factor of 9702, so 2 is a factor of z.
Then 2^2 = 4 is a factor of z^2.
Then the remainder when z^2 is divided by 4 is 0.
The answer is A.
The answer is: A | A |
mathematics | What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58? | [
"3944",
"39288",
"288",
"266",
"1881"
] | Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 58 = Rs. 3944.Answer: A
The answer is: A | A |
mathematics | If the selling price of 50 articles is equal to the cost price of 40 articles, then the loss or gain percent is? | [
"20",
"98",
"66",
"54",
"12"
] | Let C.P. of each article be Re. 1.
Then, C.P. of 50 articles = Rs. 50;
S.P. of 50 articles = Rs. 40.
Loss % = 10/50 * 100 = 20%
Answer: A
The answer is: A | A |
mathematics | How many numbers are divisible by both 2 and 3 up to 300? | [
"50",
"100",
"150",
"200",
"250"
] | Divide 300 by 6, as the numbers which are divisible by both 2 and 3 are also divisible by 6.
The quotient obtained after dividing 300 by 6 is 50, hence answer is 50.
Option A
The answer is: A | A |
mathematics | Six persons in an organization including A and B were to be divided in two groups of 3 members each. The total number of groups containing both A and B is what fraction of the total number of groups which can be formed? | [
"3/10",
"1/70",
"3/14",
"1/10",
"11/14"
] | The fraction is nothing but the probability..
Number to choose 3 out of 6= 6C3
Number to choose A and B and 2 from remaining 4=4C2..
prob of A and B choosen=4C2/6C3=3/10
Answer : A
The answer is: A | A |
mathematics | A shopkeeper expects a gain of 22.5% on his cost price. If in a week, his sale was of Rs. 441, what was his profit? | [
"s. 64",
"s. 69",
"s.72",
"s.75",
"s.81"
] | C.P. = Rs. (100/122.5)x441
= Rs. (1000/1225)x441
= Rs. 360
Profit = Rs. (441 - 360) = Rs. 81.
Answer:E
The answer is: E | E |
mathematics | The total weight of nine nougat nuggets is 7 oz. What is the average (arithmetic mean) weight of one such nougat nugget? | [
"0.18 oz.",
"0.5 oz.",
"1.8 oz.",
"0.77 oz.",
"18 oz"
] | Average = Total/Number of items
= 7/9 = 0.77.
Hence, D
The answer is: D | D |
mathematics | An investment of $3000 was made in a certain account and earned interest that was compounded annually. The annual interest rate was fixed for the duration of the investment, and after 12 years the $3000 increased to $12000 by earning interest. In how many years after the initial investment was made the $3000 have incre... | [
"16",
"22",
"20",
"18",
"30"
] | In 12 years the investment quadrupled (from $3,000 to $12,000).
Thus, at the same rate compounded annually, it would need additional 12/2=6 years to double (from $12,000 to $24,000).
Therefore, 12+6=18 years are needed $3,000 to increase to $24,000.
Answer: D.
The answer is: D | D |
mathematics | A sum of money becomes 7/6 of itself in 5 years at a certain rate of simple interest. The rate per annum is? | [
"20/7",
"20/3",
"23/6",
"10/3",
"10/7"
] | Let sum = x. Then, amount = 7x/6
S.I. = 7x/6 - x = x/6; Time = 5 years.
Rate = (100 * x) / (x * 6 * 5) = 10/3 %.
Answer:D
The answer is: D | D |
mathematics | John left home and drove at the rate of 50 mph for 2 hours. He stopped for lunch then drove for another 3 hours at the rate of 55 mph to reach his destination. How many miles did John drive? | [
"235 miles.",
"245 miles.",
"255 miles.",
"265 miles.",
"275 miles."
] | The total distance D traveled by John is given by
D = 50 * 2 + 3 * 55 = 265 miles.
