subject stringclasses 1
value | question stringlengths 3 1.14k | options listlengths 5 5 | solution stringlengths 18 3.7k | answer stringclasses 5
values |
|---|---|---|---|---|
mathematics | The average of five numbers id 27. If one number is excluded, the average becomes 25. The excluded number is | [
"25",
"27",
"30",
"35",
"None"
] | Solution
Excluded number = (27 x 5 ) - ( 25 x 4)
= 135 - 100
= 35.
Answer D
The answer is: D | D |
mathematics | 4 male and 6 female can cultivate a field in 8 days, 7 male and 3 female can cultivate a field in 10 days. then how many days will take to cultivate a field if 10 female works? | [
"120/19",
"130/19",
"140/19",
"120/18",
"120/17"
] | 4 male+6female in 8 days=> 32 male+48 female in 1day
7male+ 3 female in 10 days =>70 male+30 female in 1 day
.:32 male+48 female=70 male+30 female
18 female=38 male
1 female= 38/18 male=19/9 male
now,4 male+6 female=4 male+6*(19/9)=50/3 male=150/9 male
we have to find for 10 female workers= 10*(19/9)=190/9 male
more me... | A |
mathematics | What is the probability of rolling a nine with two, fair, six-sided dice? | [
"1/6",
"1/9",
"2/13",
"1/12",
"5/36"
] | There are 4 ways to roll a nine: 3 and 6, 6 and 3, 4 and 5, 5 and 4 with two six-sided dice. There are 6 times 6 = 36 ways to roll two dice. The probability of rolling a 9 is thus 4/36 = 1/9. B
The answer is: B | B |
mathematics | If a is a positive integer and 10^a – 74 in decimal notation has digits whose sum is 440, what is the value of a? | [
"40",
"44",
"45",
"46",
"50"
] | Answer E = 50
We have (10^a)-74, where the sum of the digits is 440.
100-74 = 26, so we already have 2+6 = 8 from the 440.
Because we have a power of 10, we will have numbers like 100, 1000, 10000 and so on. This minus 74 rests 26 and a lot of 9s. E.g: 1000-74 = 9926.
So dividing the 432/9 = 48, that`s the number of 9s... | E |
mathematics | A cube is painted red on all faces. It is then cut into 27 equal smaller cubes. How many P cubes are painted on only 2 faces? | [
"12",
"8",
"6",
"10",
"16"
] | 1) Draw a simple cube
2) Draw 9 squares on each face of the cube (so that it looks like a Rubik's Cube) - this is what the cube will look like when it's cut into 27 equal smaller cubes.
3) Remember that the OUTSIDE of the cube is the part that's painted....
The mini-cubes with 2 painted sides are ALL on the edge of the... | A |
mathematics | If x represents the sum of all the positive three-digit numbers that can be constructed using each of the distinct nonzero digits a, b, and c exactly once, what is the largest integer by which x must be divisible? | [
"3",
"6",
"11",
"22",
"222"
] | Maybe there is a faster way to do it but I did it like this:
How many ways can you arrange abc?
abc
acb
bac
bca
cab
cba
which are equivalent to:
100a + 10b + c
100a + 10c + b
100b + 10a + c
100b + 10c + a
100c + 10a + b
100c + 10b + a
if you add them all together you get 222a + 222b + 222c
ANSWER:E
The answer is: E | E |
mathematics | A shopkeeper sold an article for Rs 2524.36. Approximately what was his profit percent if the cost price of the article was Rs 2400 | [
"4%",
"5%",
"6%",
"7%",
"8%"
] | Explanation:
Gain % = (125.36*100/2400) = 5.2 % = 5% approx
Option B
The answer is: B | B |
mathematics | The speed of a car increases by 2 kms after every one hour. If the distance travelling in the first one hour was 45 kms. what was the total distance traveled in 12 hours? | [
"252 kms",
"152 kms",
"672 kms",
"752 kms",
"152 kms"
] | Explanation:
Total distance travelled in 12 hours =(45+47+49+.....upto 12 terms)
This is an A.P with first term, a=45, number of terms,
n= 12,d=2.
