subject
stringclasses 1
value | question
stringlengths 3
1.14k
| options
listlengths 5
5
| solution
stringlengths 18
3.7k
| answer
stringclasses 5
values |
|---|---|---|---|---|
mathematics | What is the length of a bridge (in meters), which a train 140 meters long and travelling at 45 km/h can cross in 30 seconds? | [
"205",
"220",
"235",
"250",
"265"
]
| speed = 45 km/h = 45000 m / 3600 s = 25/2 m/s
In 30 seconds, the train can travel 25/2 * 30 = 375 meters
375 = length of train + length of bridge
length of bridge = 375 - 140 = 235 meters
The answer is C.
The answer is: C | C |
mathematics | M = {-6, -5, -4, -3, -2}
T = {-3, -2, -1, 0, 1, 2, 3, 4, 5}
If an integer is to be randomly selected from set M above and an integer is to be randomly selected from set T above, what is the probability that the product of the two integers will be negative? | [
"0",
"3/7",
"2/5",
"1/2",
"5/9"
]
| We will have a negative product only if 1, 2, 3, 4, or 5 are selected from set T.
P(negative product) = 5/9
The answer is E.
The answer is: E | E |
mathematics | If [Y] denotes the least integer greater than or equal to Y and [Y] = 0, which of the following statements must be true? | [
"Y = 0",
"0 <= Y < 1",
"0 < Y <= 1",
"-1 < Y <= 0",
"-1 <= Y < 0"
]
| The answer for this is 0 < = Y< = 1
However it is not available in the options. The match to the above is-1 < Y <= 0
Answer = D
The answer is: D | D |
mathematics | What is the least number of squares tiles required to pave the floor of a room 2 m 25 cm long and 1 m 35 cm broad? | [
"15",
"20",
"40",
"44",
"48"
]
| Length of largest tile = H.C.F. of 225 cm and 135 cm = 45 cm.
Area of each tile = (45 x 45) cm2.
Required number of tiles =225 x 135/(45^2)= 15.
ANSWER:A
The answer is: A | A |
mathematics | The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 2025 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units? | [
"140",
"150",
"160",
"170",
"180"
]
| Given that the area of the square = 2025 sq.units
=> Side of square = √2025 = 45 units
The radius of the circle = side of the square = 45 units
Length of the rectangle = 2/5 * 45 = 18 units
Given that breadth = 10 units
Area of the rectangle = lb = 18 * 10 = 180 sq.units
Answer: Option E
The answer is: E | E |
mathematics | Mr. Kramer, the losing candidate in a two-candidate election, received 942,568 votes, which was exactly 45 percent of all votes cast. Approximately what percent of the remaining votes would he need to have received in order to have won at least 50 percent of all the votes cast? | [
"9%",
"12%",
"15%",
"17%",
"20%"
]
| Let me try a simpler one.
Lets assume that candidate got 45% votes and total votes is 100.
Candidate won = 45
Remaining = 55
To get 50%, candidate requires 5 votes from 100 which is 5% and 5 votes from 55.
5/55= 1/11 = .09 = 9%
Which is approx 9%. Hence the answer is A.
The answer is: A | A |
mathematics | Two vessels P and Q contain 62.5% and 87.5% of alcohol respectively. If 2 litres from vessel P is mixed with 4 litres from vessel Q, the ratio of alcohol and water in the resulting mixture is? | [
"19 : 7",
"17 : 5",
"19 : 8",
"19 : 5",
"29 : 5"
]
| Quantity of alcohol in vessel P = 62.5/100 * 2 = 5/4 litres
Quantity of alcohol in vessel Q = 87.5/100 * 4 = 7/2 litres
Quantity of alcohol in the mixture formed = 5/4 + 7/2 = 19/4 = 4.75 litres
As 6 litres of mixture is formed, ratio of alcohol and water in the mixture formed
= 4.75 : 1.25 = 19 : 5.
Answer:D
The answer is: D | D |
mathematics | Three friends Ravi, Baskar and Chandran divide $1200 amongs them in such a way that if $10, $20 and $15 are removed from the sums that Ravi, Baskar and Chandran received respectively, then the share of the sums that they got will be in the ratio of 10 : 12 : 13. How much did Chandran receive? | [
"$444",
"$445",
"$446",
"$447",
"$448"
]
| A+B+C = 1200
Given ratio 10:12:13
Let us say the shares of A,B,C deducting 10,20,15 be a,b,c
a+b+c = 1200-45= 1155 = 35K
c share = (1155X13)/35 = 429
C = chandran share = 429+15 = 444
Option A
The answer is: A | A |
mathematics | If P represents the product of the first 14 positive integers, then P is not a
multiple of: | [
"a) 99",
"b) 84",
"c) 72",
"d) 65",
"e) 57"
]
| a) 99 = 9*11
b) 84 = 4*7*3
c) 72 =9*11
d) 65 = 5*13
e) 57 =19*3
since 19 is not there in first 15 positive numbers it is the only possibility
E
The answer is: E | E |
mathematics | Find the missing number in the given sequence : 1,2,3,5,?,13,21,? | [
"8 & 34",
"7 & 34",
"9 & 34",
"7 & 35",
"7 & 36"
]
| 1+2=3
2+3=5
3+5=8
5+8=13
8+13=21
13+21=34
ANSWER:A
The answer is: A | A |
mathematics | How long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length? | [
"55 sec",
"40 sec",
"45 sec",
"30 sec",
"35 sec"
]
| T = (660 + 165)/54 * 18/5
T = 55
ANSWER A
The answer is: A | A |
mathematics | A and B can finish a work in 16 days while A alone can do the same work in 24 days. In how many days B alone will complete the work? | [
"38",
"48",
"27",
"21",
"20"
]
| B = 1/16 – 1/24 = 1/48 => 48 days . Answer: B
The answer is: B | B |
mathematics | If p and q are positive integers and q ≠ 1, then pq(q −2) is | [
"pq^2",
"pq^2+2pq",
"pq^2-2pq",
"pq^2+pq",
"pq^2-6pq"
]
| pq(q-2) = pq^2-2pq
Answer : C
The answer is: C | C |
mathematics | A can do a piece of work in 4 days. B can do it in 15 days. With the assistance of C they completed the work in 24 days. Find in how many days can C alone do it? | [
"0.391 days",
"0.491 days",
"0.331 days",
"1.391 days",
"0.301 days"
]
| C = 1/2 - 1/24 - 1/15 = 0.391 days
ANSWER:A
The answer is: A | A |
mathematics | (0.8)(power 3) - (0.5)(power 3)/ (0.8)(power 2) + 0.40 + (0.5)(power 2) is: | [
"0.6",
"0.5",
"0.35",
"0.3",
"None of them"
]
| Given expression
= (0.8) (power 3) - (0.5)(power 3) / (0.8)(power 2) + (0.8 x 0.5) + (0.5)(power 2)
= a (power 3) - b(power 3) / a(power 2) + ab + b(power 2)
= (a - b)
= (0.8- 0.5)
= 0.30
Answer is D.