Answer D
The answer is: D | D |
mathematics | At an elementary school, 70% of the faculty members are women and 40% of the faculty members are married. If 1⁄3 of the men are single, what fraction of the women are married? | [
"5⁄7",
"7⁄10",
"2/7",
"7⁄30",
"5⁄70"
] | --------------------M------W--------Total
Marrried----------20-----20---------40
Not married-----10-----50---------60
Total-------------30-----70--------100
need married woman/total woman, so 20/70=2/7
C
The answer is: C | C |
mathematics | A secret can be told only 2 persons in 5 minutes .the same person tells to 2 more persons and so on . How long will take to tell it to 768 persons ? | [
"25 min",
"32 min",
"33 min",
"34 min",
"35 min"
] | at start one person will tell to 2 persons, it will take 5 min, now that 1+2 = 3 persons will tell this to next 6 persons, then 1+2+6 = 9 persons will tell to next 18 persons, then 1+2+6+18 = 27 persons to 54 similarly 1+2+6+18+54 = 81 persons will tell this to 162 persons similarly 1+2+6+18+54+162 = 243 persons will t... | E |
mathematics | If $10 is invested at x percent simple annual interest for n years, which of the following represents the total amount of interest, in dollars, that will be earned by this investment in the n years? | [
"10n(x/100)",
"10,000(x/100)^n",
"10,000n(x/100)",
"10,000(1+x/100)^n",
"10,000n(1+x/100)"
] | I think answer D is for compound interest (which i assumed)
and answer A is for simple interest because it is not compounding.
The answer is: A | A |
mathematics | Last year, for every 100 million vehicles that traveled on a certain highway, 50 vehicles were involved in accidents. If 5 billion vehicles traveled on the highway last year, how many of those vehicles were involved in accidents? (1 billion = 1,000,000,000) | [
"800",
"850",
"900",
"500",
"1000"
] | To solve we will set up a proportion. We know that “100 million vehicles is to 50 accidents as 5 billion vehicles is to x accidents”. To express everything in terms of “millions”, we can use 5,000 million rather than 5 billion. Creating a proportion we have:
100/50 = 5,000/x
Cross multiplying gives us:
100x = 2,000 * 5... | E |
mathematics | In a certain deck of cards, each card has a positive integer written on it, in a multiplication game a child draws a card and multiplies the integer on the card with the next large integer. If the each possible product is between 15 and 270, then the least and greatest integer on the card would be | [
"3 and 15",
"3 and 20",
"4 and 13",
"4 and 16",
"5 and 14"
] | Given: 15<x(x+1)<270.
Now, it's better to test the answer choices here rather than to solve:
If x=4 then x(x+1)=20>15 --> so, the least value is 4. Test for the largest value: if x=16 then
x(x+1)=16*17=272>270
Answer: D.
The answer is: D | D |
mathematics | By mixing two brands of tea and selling the mixture at the rate of Rs. 177 per kg. a shopkeeper makes a profit of 18%. If to every 2 kg of one brand costing Rs. 200 per kg, 3 kg of the other brand is added, then how much per kg does the other brand cost? | [
"Rs. 110",
"Rs. 120",
"Rs. 140",
"None of these",
"Not determined"
] | Explanation:
Let the cost of the brand be Rs. X per kg.
C.P. of 5 kg = (2 * 200 + 3 * x) = Rs. (400 + 3x)
S.P of 5 kg = Rs. (5 * 177) = Rs. 885
[885 - (400 + 3x)]/(400 + 3x) * 100 = 18
24250 - 150x = 3600 + 27x
177x = 20650 => x = 116 2/3
So, cost of the other brand = Rs. 116.66.
Answer is D
The answer is: D | D |
mathematics | What percent is 2 minutes 24 seconds of an hour? | [
"6%",
"8%",
"4%",
"2%",
"9%"
] | 2mt 24s =144s
(144*100)/(60*60)=4%
ANSWER:C
The answer is: C | C |
mathematics | A student traveled 25 percent of the distance of the trip alone, continued another 40 miles with a friend, and then finished the last half of the trip alone. How many miles long was the trip? | [
"120",
"140",
"160",
"180",
"200"
] | Let x be the total length of the trip.
0.25x + 40 miles + 0.5x = x
40 miles = 0.25x
x = 160 miles
The answer is C.
The answer is: C | C |
mathematics | All the water in container A which was filled to its brim was poured into two containers B and C. The quantity of water in container B was 62.5% less than the capacity of container A. If 151 liters was now transferred from C to B, then both the containers would have equal quantities of water. What was the initial quant... | [
"1289",
"1198",
"281",
"1208",
"282"
] | Explanation:
B has 62.5% or (5/8) of the water in A. Therefore, let the quantity of water in container A(initially) be 8k.