Required distance = 12/2[2 x 45+{12-1) x 2]
=6(112)
= 672 kms.
Answer: C
The answer is: C | C |
mathematics | A man purchased 3 blankets @ Rs.100 each, 5 blankets @ Rs.150 each and two blankets at a certain rate which is now slipped off from his memory. But he remembers that the average price of the blankets was Rs.150. Find the unknown rate of two blankets? | [
"300",
"350",
"450",
"470",
"500"
] | Explanation:
10 * 150 = 1500
3 * 100 + 5 * 150 = 1050
1500 – 1050 = 450
C
The answer is: C | C |
mathematics | What percentage loss will a merchant incur if he marks his goods up by x% over his cost price and then offers a discount of x% on his selling price? | [
"0 %",
"2x/100 %",
"x^2/100 %",
"x %",
"2x %"
] | Answer is C.
Taking smart numbers:
Let, C.P = 100$ and X = 20% over C.P
then Mark Up = 120$
After discount of X%
S.P= 80% of 120
S.P = 96$
Therefore Loss is 4$ and hence Loss in % = 4%
Plugging numbers in options.
A. 0 % ---------------------------Not truebecause loss is 4%
B. 2x/100 % --------------------2*20/100 = 0.... | C |
mathematics | P and Q started a business investing Rs 10000 and Rs 15000 resp. In what ratio the profit earned after 2 years be divided between P and Q respectively. | [
"2:7",
"2:6",
"17:6",
"2:3",
"7:8"
] | Explanation:
In this type of question as time frame for both investors is equal then just get the ratio of their investments.
P:Q = 10000:15000
= 10:15
= 2:3
Option D
The answer is: D | D |
mathematics | A train 140 m long passes a man,running at 6 kmph in the direction opposite to that of the train,in 6 seconds.The speed of the train is | [
"54 kmph",
"60 kmph",
"66 kmph",
"72 kmph",
"78 kmph"
] | speed of train relative to man: 140/6 * 18/5 km/hr
= 84 km/hr
let speed of train= x
therefore x+6 = 84
x= 84-6
x=78 km/hr
ANSWER:E
The answer is: E | E |
mathematics | The average of a group of men is increased by 5 years when a person aged of 18 years is replaced by a new person of aged 38 years. How many men are there in the group? | [
"3",
"4",
"5",
"6",
"7"
] | Solution: Let N be the no. of persons in the group.
Required number of person is given by;
Member in group* aged increased = difference of replacement
N*5 = 38-18
Or, 5N = 20
Or, N = 4.
Answer: Option B
The answer is: B | B |
mathematics | A bag contains 3 blue and 5 white marbles. One by one, marbles are drawn out randomly until only two are left in the bag. What is the probability Z that out of the two, one is white and one is blue? | [
"15/56",
"41/56",
"13/28",
"15/28",
"5/14"
] | The required probability Z= probability of choosing 6 balls out of the total 8 in such a way that we remove 4 out of 5 white and 2 out of 3 blue balls.
Ways to select 6 out of total 8 = 8C6
Ways to select 4 out of 5 white balls = 5C4
Ways to select 2 out of 3 blue balls = 3C2
Thus the required probability = (5C4*3C2)/8... | D |
mathematics | If 4x + 3y = 8 and y-3x = 8, then what is the value of x + 4y? | [
"1/7",
"16",
"15",
"52/7",
"60/7"
] | 4x+3y=8 ...equation 1
-3x+y=8 ...equation 2
adding both the equations
x+4y=16
correct answer option B
The answer is: B | B |
mathematics | AMOUNT OF BACTERIA PRESENT
Time Amount
1:00 P.M. 14.0 grams
4:00 P.M. x grams
7:00 P.M. 18.4 grams
Data for a certain biology experiment are given in the table above. If the amount of bacteria present increased by the same fraction during each of the two 3-hour periods shown, how many grams of bacteria were present at ... | [
"14.0",
"16.1",
"16.0",
"12.3",
"12.4"
] | The question says that bacteria increased by same fraction, not by same amount in 2 intervals of 3 hours.