The answer is: D | D |
mathematics | A company pays 12.5% dividend to its investors. If an investor buys Rs.50 shares and gets 25% on investment, at what price did the investor buy the shares? | [
"25",
"66",
"18",
"19",
"01"
]
| Explanation:
Dividend on 1 share = (12.5 * 50)/100 = Rs.6.25
Rs.25 is income on an investment of Rs.100
Rs.6.25 is income on an investment of Rs. (6.25 * 100)/25 = Rs.25
ANSWER: A
The answer is: A | A |
mathematics | If |5x-15| = 100, then find the sum of the values of x? | [
"1",
"-2",
"6",
"-3",
"4"
]
| |5x-15| = 100
5x-15 = 100 or 5x-15 = -100
5x = 115 or 5x = -85
x = 23 or x = -17
sum = 23-17 = 6
Answer is C
The answer is: C | C |
mathematics | Sobha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents? | [
"4",
"6",
"8",
"10",
"2"
]
| Age of Sobha's father when Sobha was born =38
Age of Sobha's mother when Sobha was born =36−4=32
Required difference of age =38−32=6
Answer is B.
The answer is: B | B |
mathematics | The area of a square garden is A square feet and the perimeter is p feet. If a=2p+15, what is the perimeter of the garden, in feet? | [
"28",
"36",
"40",
"56",
"64"
]
| Perimeter of square = P
Side of square = P/4
Area of Square = (P^2)/16 =A
Given that A = 2P + 15
(P^2)/16 = 2P + 15
P^2 = 32P +240
P^2 -32P -240 = 0
P^2 -40P + 6P -240 = 0
P(P-40)+6(P+40) = 0
(P-40)(P+6) = 0
P = 40 or- 6
Discarding negative value , P = 40
Answer is C
The answer is: C | C |
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? | [
"1/7",
"2/9",
"3/10",
"3/11",
"3/14"
]
| 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 | One water pump can fill half of a certain empty tank in 5 hours. Another pump can fill half of the same tank in 5.5 hours. Working together, how long will it take these two pumps to fill the entire tank? | [
"1 7/13",
"5 5/8",
"3 1/4",
"5 5/21",
"3 1/2"
]
| One pump can fill a tank in 5 hours and another in 5.5 hours
so the rate at which both can half fill the tank is (1/5+1/5.5) => 21/55
Thus half of the tank can be filled in 55/21
so for filling the complete tank => 55/21*2 = 110/21 =5 5/21
ANSWER:D
The answer is: D | D |
mathematics | For how many different positive integers n is a divisor of n^3 + 8?
. | [
"None",
"One",
"Two",
"Three",
"Four"
]
| n^3 + 8 = (n+2)(n^2-2n+4)
--> 2 divisors possible, plus 1 and n
we have 4 divisors. ANSWER:E
The answer is: E | E |
mathematics | What should be added to 4440 so that it may become a perfect square? | [
"44",
"45",
"46",
"47",
"49"
]
| 67x67=4489
4489-4440 = 49
If added to 49 get perfect square
answer =E
The answer is: E | E |
mathematics | Entry fee is Re.1.there are 3 rides each is of Re.1. total boys entering are 3000.total income is Rs.7200. 800 students do all 3 rides. 1400 go for atleast 2 rides.none go the same ride twice. then no of students who do not go any ride is? | [
"1328",
"1000",
"2378",
"8287",
"1872"
]
| Total entries are 3000 So fee collected through entry fee = 3000 x 1 = Rs.3000
Income generated through rides = 7200 - 3000 = 4200
Now 800 went for 3 rides so total fee paid by these 800 = 800 x 3 = 2400
(1400 - 800) went for 2 rides so fee paid by these 600 = 600 x 2 = 1200
Assume K went for exactly 1 ride
Then K x 1 + 1200 + 2400 = 4200 ⇒⇒ K = 600
So number of boys who did not go for any ride = 3000 - (600 + 600 + 800 ) = 1000
Answer:B
The answer is: B | B |
mathematics | Of the employees in a company, 20 % are female who have a master degree. If 10 % of the female employees do not have a master degree, what percent of the employees in the company are female? | [
"27.24%",
"26.22%",
"25.22%",
"22.25%",
"22.22%"
]
| Let E be total no. of employees and F be total no of female employees.
Question asked what is F/E X 100%?
No. of female employees with Masters = 0.2 x E (From the question)
No. of female employees without masters = 0.1 x F (From the question)
Therefore No. of female employees with masters = F - 0.1 F = 0.9 F
The 2 expressions equal each other therefore 0.9F = 0.2E; F/E = 0.2/0.9 = 22.22%
Ans: E
The answer is: E | E |
mathematics | 4 couples are seating at a round tables how many ways can the 4 women sit together | [
"4!*4!",
"3!*4!",
"4!*3!",
"5!*4!",
"6!*4!"