Quantity of water in B = 8k - 5k = 3k.
Quantity of water in container C = 8k - 3k = 5k
Container: A B C
Quantity of water: 8k 3k 5k
It is given that if 151 liters was transferred from container C t... | D |
mathematics | |x+3| – |4-x| = |8+x| How many K solutions will this equation have? | [
"0",
"1",
"2",
"3",
"4"
] | |x| = x when x >= 0 (x is either positive or 0)
|x| = -x when x < 0 (note here that you can put the equal to sign here as well x <= 0 because if x = 0,
|0| = 0 = -0 (all are the same)
So the '=' sign can be put with x > 0 or with x < 0. We usually put it with 'x > 0' for consistency.A
The answer is: A | A |
mathematics | Gill drives 120 miles from Los Angeles to San Diego to fetch a package. On her way there she drives at 40 miles per hour. On her way back she drives 50% faster. What is Gill's average velocity W for the round trip? | [
"24 miles per hour",
"48 miles per hour",
"50 miles per hour",
"53 1/3 miles per hour",
"68 miles per hour"
] | Here's an Average Speed question in which the prompt gives you almost all of the immediate numbers needed to work with.
Driving from LA to SD, we have a distance of 120 miles and a speed of 40 miles/hour.
D = (R)(T)
120 = (40)(T)
120/40 = 3 = T
3 hours to drive to SD
On the way back, she drives 50% FASTER. Gill's retur... | B |
mathematics | The jogging track in a sports complex is 726 m in circumference. Deepak and his wife start from the same point and walk in opposite directions at 4.5 km/hr and 3.75 km/hr respectively. They will meet for the first time in? | [
"4.9 min",
"5.28 min",
"5.5 min",
"6 min",
"7 min"
] | Clearly, the two will meet when they are 726 m apart.
To be (4.5 + 3.75) = 8.25 km apart, they take 1 hour.
To be 726 m apart, they take (100/825 * 726/1000) hrs = (242/2750 * 60) min = 5.28 min.
ANSWER:B
The answer is: B | B |
mathematics | How many such 3's are there in the following number sequence which are immediately Preceded by an odd number and immediately followed by an even number ? 5 3 8 9 4 3 7 2 3 8 1 3 8 4 2 3 5 7 3 4 2 3 6 | [
"1",
"2",
"3 three",
"4",
"More than four"
] | A is followed by B means : A comes first,B comes next
A preceded by B means : B comes first, A comes next
The sets which satisfy the condition is: 5 3 8
1 3 8
7 3 4
ANSWER:C
The answer is: C | C |
mathematics | Johnny makes $3.25 per hour at his work. If he works 8 hours, how much money will he earn? | [
"$30",
"$54",
"$26",
"$12",
"$9.60"
] | 3.25*8=26. Answer is C.
The answer is: C | C |
mathematics | Find the least number must be added to 228712 so that remaining no.is divisible by 9? | [
"5",
"3",
"1",
"6",
"2"
] | On dividing 228712 by 9 we get the remainder 4, so 5 should be subtracted
A
The answer is: A | A |
mathematics | We have 7770 balls available, and there is 1 ball on d top of rack and then 3 balls on d 1st floor behind the top rack (horizontal rack) and then 6 balls on 2nd floor then 10 balls on 3rd floor,
How many floors can be accomdated with the given no of balls...??? | [
"36",
"35",
"34",
"33",
"32"
] | 1+3+6+10+........=7770 sum of triangular number
n*(n+1)*(n+2)/6 gives 35
ANSWER:B
The answer is: B | B |
mathematics | A circular metal plate of even thickness has 12 holes of radius 1 cm drilled into it. As a result the plate lost 1/6th its original weight. The radius of the circular plate is | [
"16sqrt2",
"8sqrt2",
"32sqrt2",
"sqrt72",
"sqrt82"
] | Area of 12 holes=12*Pi*1^2=12*Pi
As 12*Pi=(1/6)th weight,so total Area of Plate=12*Pi/(1/6)=72*Pi
If r=radius of the plate,then its Area=Pi*r^2=72*Pi, So r=Sqrt72
ANSWER:D
The answer is: D | D |
mathematics | An athlete runs 200 metres race in 24 seconds. His speed is : | [
"20 km/hr",
"24 km/hr",
"28.5 km/hr",
"30 km/hr",
"None of these"
] | Speed = 200/24 m/sec=25/3 m/sec=(25/3*18/5)km/hr=30 km/hr.