Let X represent the amount of bacteria present at 4:00 PM. Since the fractional increase must remain constant from 1 to 4pm as it is from 4pm to 7pm:
Fractional increase from 1 PM to 4 PM = X / 14.0
Fractional incr... | C |
mathematics | Statement : A large majority of the work force in India is unorganised. Most of them earn either the minimum or uncertain wages while others are engaged in sundry jobs.
Conclusions :
I. The workers in the organised sector get better facilities and stay longer in their jobs.
II. Some workers in the unorganised sector of... | [
"Only conclusion I follows",
"Only conclusion II follows",
"Either I or II follows",
"Neither I nor II follows",
"Both I and II follow"
] | Explanation:
Conclusion I is not stated in the statement.
Only Conclusion II follows.
Option B
The answer is: B | B |
mathematics | A girl scout was selling boxes of cookies. In a month, she sold both boxes of chocolate chip cookies ($1.25 each) and boxes of plain cookies ($0.75 each). Altogether, she sold 1,585 boxes for a combined value of $1,587.75. How many boxes of plain cookies did she sell? | [
"0",
"233",
"500",
"695",
"787"
] | Let #plain cookies sold be X then #chocolate cookies = (total cookies-X)
Equating for X
(0.75)*X +(1.25)*(1585-X)=1587.75
=>x=787
E
The answer is: E | E |
mathematics | Find the area of the quadrilateral of one of its diagonals is 20 cm and its off sets 9 cm and 6 cm? | [
"128",
"150",
"882",
"272",
"121"
] | 1/2 * 20(9 + 6) = 150 cm2
Answer: B
The answer is: B | B |
mathematics | Sum of 3 consecutive even no.'s is 26 more than the 1st no. of the series. Find the middle no.? | [
"10",
"12",
"14",
"17",
"18"
] | Let the numbers be x, x+2 and x+4 then
x + x+2 + x+4 = x+26
3x + 6 = x + 26
2x = 20
\inline \therefore x = 10
\inline \therefore Middle number = x + 2 = 10+2 = 12
B
The answer is: B | B |
mathematics | In a certain region, the number of children who have been vaccinated against rubella is twice the number who have been vaccinated against mumps. The number who have been vaccinated against both is twice the number who have been vaccinated only against mumps. If 4,000 have been vaccinated against both, how many have bee... | [
"2,5000",
"8,000",
"10,000",
"15,000",
"17,500"
] | Use a single variable as far as possible.
Number vaccinated only against mumps = x
Number vaccinated against both = 2x = 4000 (so x = 2000)
Then, number vaccinated against mumps (including both) = x + 2x = 3x
Number vaccinated against rubella = 2*3x = 6x
Then, number vaccinated against only rubella = 6x - 2x = 4x = 4*2... | B |
mathematics | A guy was asked to specify his age in years. He said, “Take my age 4 years hence, multiply it by four and subtract four times of my age 4 years ago and you will know my age.” What was the age of that guy? | [
"18",
"15",
"13",
"32",
"40"
] | Current age of the guy = A years.
Then, 4 (A + 4) – 4 (A – 4) = A
(4A + 16) – (4A – 16) = A
A = 32
D
The answer is: D | D |
mathematics | Half the people on a bus get off at each stop after the first, and no one gets on after the first stop. If only one person gets off at stop number 3, how many people got on at the first stop? | [
"128",
"64",
"32",
"16",
"8"
] | Before stop 3, there were 2 passengers on the bus.
Before stop 2, there were 4 passengers on the bus.
Before stop 1, there were 8 passengers on the bus.
The answer is E.