]
| 4 men can be arranged around a table in (4-1)!=3! ways;
Now, we can place 4 women in 4 slots between any two men and arrange these women in this slot in 4! ways.
So, total # of ways is 3!*4*4!=4!*4!
ANS:A
The answer is: A | A |
mathematics | The mean of a data set is equal to 10 and its standard deviation is equal to 1. If we add 5 to each data value, then the mean and standard deviation become | [
"mean = 15 , standard deviation = 6",
"mean = 10 , standard deviation = 6",
"mean = 15 , standard deviation = 1",
"mean = 10 , standard deviation = 1",
"None"
]
| Solution
Since 5 is added to all data values, the mean will also increase by 5 and becomes 15. But the standard deviation which measure the "distance" between the mean and the data values does not change.
Answer C
The answer is: C | C |
mathematics | By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 35%? | [
"228",
"480",
"267",
"416",
"276"
]
| SP = 800
Profit = 25%
CP = (SP)*[100/(100+P)]
= 800 * [100/125]
= 640
Loss = 25% = 25% of 640 = Rs.224
SP = CP - Loss = 640 - 224 = Rs.416
Answer: D
The answer is: D | D |
mathematics | n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4 ? | [
"2",
"4",
"7",
"9",
"11"
]
| Let n = 4q + 3. Then 2n = 8q + 6 = 4(2q + 1 ) + 2.
Thus, when 2n is divided by 4, the remainder is 2.
Option A
The answer is: A | A |
mathematics | Find the area of circle whose radius is 7m? | [
"298",
"154",
"267",
"268",
"298"
]
| 22/7 * 7 * 7 = 154
Answer: B
The answer is: B | B |
mathematics | In a renowned city, the average birth rate is 6 people every two seconds and the death rate is 2 people every two seconds. Estimate the size of the population net increase that occurs in one day. | [
"32,300",
"172,800",
"468,830",
"338,200",
"259,200"
]
| Every 2 seconds, 4 persons are added (6-2). Every second 2 persons are added.
In a day 24hrs = 24 * 60 Minutes = 24 * 60 * 60 = 86400 seconds.
86400 * 2 = 172800
Option B is the answer.
The answer is: B | B |
mathematics | The average of 11 numbers is 10.9. If the average of the first six numbers is 10.5 and that of the last six numbers is 11.4, then the middle number is | [
"21.5",
"11.5",
"61.5",
"41.5",
"31.5"
]
| Middle numbers = [(10.5 x 6 + 11.4 x 6) - 10.9 x 11]
= (131.4 - 119-9) = 11.5.
Answer: B
The answer is: B | B |
mathematics | The number of sailors on a ship is 78% more than the number of officers. The ratio of sailors to officers would be | [
"33:25",
"47:20",
"47:25",
"89:50",
"97:50"
]
| Sailor = 1.78 * Officer
Sailor/Officer = 1.78/1 = 178/100 = 89/50
Answer will be D
The answer is: D | D |
mathematics | In a rectangular coordinate system, what is the area of a quadrilateral whose vertices have the coordinates (4,-3), (4, 7), (10, 4), (10,-7)? | [
"51",
"54",
"57",
"60",
"63"
]
| By graphing the points, we can see that this figure is a trapezoid. A trapezoid is any quadrilateral that has one set of parallel sides, and the formula for the area of a trapezoid is:
Area = (1/2) × (Base 1 + Base 2) × (Height), where the bases are the parallel sides.
We can now determine the area of the quadrilateral:
Area = 1/2 × (10 + 11) × 6 = 63.
The answer is E.
The answer is: E | E |
mathematics | A certain league has two divisions. The respective divisions had 11 and 13 teams qualify for the playoffs. Each division held its own double-elimination tournament -- where a team is eliminated from the tournament upon losing two games -- in order to determine its champion. The four division champions then played in a single-elimination tournament -- where a team is eliminated upon losing one game -- in order to determine the overall league champion. Assuming that there were no ties and no forfeits, what is the maximum number of games that could have been played in order to determine the overall league champion? | [
"41",
"42",
"45",
"47",
"49"
]
| Overall, there can be 47 minuses. Tus, it is D.
The answer is: D | D |
mathematics | The floor of a rectangular room is 17 m long and 12 m wide. The room is surrounded by a veranda of width 2 m on all its sides. The area of the veranda is : | [
"124 m2",
"132 m2",
"148 m2",
"152 m2",
"None of these"
]
| Area of the outer rectangle = 21 × 16 = 336 m2
Area of the inner rectangle = 17 × 12 = 204 m2
Required area = (336 – 204) = 132 m2
Answer B
The answer is: B | B |
mathematics | If a coin is tossed twice, what is the probability that on the first toss the coin lands tails and on the second toss the coin lands tails? | [
"1/6",
"1/3",
"1/2",
"1/4",
"1"
]
| Since there are two options for how a coin can land (heads or tails), that means there is a 1/2 chance to land on tails and a 1/2 chance to land heads. To solve this problem you multiply each probability for each flip together. (1/2) chance to land tails the first time * (1/2) chance to land tails the second time = (1/4) chance to land tails both times.
Answer: D
The answer is: D | D |
mathematics | At a conference table, 6 employees gather around a table. One of the employees is the manager and he sits at the head of the table. Two of the employees sit on either side of the table. How many different seating arrangements can be made with these six employees? | [
"60",
"80",
"100",
"120",
"140"
]
| Head's sit is fixed. Now 5 people is left with 5 seats.
5 people can sit on 5 seats in 5! ways or 120 ways.
Ans is D
The answer is: D | D |
mathematics | A charity collected $1,299 from donors during the last month. If each donor gave at least $20, what is the greatest possible number of donors the charity could have? | [
"60",
"64",
"66",
"68",
"69"
]
| Min fund = 20
Total = 1299
The closest multiple of 20 to 1299 is : 63
Which implies 63 people gave 20 and 1 person gave 39
Ans. B
The answer is: B | B |
mathematics | What is the area of the square with the following coordinates: (x, y), (20, 20), (20, 11), (x, 11)? | [
"49",
"64",
"75",
"81",
"96"
]
| To find the area of a square, knowing the length of one side is sufficient.