Correct Option: D
The answer is: D | D |
mathematics | Machine A and machine B are each used to manufacture 550 sprockets. It takes machine A 10 hours longer to produce 550 sprockets than machine B. Machine B produces 10 percent more sprockets per hour than machine A. How many sprockets per hour does machine A produces? | [
"6",
"5",
"7",
"8",
"9"
] | Machine B: Takes x hours to produce 550 sprockets
Machine A: Takes (x+10) hours to produce 550 sprockets
Machine B: In 1 hour, B makes 550/x sprockets
Machine A: In 1 hour, A makes 550/(x+10) sprockets
Equating:
1.1(550/(x+10)) = 550/x
605/(x+10) = 550/x
605x = 550x+5500
55x = 5500
x = 100
A makes 550/(110) = 5 sprocke... | B |
mathematics | On 8th Feb, 1995 it was Wednesday. The day of the week on 8th Feb, 1994 was | [
"wednesday",
"Tuesday",
"Thursday",
"Friday",
"None"
] | 1994 being an ordinary year, it has 1 odd day. So, the day on 8th Feb, 1995 is one day beyond the day on 8th Feb, 1994. But, 8th Feb, 1995 was Wednesday. 8th Feb, 1994 was Tuesday.
Answer B
The answer is: B | B |
mathematics | From the starting point in a boat race, one competitor started to sail north at a speed of 1.1 Km/h, the other competitor started to sail west at a speed of 1.2 Km/h. What is the distance in Km between the two competitors after 5 hours? | [
"8.1",
"12.",
"12.5.",
"14.",
"15.4."
] | Both competitors are sailing making angle of 90 degrees.
After 5 hrs one competitor will cover a distance of = 1.1 *5= 5.5 KM
And, other competitor will cover a distance of = 1.2*5= 6KM
distance between them after 5 hrs = (5.5^2+ 6^2)^1/2= 8.1 KM
A is the answer
The answer is: A | A |
mathematics | In a 300 member association consisting of men and women, exactly 20% of men and exactly 25 % women are homeowners. What is the least number of members who are homeowners? | [
"79",
"77",
"85",
"83",
"61"
] | Solution simple
Out of 300 20% are male i.e 60 and 25% are female i.e 75 , so total homeowner is 135.
Now min number homeowner is 60 and max is 135 so question ask us to find least and 61 has least value among all option.
So ans is 61.
Answer : E
The answer is: E | E |
mathematics | On Saturday morning, John will begin a camping vacation and he will return home at the end of the first day on which it rains. If on the first three days of the vacation the probability of rain on each day is 0.6, what is the probability that Malachi will return home at the end of the day on the following Monday? | [
"0.096",
"0.125",
"0.128",
"0.512",
"0.64"
] | Re-phrasing the question:
What is the probability of: Saturday: No rain, Sunday: No rain, Monday: Rain
Probability of rain = 0.6
Therefore, probability of no rain = 0.4
0.6*0.6*0.4 = 0.096
Hence A
The answer is: A | A |
mathematics | The price of a book is increased from $300 to $360. What is the % of increase in its price? | [
"10%",
"20%",
"40%",
"50%",
"60%"
] | Explanation: Change in the price = Rs 360 – Rs 300
= Rs 60
Percentage of increase = Change in the price Initial Price
* 100.
Percentage increase in price =( 60 300
) *100 = 20%
B
The answer is: B | B |
mathematics | If x is less than y by 50% then y exceed x by: | [
"33.33%",
"100%",
"75%",
"66.66%",
"None of these"
] | Using formula (x/(100-x)*100) where x is Percentage decrease (here it is 25%)
=> 50(100-50)*100
=100%
ANSWER:B
The answer is: B | B |
mathematics | A special lottery is to be held to select a student who will live in the only deluxe room in a hostel. There are 100 Year-III, 150 Year-II and 200 Year-I students who applied.
Each Year-III's name is placed in the lottery 3 times; each Year-II's name, 2 times and Year-I's name, 1 time. What is the probability that a Ye... | [
"1/8",
"2/9",
"2/7",
"3/8",
"3/9"
] | Explanation :
Total names in the lottery,
=3×100+2×150+200
=800.