The answer is: E | E |
mathematics | Excluding stoppages, the average speed of a bus is 60 km/hr and including stoppages, the average speed of the bus is 40 km/hr. For how many minutes does the bus stop per hour? | [
"15 min",
"18 min",
"16 min",
"20 min",
"26 min"
] | In 1hr, the bus covers 60 km without stoppages and 40 km with stoppages.
Stoppage time = time take to travel (60 - 40) km i.e 20 km at 60 km/hr.
stoppage time = 20/60 hrs
= 20 min
Answer: D
The answer is: D | D |
mathematics | In what time will a train 100 m long cross an electric pole, it its speed be 162 km/hr? | [
"2.5",
"2.9",
"2.4",
"2.8",
"2.22"
] | Speed = 162 * 5/18 = 45 m/sec
Time taken = 100/45
= 2.22 sec.
Answer:E
The answer is: E | E |
mathematics | If f(x)=x^2 and x is a positive integer, which of the following CAN be the value of f(f(x))? | [
"25",
"17",
"81",
"144",
"258"
] | f(x)=x^2
f(f(x)) = (x^2)^2
f(f(3) = (3^2)^2 = 81
Answer C
The answer is: C | C |
mathematics | y =2x^2 +2bx + 512 cuts the x axis at (h, 0) and (k, 0). If h and k are integers, what is the least value of b? | [
"256",
"-256",
"-128",
"-64",
"-257"
] | As the curve cuts the x-axis at (h,0) and (k,0). Therefore h,k are the roots of the quadratic equation.
For the quadratic equation is in the form ofax^2+bx+c=0,
The product of the roots =c/a= 512/2=256 and the sum of the roots =-b/a=-b
256 can be expressed as product of two numbers in the following ways:
1 * 256
2 * 12... | E |
mathematics | Sushil got thrice as many marks in English as in Science. His total marks in English, Science and Maths are 162. If the ratio of his marks in English and Maths is 3:5, find his marks in Science? | [
"24",
"18",
"20",
"25",
"16"
] | S:E = 1:3
E:M = 3:5
------------
S:E:M = 3:9:15
3/27 * 162 = 18
ANSWER B
The answer is: B | B |
mathematics | During a trip on an expressway, Lon drove a total of x miles. His average speed on a certain 5-mile section of the expressway was 30 miles per hour, and his average speed for the remainder of the trip was 60 miles per hour. His travel time for the x-mile trip was what percent greater than it would have been if he had t... | [
"8.5%",
"50%",
"x/12%",
"60/x%",
"500/x%"
] | so Lon drove (x-5) miles at 60mph and 5 miles at 30mph:
(x-5)/60 + (10/60) = (X+5)/60 - current time to drive the whole distance
if the entire trip @60mph than time = x/60
so to get percent [(X+5)/60 ]/[x/60] x100
=(x+5)/x *100
=100+500/x
so increase of 500/x%[/u]=E
The answer is: E | E |
mathematics | Each month, after Jill pays for rent, utilities, food, and other necessary expenses, she has one fifth of her net monthly salary left as discretionary income. Of this discretionary income, she puts 30% into a vacation fund, 20% into savings, and spends 35% on eating out and socializing. This leaves her with $102 dollar... | [
"$3400",
"$3200",
"$6000",
"$6400",
"$9600"
] | let x be the monthly salary
15%of 1/5*x=102
x=3400
answer A
The answer is: A | A |
mathematics | In a class there are 55 pupil, out of them 10 are in debate only and 18 in singing only. Then how many in both? | [
"132",
"26",
"17",
"11",
"12"
] | Explanation:Total pupil = 55
Debate + Singing = 10 + 18 = 28
The intersection for two = 55 – 10 – 28 = 17 play both games.