From the coordinates given, we can see that one side equals 9.
The area is 9*9 = 81.
The answer is D.
The answer is: D | D |
mathematics | 3 boys and 7 girls can complete John work in 10 days. 4 boys and 6 girls need 8 days to complete the same work . In how many days will 10 girls complete the same work? | [
"20 days",
"30 days",
"40 days",
"60 days",
"70 days"
]
| Work done by 4 boys and 6 girls in 1 day = 1/8
Work done by 3 boys and 7 girls in 1 day = 1/10
Let 1 man does m work in 1 day and 1 woman does w work in 1 day. The above equations can be written as
4m + 6w = 1/8 ---(1)
3m + 7w = 1/10 ---(2)
Solving equation (1) and (2) , we get m=11/400 and w=1/400
Amount of work 10 girls can do in John day = 10 × (1/400) = 1/40
Ie, 10 girls can complete the work in 40 days
C
The answer is: C | C |
mathematics | A group consists of 4 men, 6 women and 5 children. In how many ways can 3 men, 2 women and 3 children selected from the given group? | [
"987 ways",
"346 ways",
"600 ways",
"157 ways",
"134 ways"
]
| The number of ways of selecting three men, two women and three children is:
= ⁴C₃ * ⁶C₂ * ⁵C₃
= (4 * 3 * 2)/(3 * 2 * 1) * (6 * 5)/(2 * 1) * (5 * 4 * 3)/(3 * 2 * 1)
= 4 * 15 * 10
= 600 ways.
Answer: C
The answer is: C | C |
mathematics | I have a few sweets to be distributed. If I keep 2, 3 or 4 in a pack, I am left with one sweet. If I keep 5 in a pack, I am left with none. What is the minimum number of sweets I have to pack and distribute ? | [
"5",
"7",
"23",
"4",
"2"
]
| Clearly, the required number would be such that it leaves a remainder of 1 when divided by 2, 3 or 4 and no remainder when divided by 5.
Answer: A
The answer is: A | A |
mathematics | If the average (arithmetic mean) of 2a+16, 3a-8 is 94, what is the value of a? | [
"25",
"30",
"28",
"36",
"42"
]
| AM of 2a+16, 3a-8=2a+16+ 3a-8 /2= 5a+8/2
Given that 5a+8 /2 = 94
a= 36
Answer is D
The answer is: D | D |
mathematics | A straight pipe 1 meter 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 meter? | [
"1/6 and 1/4 only",
"1/4 and 1/3 only",
"1/12, 1/6 and 1/4",
"1/6, 1/4, and 1/3",
"1/12, 1/6, and 1/3"
]
| Generally fast way to solve such problem is writing the different marks in ascending/descending order with same denominator:
Here 4th : 0/4, 1/4, 2/4, 3/4, 4/4
and 3rd : 0/3, 1/3, 2/3, 3/3
Now with understood common denominator 12 write the numbers : for 4th : 0,3,6,9,12 and for 3rd : 0,4,8,12
Now comine : 0,3,4,6,8,9,12
Now find the cut with denominator 12 (Substracrt adjacent terms : 3/12, 1/12, 2/12, 1/12,3/12 i.e. 1/4, 1/12 and 1/6 after removing duplicates.
Answer - C
The answer is: C | C |
mathematics | Using all the letters of the word "THURSDAY", how many different words can be formed? | [
"7",
"8!",
"7",
"5",
"2"
]
| Total number of letters
= 8
Using these letters the number of 8 letters words formed is ⁸P₈
= 8!.
Answer: B
The answer is: B | B |
mathematics | If m and n are nonzero integers and 390m = 150n, then mn must be divisible by | [
"10",
"45",
"50",
"65",
"75"
]
| 390m = 150n;
m/n = 5/13.
m is a multiple of 5 and n is a multiple of 13, therefore mn must be a multiple of 5*13 = 65.
Answer: D.
The answer is: D | D |
mathematics | A certain hall contains two cuckoo clocks. If the first clock chirps 20 times per hour and the second clock chirps 8 times per hour, and both clocks chirp for the first time at 2:03 pm, at what time will the first clock have chirped three times as many times as the second clock can chirp per hour? | [
"2:40 pm",
"2:55 pm",
"3:12 pm",
"3:24 pm",
"3:45 pm"
]
| The question is asking when the first clock will have chirped 24 times (3*8 chirps).
The first clock chirps once every 3 minutes.
If the first chirp is at 2:03, then the 24th chirp is at 72 minutes after 2:00.
The answer is C.
The answer is: C | C |
mathematics | A boat having a length 5 m and breadth 2 m is floating on a lake. The boat sinks by 1cm when a man gets on it. The mass of the man is: | [
"100 kg",
"60 kg",
"72 kg",
"96 kg",
"None of these"
]
| Explanation:
Volume of water displaced = (5 x 2 x 0.01) m3
= 0.10 m3.
∴ Mass of man = Volume of Water displaced x Density of water
= (0.10 x 1000)kg
= 100 kg.
Answer: A
The answer is: A | A |
mathematics | Two trains of equal are running on parallel lines in the same direction at 46 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is? | [
"50",
"88",
"77",
"66",
"45"
]
| Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 46 - 36 = 10 km/hr.
= 10 * 5/18 = 25/9 m/sec.
2x/36 = 25/9 => x = 50.
Answer: A
The answer is: A | A |
mathematics | Can you please walk me through how to best approach this problem? Thanks
If #p# = ap^3+ bp – 1 where a and b are constants, and #-2# = 2, what is the value of #2#? | [
"5",
"0",
"-4",
"-3",
"-5"
]
| #p# = ap^3 + bp - 1
#-2# = 2
putting p = -2 in above equation
-8a -(2b +1) = 2 or
#-2# = (8a+2b+1) = -2
therefore 8a+2b = -3 .....(1
now putting p =2
#2# = 8 a+2b - 1
using equation 1(8a+2b = -3)
#5# = -3-1 = -4
hence C
The answer is: C | C |
mathematics | A merchant marks his goods up by 30% and then offers a discount of 20% on the marked price. What % profit does the merchant make after the discount? | [
"8%",
"10%",
"21%",
"15%",
"4%"
]
| Let the price be 100.