Number of Year-III's names,
=3×100
=300.
The required probability,
=300/800.
=3/8.
Answer : D
The answer is: D | D |
mathematics | The length of the bridge, which a train 180 metres long and travelling at 45 km/hr can cross in 30 seconds, is? | [
"245",
"777",
"282",
"195",
"288"
] | Speed = [45 X 5/18] m/sec = [25/2] m/sec Time = 30 sec Let the length of bridge be x metres. Then, (180 + x)/30 = 25/2 => 2(180 + x) = 750 => x = 195 m.
Answer: D
The answer is: D | D |
mathematics | What is the square root of 36, divided by 6? | [
"9",
"36",
"122",
"6",
"1"
] | Square root is a number times itself
Square root of 36=6, 6/6=1
(E)1
The answer is: E | E |
mathematics | 16,25,36,72,144,196,225 | [
"36",
"196",
"225",
"144",
"72"
] | Each of the numbers except 72 is a perfect square.
answer :E
The answer is: E | E |
mathematics | In a stack of boards at a lumber yard, the 13th board counting from the top of the stack is immediately below the 12th board counting from the bottom of the stack. how many boards are in the stack? | [
"33",
"23",
"25",
"32",
"42"
] | 1 2 3 ....
..............13 12 ................. 1
So the number of boards = 13+10 =23.
Option: B
The answer is: B | B |
mathematics | A woman has three blouses of different colors, four skirts of different colors, and two different pairs of shoes. She refuses to wear her pink blouse with her green skirt. How many different blouseskirt-shoe combinations could she wear? | [
"8",
"12",
"16",
"17",
"22"
] | total ways = 3*4*2=24..
now its better to find the ways in which the pink blose and green skirty are together and subtract from total to get the answer..
the ways in which the pink blose and green skirty are together=1*1*2=2..
total ways =24-2=22..
E
The answer is: E | E |
mathematics | A can do a job in 3 days less time than B. A works at it alone for 4 days and then B takes over and completes it. If altogether 14 days were required to finish the job, how many days would each of them take alone to finish it? | [
"17 days, 20 days",
"12 days, 15 days",
"13 days, 16 days",
"14 days, 11 days",
"None of these"
] | Let B can finish the work in x days.
Then A can finish the work in (x – 3) days.
B’s one day’s work = 1⁄xth work.
A’s one day’s work = 1⁄(x - 3)th work.
A’s 4 days’ work = 4⁄(x - 3)th work.
Remaining work = 1 - 4⁄(x - 3) = x−7 /x−3
The remaining work done by B in 14 – 4 = 10 days.
Now, in 10 days, work done by B = x−7/... | B |
mathematics | If x is a positive even number, then each of the following is even odd EXCEPT | [
"(x + 3)(x + 5)",
"x^2 +4",
"x^2 + 6x + 9",
"3x^2 + 4",
"5(x + 3)"
] | Since it is given tht x is even number, so any integer multiplied with x will also be even..
so, we should concentrate only on other terms..
lets see the choices..
A. (x + 3)(x + 5)
We have two terms with x and each is added with a odd number..
each bracket becomes odd and Odd*Odd=Odd
B. x^2 + 5
here we are adding an O... | B |
mathematics | A man has Rs. 480 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 ? | [
"45",
"60",
"75",
"90",
"95"
] | Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
16x = 480
x = 30.
Hence, total number of notes = 3x = 90.
Answer: Option D
The answer is: D | D |
mathematics | Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 3 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is? | [
"299",
"2767",
"120",
"287",
"261"
] | Work done by the waste pipe in 1 minute = 1/15 - (1/20 + 1/24) = - 1/40
Volume of 1/40 part = 3 gallons\
Volume of whole = 3 * 40 = 120 gallons.