Answer: C
The answer is: C | C |
mathematics | In a group of Peacocks and cows, the total number of legs are 36 more than twice the no. of heads. Find the total no.of buffaloes. | [
"10",
"19",
"12",
"16",
"18"
] | Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 36
=> 2x = 36 => x = 18
E
The answer is: E | E |
mathematics | The ratio of the volumes of two cubes is 125 : 216. What is the ratio of their total surface areas? | [
"25:36",
"12:25",
"25:46",
"18:22",
"12:24"
] | Ratio of the sides = ³√125 : ³√216
= 5 : 6
Ratio of surface areas =25:36
Answer: A
The answer is: A | A |
mathematics | 250 men work for 16 days and finish a work. How many men would do a job 3 times the previous one in 20 days? | [
"700",
"666",
"600",
"400",
"800"
] | Number of men needed to finish the required work (variation, proportion method ) =3*16*250/20 =600 Answer : C
The answer is: C | C |
mathematics | A furniture dealer purchased a desk for $120 and then set the selling price equal to the purchase price plus a markup that was 40% of the selling price. If the dealer sold the desk at the selling price, what was the amount of the dealer's gross profit from the purchase and the sale of the desk? | [
"$40",
"$60",
"$80",
"$90",
"$100"
] | Purchase price = 120
Selling price = x
120 + 0.4*x = x
0.6*x = 120
x = 200
Profit = 200 - 150 = 50
ANSWER:A
The answer is: A | A |
mathematics | In 1979 approximately 1/3 of the 32.3 million airline passengers traveling to or from the United States used Kennedy Airport. If the number of such passengers that used Miami Airport was 1/2 the number that used Kennedy Airport and 4 times the number that used Logan Airport, approximately how many millions of these pas... | [
"18.6",
"9.3",
"6.2",
"1.33",
"1.6"
] | number of
passengers using Kennedy airport = 32/3 =~10.67
Passengers using Miami airport = 10.67/2=~5.34
passengers using logan airport = 5.34/4 =~1.33
so D
The answer is: D | D |
mathematics | Exactly 12% of the reporters for a certain wire service cover local politics in Country X. If 40% of the reporters who cover politics for the wire service do not cover local politics in Country X, what percent of the reporters for the wire service do not cover politics? | [
"20%",
"42%",
"44%",
"80%",
"84%"
] | Let's assume there are 100 reporters --> 12 reporters cover local politics.
Now, as 40% of the reporters who cover all politics do not cover local politics then the rest 60% of the reporters who cover politics do cover local politics, so if there are x reporters who cover politics then 60% of them equal to 12 (# of rep... | D |
mathematics | In a division sum, the remainder is 6 and the divisor is 5 times the quotient and is obtained by adding 12 to the thrice of the remainder. The dividend is | [
"74",
"78",
"86",
"126",
"98"
] | Divisor = (6 * 3) + 12 = 30
5 * Quotient = 30
Quotient = 6.
Dividend = (Divisor * Quotient) + Remainder
Dividend = (20 * 6) + 6 = 126.
D)
The answer is: D | D |
mathematics | In a 200-mile trip, the first 50 miles were completed at 40 mph. If the average speed for the whole trip was 50 mph, what was the average speed in the last 150 miles? | [
"592/11 mph",
"594/11 mph",
"596/11 mph",
"598/11 mph",
"600/11 mph"
] | The time to complete the first 50 miles was (50 miles / 40 mph) = (5/4) hours.
The time to complete the whole trip was (200 miles / 50 mph) = (4) hours.
The time to complete the last 150 miles was (4) - (5/4) = (11/4) hours.
The average speed in the last 150 miles was (150 miles / (11/4) hours) = 600/11 mph.
The answer... | E |
mathematics | Jacob is now 13 years younger than Michael. If 9 years from now Michael will be twice as old as Jacob, how old will Jacob be in 4 years? | [
"8",
"7",
"15",
"21",
"25"
] | Jacob=x years, Michael=x+13 years
9 years from now,
2(x+9)=x+22
2x+18=x+22
x=4
x+4=8 years
Answer A
The answer is: A | A |
mathematics | In a family, the father took 1/4 of the cake and he had 3 times as much as each of the other members had. The total number of family members is | [
"3",
"7",
"10",
"12",
"15"
] | 1-1/4 = remain cake 3/4
3/4*3 = 9/4
9/4+1/4 = 10
ANSWER:C
The answer is: C | C |
mathematics | Which of the following equations has a solution in common with 2x^2 - 5x - 42? | [
"2x^2 + 8x - 42 = 0",
"x^2 - 14x + 24 = 0",
"2x^2 - 8x + 8 = 0",
"x^2 + 13x + 13 = 0",
"none of the above"
] | Given : 2x^2 - 5x - 42 => (2x + 7) (x - 6) = 0 => -7/2 and 6 are the roots..