The price becomes 130 after a 30% markup.
Now a discount of 20% on 130.
Profit=104-100
4%
answer E
The answer is: E | E |
mathematics | f (x + y)/(2x + y) = 4/5, then find (2x + y)/(3x + y) ? | [
"5/9",
"5/6",
"5/7",
"5/4",
"5/1"
]
| (x + y)/(2x + y) = 4/5
=> 5x + 5y = 8x + 4y => y = 3x
Now, (2x + y)/(3x + y) = 5x/6x = 5/6.
Answer: B
The answer is: B | B |
mathematics | Jane biked 21 2/3 miles in 3 hours and 20 minutes. What was her average rate of speed in miles per hour? | [
"6 1/2",
"7",
"7 1/2",
"7 3/4",
"8"
]
| D = 21(2/3) = 65/3
T = 3(1/3) = 10/3
S = D/T = 6 1/2
Answer = A
The answer is: A | A |
mathematics | A researcher computed the mean, the median, and the standard deviation for a set of performance scores. If7 were to be added to each score, which of these three statistics would change? | [
"The mean only",
"The median only",
"The standard deviation only",
"The mean and the standard deviation",
"The mean and the median"
]
| The correct answer is E.
The answer is: E | E |
mathematics | A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current? | [
"1.9",
"1.5",
"2.8",
"3.0",
"3.9"
]
| 72 --- 9 DS = 8
? ---- 1
45 ---- 9 US = 5
? ---- 1 S = ?
S = (8 - 5)/2 = 1.5
Answer: B
The answer is: B | B |
mathematics | Compare the rates of two trains, one travelling at 45 km/hr and other is at 10m/s? | [
"5:4",
"3:2",
"1:5",
"2:7",
"3:5"
]
| speed of the 1st train = 45km/hr
speed of the 2nd train = 10m/s = 10*18/5 = 36km/hr
ratio of the speeds of the train = 45:36 = 5:4
Answer is A
The answer is: A | A |
mathematics | A vendor bought toffees at 6 for a rupee. How many for a rupee must he sell to gain 20%? | [
"3",
"4",
"5",
"6",
"7"
]
| C.P. of 6 toffees = Rs. 1
S.P. of 6 toffees = 120% of Rs. 1 = Rs 6/5
For Rs. 6/5 Toffees Sold 6
For Rs. 1, toffees sold = 6x (5/6)= 5
answer :C
The answer is: C | C |
mathematics | Three numbers which are co-prime to each other are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is? | [
"33",
"76",
"85",
"22",
"99"
]
| Since the numbers are co-prime, they contain only 1 as the common factor.
Also, the given two products have the middle number in common.
So, middle number = H.C.F of 551 and 1073 = 29;
First number = 551/29 = 19
Third number = 1073/29 = 37.
Required sum = 19 + 29 + 37 = 85.
Answer:C
The answer is: C | C |
mathematics | Last year Manfred received 26 paychecks. Each of his first 6 paychecks was $750; each of his remaining paychecks was $40 more than each of his first 6 paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his pay checks for the year? | [
"$781",
"$755",
"$765",
"$773",
"$775"
]
| = (750*6+ 790 *20)/26
= 781
Answer is A.
Posted from my mobile device
The answer is: A | A |
mathematics | What will be the day of the week 15th August, 2010? | [
"Sunday",
"Monday",
"Tuesday",
"Thursday",
"Friday"
]
| 15th August, 2010 = (2009 years + Period 1.1.2010 to 15.8.2010)
Odd days in 1600 years = 0
Odd days in 400 years = 0
9 years = (2 leap years + 7 ordinary years) = (2 x 2 + 7 x 1) = 11 odd days 4 odd days.
Jan. Feb. March April May June July Aug.
(31 + 28 + 31 + 30 + 31 + 30 + 31 + 15) = 227 days
227 days = (32 weeks + 3 days) 3 odd days.
Total number of odd days = (0 + 0 + 4 + 3) = 7 0 odd days.
Given day is Sunday.
Answer: Option A
The answer is: A | A |
mathematics | 40% of Ram's marks is equal to 20% of Rahim's marks which percent is equal to 30% of Robert's marks. If Robert's marks is 80, then find the average marks of Ram and Rahim? | [
"76",
"56",
"56",
"90",
"15"
]
| Given, 40% of Ram's marks = 20% of Rahim's marks = 30% of Robert's marks.
Given, marks of Robert = 80
30% of 80 = 30/100 * 8 = 24
Given, 40% of Ram's marks = 24.
=> Ram's marks = (24 * 100)/40 = 60
Also, 20% of Rahim's marks
= 24
=> Rahim's marks
= (24 * 100)/20 = 120
Average marks of Ram and Rahim
= (60 + 120)/2 = 90.
Answer: D
The answer is: D | D |
mathematics | A bag contains 23 purple jellybeans, 12 green jellybeans, and 15 yellow jellybeans; these jellybeans are the only items in the bag. If a person picks a jellybean at random out of the bag, what is the probability that the jellybean will be purple? | [
"15%",
"20%",
"25%",
"30%",
"46%"
]
| p = 23 , g=12 , y=15
total = 50
p(purple)=(23/50)*100 = 46% . Ans = E
The answer is: E | E |
mathematics | A larger hose connected to a swimming pool can fill the pool in 6 hours. A smaller hose can fill the pool in 12 hours. How many hours will it take for both of them to fill the pool? | [
"3",
"7 1/2",
"5 3/5",
"8",
"4"
]
| Work hrs=AB/(A+B)= 72/18 =4
Answer is E
The answer is: E | E |
mathematics | A can do a piece of work in 20 days and B can do it in 30 days and C can do it 10 days. They started the work together and A leaves after 2 days and C leaves after 4 days from the beginning. How long will work lost? | [
"13",
"16",
"25",
"14",
"15"
]
| 2/20 + x/30 + 4/10 = 1
x = 300/20= 15
Answer: E
The answer is: E | E |
mathematics | A strain of bacteria reproduces @ 25% every 12 min. In how much time will it triple itself ?? | [
"96 min",
"72 min",
"60 min",
"48 min",
"40 min"
]
| The original question is:
A strain of bacteria reproduces at the rate of 25% every 12 min. In how much time will it triple itself ?