Answer: C
The answer is: C | C |
mathematics | S is the infinite sequence S1 = 2, S2 = 22, S3 = 222,...Sk = Sk–1 + 2(10k–1). If p is the sum of the first 30 terms of S, what is the ninth digit of p, counting right to left from the units digit? | [
"1",
"2",
"4",
"6",
"9"
] | C
Sum of unit digits of first 30 terms = 60
Sum of tens digits of first 30 terms = 58
Sum of thousands digits of first 30 terms = 56
and so on..
p1 = 0
p2 = (6+58) = 4
p3 = (6+56) = 2
p4 = (6+54) = 0
p5 = (6+52) = 8
p6 = (5+50) = 5
p7 = (5+48) = 3
p8 = (5+46) = 1
p9 = (5+44) = 9
ANSWER: E
The answer is: E | E |
mathematics | If 3^x*4^y = 1,594,323 and x – y = 13, then x = ? | [
"10",
"11",
"12",
"13",
"14"
] | Since 1,594,323 is an odd number, it is not a multiple of 4.
This means that y must equal zero.
Since x - y = 13 and y = 0, then x = 13.
The answer is D.
The answer is: D | D |
mathematics | Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one? | [
"40",
"45",
"48",
"51",
"44"
] | Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000 * 6/125 = 48 sec.
Answer: Option C
The answer is: C | C |
mathematics | A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was: | [
"14",
"67",
"56",
"89",
"34"
] | Let the son's present age be x years. Then, (38 - x) = x
2x = 38.
x = 19.
Son's age 5 years back (19 - 5) = 14 years.
Answer:A
The answer is: A | A |
mathematics | In doing a division of a question with zero remainder,a candidate
took 12 as divisor instead of 21.The quotient obtained by him was 35.
The correct quotient is? | [
"12",
"21",
"20",
"35",
"10"
] | Dividend=12*35=420.
Now dividend =420 and divisor =21.
Therefore correct quotient =420/21=20.
ANSWER C 20
The answer is: C | C |
mathematics | In one hour, a boat goes 13 km along the stream and 5 km against the stream. The speed of the boat in still water (in km/hr) is: | [
"2",
"4",
"9",
"12",
"15"
] | Sol.
Speed in still water = 1/2 (13+5) kmph = 9 kmph.
Answer C
The answer is: C | C |
mathematics | A man can row with a speed of 15 kmph in still water. If the stream flows at 20 kmph, then the speed in downstream is? | [
"27",
"27",
"20",
"99",
"35"
] | M = 15
S = 25
DS = 15 + 25 = 35
Answer:E
The answer is: E | E |
mathematics | In a office work is distribute between p persons. If 1/5 members are absent then work increased for each person is? | [
"13.28%",
"14.28%",
"15.28%",
"16.28%",
"25%"
] | let total % of work is 100%
total person=p
1/5 person are absent of total person . so absent person is 1/5p ie p/5.
left person is, p-p/5=4p/5.
p person do the work 100%
1 person do the work 100*p%
4p/5 person do the work (100*p*5)/4p%=125%
work increased for each person is=(125-100)%=25%
ANSWER:E
The answer is: E | E |
mathematics | Bob bikes to school every day at a steady rate of x miles per hour. On a particular day, Bob had a flat tire exactly halfway to school. He immediately started walking to school at a steady pace of y miles per hour. He arrived at school exactly t hours after leaving his home. How many miles is it from the school to Bob'... | [
"(x + y) / t",
"2(x + t) / xy",
"2xyt / (x + y)",
"2(x + y + t) / xy",
"x(y + t) + y(x + t)"
] | Say the distance to school is 10 miles, x=5 miles per hour and y=1 miles per hour, then:
Time Bob spent biking would be 5/5=1 hour, and time he s pent walking would be 5/1=5 hours, so t=1+5=6 hours.
Now, plug x=5, y=1, and t=6 into the answer choices to see which one yields the distance of 10 miles. Only answer choice ... | C |
mathematics | A train 400 m long can cross an electric pole in 20 sec and then find the speed of the train? | [
"88 Kmph",
"89 Kmph",
"72 Kmph",
"16 Kmph",
"18 Kmph"
] | Length = Speed * time
Speed = L/T
S = 400/20
S = 20 M/Sec
Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 72 Kmph
Answer: C
The answer is: C | C |
mathematics | A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 40 years now, the son's age 10 years back was? | [
"12yr",
"15yr",
"14yr",
"10yr",
"20yr"
] | Let the son's present age be x years
Then, 40-x = x
x = 20
Son's age 10 years back = 20-10 = 10years
Answer is D
The answer is: D | D |
mathematics | What number has a 5:1 ratio to the number 10? | [
"74",
"50",
"94",
"59",
"48"
] | Answer: Option B
Explanation:
5:1 = x: 10
x = 50
Answer: Option B
The answer is: B | B |
mathematics | Seven fencers participate in a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded? | [
"30",
"36",
"42",
"48",
"49"
] | 7*6 = 42
The answer is C.