1.25^x = 3 --> x = ~5 --> five 12 minute periods = 60 minutes.
Answer: C.
The answer is: C | C |
mathematics | The sum of three consecutive odd numbers is always divisible by:
I. 2 II. 3 III. 5 IV. 6 | [
"Only I",
"Only II",
"Only I and II",
"Only II and IV",
"None of these"
]
| Let the three consecutive odd numbers be (2x+1), (2x+3) and (2x+5). Their sum = (6x=9)= 3 (2x+3), which is always divisible by 3.
Answer: B
The answer is: B | B |
mathematics | What is the prime factors’ number of 12? | [
"2",
"3",
"4",
"5",
"6"
]
| prime factors’ number, as I assume, for a number X=a^n*b^m*c^o*d^p... is = n+m+o+p...
So, 24 = 2^2*3^1
prime factors’ number will be 2+1 = 3.
Hence, answer is B.
The answer is: B | B |
mathematics | If a and n are integers, and a^2 = 24n, then n must be divisible by which of the following? | [
"2",
"4",
"12",
"18",
"24"
]
| a^2=24n
a^2=2^2∗6n
Least value of n to make "a" a perfect square is 6
Answer = A = 2
The answer is: A | A |
mathematics | Last year Jackie saved 5% of her annual salary. This year, she made 10% more money than last year, and she saved 8% of her salary. The amount saved this year was what percent of the amount she saved last year? | [
"56%",
"76%",
"158%",
"176%",
"188%"
]
| Assuming Annual salary of last year = 100
5 % Salary Saving (last year) would give = (5/100) * 100 = 5
she made 10% more money than last year = 110 (This year Salary)
8 % Salary saving this year = (8/100) * 110 = 88/10 = 8.8
(Amount saved this year/Amount saved last year) * 100= (8.8/5) * 100 = 8.8 * 20 = 176 %
ANSWER:D
The answer is: D | D |
mathematics | What approximate value should come in place of the question mark (?) in the following equation?
159% of 6531.8 + 5.5 × 1015.2 = ? + 5964.9 | [
"10,000",
"10,900",
"11,000",
"10,600",
"12,000"
]
| ? ≈ 160% of 6530 + 5.5 × 1010 – 5965
≈ 10448 + 5555 – 5965 ≈ 10,000
Answer A
The answer is: A | A |
mathematics | Find the sum of prime numbers lying between 58 and 75? | [
"198",
"331",
"252",
"272",
"None"
]
| Solution
Required sum =59 + 61 + 67 + 71 + 73)
= 331.
Answer B
The answer is: B | B |
mathematics | A and B invested Rs.15000 and Rs.20,000 respectively in a business. How should a loss of Rs.2800 be divided between them at the end of year? (in rupees) | [
"1500,1300",
"1200,1600",
"1300,1500",
"1600,1200",
"1700,1200"
]
| Ratio btwn invest is == 3:4
loss==2800
so 2800/7==400
A==3*400==1200
B==4*400==1600
ANSWER:B
The answer is: B | B |
mathematics | How many minutes does it take John to type z words if he types at the rate of x words per minute? | [
"x/y",
"z/x",
"xy",
"60x/y",
"y/(60x)"
]
| time*rate=job --> time*x=z --> time=z/x.
Answer: B.
The answer is: B | B |
mathematics | A man purchased a fan and a tv for Rs. 5000 &Rs. 10000 respectively. He sold the fan at a loss of 6% and the tv at a profit of 12%. Overall how much he make a profit. | [
"100",
"300",
"900",
"600",
"400"
]
| Let the SP of the fan and the tv be Rs. r and Rs. m respectively.
r = 5000(1 - 6/100) = 5000 - 300
m = 10000(1 + 12/100) = 10000 + 1200
Total SP - Total CP = r + m - (15000 + 8000) = -300 + 1200 = Rs. 900
As this is positive, an overall profit of Rs. 900 was made.
C
The answer is: C | C |
mathematics | In a bag containing 3balls, a white ball was placed & then 1ball was taken out atrandom. What is the probability that the extracted ball would turn on to be white, if all possible hypothesis concerning the color of theballs that initiallyin the bag were equally possible ? | [
"3",
"5/8",
"27",
"54",
"81"
]
| Since, all possible hypothesis regarding the colour of the balls are equally likely, therefore these could be 3 white balls, initially in the bag.
∴ Required probability = 1/4 [1 + 3/4 + 1/2 + 1/4]
= 1/4 [(4 + 3 + 2 + 1)/4] = 5/8
B
The answer is: B | B |
mathematics | The average age of seven persons sitting in a row facing east is 28 years. If the average age of the first three persons is 25 years and the average age of the last three persons is 32 years, then find the age of the person sitting in the middle of the row? | [
"9 years",
"29 years",
"25 years",
"19 years",
"17 years"
]
| Total age seven persons = (28 * 7)years
Total age of the first three persons and the last three persons are (25 * 3) years and (32 * 3) years respectively.
Age of the person sitting in the middle of the row = 28 * 7 - 25 * 3 - 32 * 3 = 196 - 75 - 96 = 25 years.
ANSWER:C
The answer is: C | C |
mathematics | A windmill is taking advantage of strong air currents in order to produce electrical energy. On a typical day the wind speed is around 20 mph and in that speed the windmill produces 900 kw/h (kilowatts per hour). On a stormy day a windmill produces 20% more energy. How much kw/h can three windmills produce in two hours on a stormy day? | [
"2880.",
"4860.",
"5780.",
"5760.",
"6480."
]
| Efficiency per machine = 900 watt/hr
Efficiency due to increase in wind speed = 900*120% => 1080 watt/hr
Production by each machine in 2 hours is 1080*2 => 2160 watt
Production by 3 machines => 2160 watt * 3 = 6480 watt
Answer will be (E)
The answer is: E | E |
mathematics | If a and b are different positive integers and a + b+1 = a(a + b), then which of the following must be true?
I. a = 1
II. b = 1
III. a < b | [
"I only",
"II only",
"III only",
"I and II",
"I and III"
]
| Number picking might not be the best way to solve MUST BE TRUE questions.
The question asks which of the followingMUSTbe true, or which of the following isALWAYStrue no matter what set of numbers you choose. For such kind of questionsif you can prove that a statement is NOT truefor one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.
So the set you chose just proves that II is not always true and hence it's not a part of a correct choice. As for I and III: they might be true for this particular set of numbers but not true for another set, so you can not say that I and III are always true just based on one set of numbers (it just happens to be that I and III are always true).
As forCOULD BE TRUEquestions:
The questions asking which of the followingCOULDbe true are different:if you can prove that a statement is truefor one particular set of numbers, it will mean that this statement could be true and hence is a correct answer.
D
The answer is: D | D |
mathematics | The length of the rectangular field is double its width. Inside the field there is square shaped pond 4m long. If the area of the pond is 1/8 of the area of the field. What is the length of the field? | [
"54",
"32",
"75",
"28",
"16"
]
| A/8 = 4 * 4 => A = 4 * 4 * 8
x * 2x = 4 * 4 * 8
x = 8 => 2x = 16
Answer:E
The answer is: E | E |
mathematics | The overall age of X and Y is 18 year greater than the overall age of Y and Z. Z is how many decades younger that X? | [
"11",
"15",
"12",
"17",
"18"
]
| E
18
(X + Y) – (Y + Z) = 18
X – Z = 18
The answer is: E | E |
mathematics | In how many different number of ways 4 boys and 3 girls can sit on a bench such that girls always sit together. | [
"720",
"740",
"760",
"790",
"800"
]
| 720
Option 'A'
The answer is: A | A |
mathematics | Sam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit? | [
"3.5",
"4.5",
"5.6",
"6.5",
"None"
]
| Solution
C.P of 1 toy = Rs.(375/12)
= Rs.31.25
S.P of 1 toy = Rs.33.
Therefore,Profit = (1.75/31.25×100)%
=(28/5)%
=5.6%.
Answer C
The answer is: C | C |
mathematics | Q' = 3Q - 3, what is the value of (7')' ? | [
"6",
"106",
"206",
"306",
"406"
]
| (7')'=(3*7-3)'=18'=18*18-18=306
Answer D
The answer is: D | D |
mathematics | A, B and C started a shop by investing Rs. 10,000, Rs. 10,000 and Rs. 20,000 respectively. At the end of the year, the profits were distributed among them. If C’s share of profit be Rs. 4,000, then the total profit was : | [
"30,000",
"60,000",
"8,000",
"120,000",
"None"
]
| Sol.
A : B : C = 10000 : 10000 : 20000 = 1: 1 : 2. so, C’s share : Total Profit = 2 : 4
Let the total profit be Rs. x. Then, 2/4 = 36000/x or x
= 4000 * 4 / 2 = 8000.
Answer C
The answer is: C | C |
mathematics | 10 men and 10 women are there, they dance with each other, is there possibility that 2 men are dancing with same women and vice versa? | [
"22",
"20",
"10",
"15",
"none"
]
| it is written that 10 men and 10 women dance with each other. so there is no chance of matching more than 2 partners at a time. so 2 men & 1 women is not possible.
ANSWER:E
The answer is: E | E |
mathematics | What is 35% of 4/13 of 585? | [
"52",
"63",
"74",
"85",
"96"
]
| This problem can be solved easily if we just use approximation: 35% is a little over 1/3, while 4/13 is a little less than 4/12, which is 1/3. Thus, the answer is about 1/3 of 1/3 of 585, or 1/9 of 585. Since the first 1/3 is a slight underestimate and the second 1/3 is a slight overestimate, the errors will partially cancel each other out. Our estimate will be relatively accurate.
The number 585 is between 540 and 630, so (1/9)*585 will be about 65.
Keeping track not only of your current estimate, but also of the degree to which you have overestimated or underestimated , can help you pinpoint the correct answer more confidently.
The closest answer is 63, so this is the answer to choose.
The answer is B.
The answer is: B | B |
mathematics | How many ways are there to award a gold, silver and bronze medal to 6 contending teams? | [
"10 × 9 × 8",
"10!/(3!7!)",
"6!/3!",
"564",
"6 * 5 * 4"
]
| we clearly know that there can be only one winning team which deserves the gold medal. we can do the selection in 10 ways
if gold medal is given to 1 of the teams then only possible 5 teams can be considered for silver medal. we can do selection in 5 ways
similarly if gold and silver medals are awarded then only remaining 4 teams can be considered for a bronze medal. we can do the selection in 4 ways
Total number of ways to select the 3 possible medal winners = 6 * 5 * 4
Correct answer - E
The answer is: E | E |
mathematics | 20/25 = 4/5 . which method did you use to determine whether this proportion is true or false? | [
"true",
"neutral",
"false",
"not sure",
"none"
]
| 20/25= 4/5 cross multiplication: 20 * 5= 100, 4 * 25 =100,
we see that 100 are not equal to 100. so there is proportion. corrcet answer: (A)
The answer is: A | A |
mathematics | A car gets 40 kilometers per gallon of gasoline. How many gallons of gasoline would the car need to travel 120 kilometers? | [
"4.5",
"5.5",
"6.5",
"3",
"8.5"
]
| Each 40 kilometers, 1 gallon is needed. We need to know how many 40 kilometers are there in 120 kilometers?