The answer is: C | C |
mathematics | If the sum of two numbers is 30 and the sum of their squares is 840, then the product of the numbers is | [
"40",
"44",
"80",
"88",
"30"
] | Sol.
Let the numbers be x and y.
Then, (x+y) = 30 and x2 + y2 = 840.
Now, 2xy = (x+y)2 - (x2 + y2)
= (30)2 - 840= 900 - 840= 60
xy = 30.
Answer E
The answer is: E | E |
mathematics | If P is a prime number greater than 5, what is the remainder when P^2 is divided by 6. | [
"4",
"Cannot be determined",
"2",
"6",
"1"
] | take square of any prime number
remainder will be 1
Ans E
The answer is: E | E |
mathematics | Tina has 5 socks and 3 pair of shoes. How many combinations does Barbara have, if she doesn’t wear 2 specific socks with 1 specific pair of shoes? | [
"4",
"7",
"10",
"11",
"13"
] | Total no of combinations available is= 5 Socks X 3 pair of shoes = 15
Eliminate the 2 socks X 1 pair of shoes combo = 2 which gives.......>> 15-2=13
ANSWER: E
The answer is: E | E |
mathematics | How must a grocer mix 4 types of peanuts worth 54 c, 72 c, $1.2 and $1.44 per pound so as to obtain a mixture at 96 cents per pound? | [
"8:4:4:7",
"24:12:12:50",
"4:8:7:4",
"16:42:28:10",
"Cannot be uniquely determined"
] | As we know Sum of (Respective Quantity x Respective Price) = Total Price = Average price x Total Quantity
Option 1
Ratio of quantity mixed - 8a:4a:4a:7a
Total quantity = 23a parts (8+4+4+7)
(8a.9 + 4a.12 + 4a.20 + 7a.24) = 16.23a
368a = 368a
LHS = RHS
Thus option 1 satisfy the condition
Option 2
Ratio of quantity mixed... | E |
mathematics | 25.25/2000 is equal to: | [
"1.012526",
"0.012625",
"0.12526",
"0.12625",
"0.12725"
] | 25.25/2000 = 2525/200000
= 0.012625
ANSWER:B
The answer is: B | B |
mathematics | 3x^2-6x+3 = 0
Find the above equation find the value of x | [
"0",
"1",
"2",
"4",
"5"
] | a = 3, b = -6, c = 3
x1,2 = (6 ± √( (-6)2 - 4×3×3)) / (2×3) = (6 ± √(36-36)) / 6 = (6 ± 0) / 6
x1 = x2 = 1
B
The answer is: B | B |
mathematics | For a group of n people, k of whom are of the same sex, the (n-k)/n expression yields an index for a certain phenomenon in group dynamics for members of that sex. For a group that consists of 20 people, 6 of whom are females, by how much does the index for the females exceed the index for the males in the group? | [
"0.4",
"0.0625",
"0.2",
"0.25",
"0.6"
] | Index for females = (20-6)/20 = 7/10 = 0.7
Index for males = (20-14/20 = 3/10 = 0.3
Index for females exceeds males by 0.7 - 0.3 = 0.4
Answer: A
The answer is: A | A |
mathematics | A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform? | [
"177",
"166",
"350",
"198",
"161"
] | Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 39 = 50/3
3(x + 300) = 1950 è x = 350m.
Answer: C
The answer is: C | C |
mathematics | A, B, C enter into a partnership investing Rs. 35,000, Rs. 45,000 and Rs. 55,000 respectively. The respective shares of A, B, C in annual profit of Rs. 40,500 are? | [
"Rs. 10,500, Rs. 13,500, Rs. 16,500",
"Rs. 10,500, Rs. 13,500, Rs. 16,509",
"Rs. 10,500, Rs. 13,500, Rs. 16,555",
"Rs. 10,500, Rs. 13,500, Rs. 16,506",
"Rs. 10,500, Rs. 13,500, Rs. 16,504"
] | A:B:C = 35000 : 45000 : 55000 = 7:9:11
A's share = 40500 * 7/27 = Rs. 10500
B's share = 40500 * 9/27 = Rs. 13500
C's share = 40500 * 11/27 = Rs. 16500
Answer: A
The answer is: A | A |
mathematics | In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together? | [
"6! / 2!",
"3! * 3!",
"4! / 2!",
"(4! * 3!) / 2!",
"(3! * 3!) / 2!"