120 ÷ 40 = 3 × 1 gallon = 3 gallons
correct answer D
The answer is: D | D |
mathematics | If (x - 1)^2 = 324, which of the following could be the value of x - 4? | [
"16",
"14",
"-19",
"-21",
"-23"
]
| (x - 1)^2 = 324
(x - 1) = 18 or -18
x = 19 or -17
x - 4 = 15 or -21
The answer is D.
The answer is: D | D |
mathematics | The two lines y=x and x=-8 intersect on the coordinate plane. What is the value of the area of the figure formed by the intersecting lines and the x-axis? | [
"28",
"32",
"36",
"40",
"44"
]
| The point of intersection is (-8,-8).
The triangle has a base of length 8 and a height of 8.
area = (1/2)*base*height = (1/2)*8*8 = 32
The answer is B.
The answer is: B | B |
mathematics | If 9 men and 2 boys working together, can do eight times as much work per hour as a man and a boy together. Find the ratio of the work done by a man and that of a boy for a given time? | [
"2:5",
"1:3",
"5:8",
"6:1",
"7:2"
]
| 9M + 2B =8(1M + 1B)
9M + 2B = 8M + 8B
1M = 6B
The required ratio of work done by a man and a boy =6:1
Answer:D
The answer is: D | D |
mathematics | Working simultaneously at their respective constant rates, Machines A and B produce 800 nails in x hours. Working alone at its constant rate, Machine A produces 800 nails in t hours. In terms of x and t, how many hours does it take Machine B, working alone at its constant rate, to produce 800 nails? | [
"x/(x+y)",
"y/(x+y)",
"xy/(x+y)",
"xy/(x-y)",
"xt/(t-x)"
]
| Pick some smart numbers for x and t.
Say x=1 hour and t=2 hours (notice that t must be greater than x, since the time for machine A to do the job, which is t hours, must be more than the time for machines A and B working together to do the same job, which is x hours).
In this case, the time needed for machine B to do the job must also be 2 hours: 1/2+1/2=1.
Now, plug x=1 and t=2 in the options to see which one yields 2. Only option E fits.
Answer: E.
The answer is: E | E |
mathematics | Weights of two friends Ram and Shyam are in the ratio 1:5. If Ram's weight is increased by 10% and total weight of Ram and Shyam become 82.8 kg, with an increases of 15%. By what percent did the weight of Shyam has to be increased? | [
"19%",
"10%",
"21%",
"16%",
"None"
]
| Solution:
given ratio of Ram and Shayam's weight = 1:5
Hence, (x-15)/(15-10) = 1/5
Or, x = 16%.
Answer: Option D
The answer is: D | D |
mathematics | nine children — A, B, C, D, E, F, and G — are going to sit in seven chairs in a row. Children AB must sit next to each other, and child C must be somewhere to the right of AB. How many possible configurations are there for the children? | [
"600",
"720",
"1440",
"1650",
"4800"
]
| A, B, C, D, E, F, G- seven children, of which AB must sit next to each other. Considering them as one X (A, B), we have X, C, D, E, F, G. These can be arranged in 6! ways. But A,B can arrange themselves in 2! ways. So a total of 6!*2! ways = 1440. Since in exactly half of them, C will be to the right of AB, and exactly half, C will be to the left of AB, therefore 1440/2 = 1650
D is the right answer.
The answer is: D | D |
mathematics | What is the least number which should be added to 2782 so that the sum is exactly divisible by 5, 6, 4, and 3? | [
"26",
"32",
"38",
"46",
"52"
]
| L.C.M. of 5, 6, 4 and 3 = 60.
When dividing 2782 by 60, the remainder is 22.
The number to be added = 60 - 22 = 38.
The answer is C.
The answer is: C | C |
mathematics | If Jan spent 40% of her monthly income on housing and 20% less than she spent on housing on a car payment, what percent of her monthly income did she have left after making both her housing payment and her car payment? | [
"20%",
"28%",
"42%",
"50%",
"60%"
]
| Lets say the total income of Jan is 100
Then
She spends 40 on Housing
20% less than she spent on Housing = 40−20/100∗40=3240−20/100∗40=32
Total expenditure = 40 + 32 = 72
Remaining = 100 - 72 = 28
Hence the answer is B 28 %
The answer is: B | B |
mathematics | In a colony of 70 residents, the ratio of the number of men and women is 4 : 3. Among the women, the ratio of the educated to the uneducated is 1 : 4. If the ratio of the number of educated to uneducated persons is 8 : 27, then find the ratio of the number of educated to uneducated men in the colony? | [
"1:6",
"1:1",
"1:8",
"1:9",
"1:3"
]
| Number of men in the colony = 4/7 * 70 = 40.
Number of women in the colony = 3/7 * 70 = 40.
Number educated women in the colony = 1/5 * 30 = 6.
Number of uneducated women in the colony = 4/5 * 50 = 24.
Number of educated persons in the colony = 8 /35 * 70 = 16.
As 6 females are educated, remaining 10 educated persons must be men.
Number of uneducated men in the colony = 40 - 10 = 30.
Number of educated men and uneducated men are in the ratio 10 : 30 i.e., 1:3.
Answer:E
The answer is: E | E |
mathematics | In how many different ways can the letters of the word 'SENDING' be arranged in such a way that the vowels always come together? | [
"A)360",
"B)480",
"C)720",
"D)5040",
"of these"
]
| The word 'SENDING' has 7 different letters.
When the vowels EI are always together, they can be supposed to form one letter.
Then, we have to arrange the letters SNDNG (EI).
Now, 6 (5 + 1 = 6) letters can be arranged in 6! = 720 ways.
The vowels (EI) can be arranged among themselves in 2! = 2 ways.
Required number of ways = (720 x 2) = 1440.
ANSWER:B
The answer is: B | B |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.