] | Explanatory Answer
Step 1: Group the vowels as one unit and rearrange
ABACUS is a 6 letter word with 3 of the letters being vowels.
Because the 3 vowels have to appear together, let us group the AAU as one unit.
There are 3 consonants in addition to one unit of vowels.
These 4 elements can be rearranged in 4! ways.
Ste... | D |
mathematics | If the population of a certain country increases at the rate of one person every 15 seconds, by how many persons does the population increase in 60 minutes? | [
"80",
"100",
"150",
"240",
"300"
] | Since the population increases at the rate of 1 person every 15 seconds, it increases by 4 people every 60 seconds, that is, by 4 people every minute. Thus, in 60 minutes the population increases by 60 x 4 = 240 people.
Answer. D.
The answer is: D | D |
mathematics | The average age of a class of 39 students is 15 years. If the age of the teacher be included, then the average increases by3 months. Find the age of the teacher. | [
"20",
"23",
"25",
"21",
"22"
] | Total age of 39 persons = (39 x 15) years
= 585 years.
Average age of 40 persons= 15 yrs 3 months
= 61/4 years.
Total age of 40 persons = (61/4 )x 40) years= 610 years.
:. Age of the teacher = (610 - 585) years=25 years.
Answer is C.
The answer is: C | C |
mathematics | A monkey ascends a greased pole 20 metres high. He ascends 2 metres in first minute and slips down 1 metre in the alternate minute. In which minute, he reaches the top ? | [
"21st",
"22nd",
"23rd",
"24th",
"37th"
] | In 2 minutes, he ascends = 1 metre
∴ 18 metres, he ascends in 36 minutes.
∴ He reaches the top in 37th minute.
Answer E
The answer is: E | E |
mathematics | To fill a tank, 25 buckets of water is required. How many buckets of water will be required to fill the same tank if the capacity of the bucket is reduced to two-fifth of its present ? | [
"65.5",
"63.5",
"60.5",
"61.5",
"62.5"
] | Let the capacity of 1 bucket = x.
Then, the capacity of tank = 25x.
New capacity of bucket = 2/5 x
Therefore, Required number of buckets = (25x)/(2x/5)
= (25x) x 5/2x
= 125/2
= 62.5
Answer is E.
The answer is: E | E |
mathematics | 6/8 of the population of the country of Venezia lives in Montague Province, while the rest lives in Capulet Province. In the upcoming election, 80% of Montague residents support Romeo, while 70% of Capulet residents support Juliet; each resident of Venezia supports exactly one of these two candidates. Rounded if necess... | [
"28%",
"54%",
"45%",
"72%",
"78%"
] | Total population = 80 (assume).
6/8*80=60 people from Montague.
2/8*80=20 people from Capulet.
0.2*60=12 people from Montague support Juliet.
0.7*20=14 people from Capulet support Juliet.
The probability that a Juliet supporter chosen at random resides in Capulet is 14/(12+14)=~54
Answer: B.
The answer is: B | B |
mathematics | The average weight of 16 children in a class is 50.25 kg and that of the remaining 8 children is 45.15 kg. Find the average weights of all the children in the class. | [
"A)48.55",
"B)49",
"C)51",
"D)61",
"E)62"
] | Required average
= (50.25 x 16 + 45.15 x 8)/(16 + 8)
= (804 + 361.20)/24
= 1165.20/24
= 48.55kg
Answer is A
The answer is: A | A |
mathematics | One boy forgot the lastdigit of a 7 digit telephone no. If he randomly dialthe final 3 digits after correctly dialing the 1st four, then what is the chance of dialing the correct no.? | [
"2/995",
"1/998",
"1/1000",
"1/1100",
"1/1200"
] | it is given that last 3 digits are randomly dialed
Then, each of the digit can be selected out of 10 digits in 10 ways. Hence, required probability
= 1/(10)3 = 1/1000
C
The answer is: C | C |
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