A. 2x^2 + 8x - 42 = 0 => (2x - 6) (x + 7)
B. x^2 - 14x + 24 = 0 => (x - 6) (x - 8)
C. x^2 + 13x + 13 = 0 => (2x -7) ( x - 1)
D. x^2 + 13x + 13 = 0 => (x + 6) (x + 7)
None of the answer equations have exactly both the same roots as the question... | B |
mathematics | If x=3y=4z, what is z+y, in terms of x? | [
"3x/5",
"4x/9",
"11x/13",
"7x/12",
"5x/11"
] | x=3y=4z
x/4 = z
and y = x/3
z+y = x/4 + x/3 = 7x/12
Answer is D
The answer is: D | D |
mathematics | A car is traveling 75 kilometers per hour. How many meters does the car travel in one minute? | [
"1250m/min",
"1360m/min",
"2560m/min",
"1670m/min",
"1890m/min"
] | Convert hour into minutes ( 1 hour = 60 minutes) and kilometers into meters (1 km = 1000 m) and simplify
75 kilometers per hour = 75 km/hr
= (75 × 1000 meters) / (60 minutes) = 1,250 meters / minute
correct answer is A)1250m/min
The answer is: A | A |
mathematics | A vessel of capacity 90 litres is fully filled with pure milk. Nine litres of milk is removed from the vessel and replaced with water. Nine litres of the solution thus formed is removed and replaced with water. Find the quantity of pure milk in the final milk solution? | [
"23:89",
"72.9",
"38:3",
"78:3",
"79:3"
] | Explanation:
Let the initial quantity of milk in vessel be T litres.
Let us say y litres of the mixture is taken out and replaced by water for n times, alternatively.
Quantity of milk finally in the vessel is then given by [(T - y)/T]n * T
For the given problem, T = 90, y = 9 and n = 2.
Hence, quantity of milk finally ... | B |
mathematics | In the rectangular coordinate system, points (16, 0) and (– 16, 0) both lie on circle C. What is the maximum possible value of the radius of C ? | [
"2",
"4",
"8",
"16",
"None of the above"
] | D
It takes 3 distinct points to define a circle. Only 2 are given here.
The two points essentially identify a single chord of the circle C. Since no other information is provided, however, the radius of the circle can essentially be anything. All this information tell us is that the radius isgreater 16 D
The answer is:... | D |
mathematics | A can do in 6 day and B can do in 8 and C can do in 12 days but b left after working for 6 days for how many no of day A and C shluld work ? | [
"2 days",
"1 day",
"3 days",
"4 days",
"5 days"
] | B for one day work is 1/8
he worked for 6 days, so 6*1/8=3/4 work will be completed.
remaining work is 1-3/4=1/4
A and C can complete the work in 4 days
but there is only 1/4 work that is to be completed, so A and C can complete 1/4 work in 1 day..
ANSWER:B
The answer is: B | B |
mathematics | Twelve contestants at the county fair have entered their cakes to be judged in the cake decorating competition. A purple ribbon, blue ribbon, red ribbon, and white ribbon will be given to the first, second, third, and fourth place competitors, respectively. How many different ways are there to award the four ribbons to... | [
"8!(4!*4!)",
"12!(8!*4!)",
"8!/4!",
"12!/8!",
"12!/4!"
] | The mistake you are doing is that you are neglecting the 4! ways in you can arrange 4 contestants for the 4 prizes.
Number of ways you can select 4 people out of 12 = 12C4
Once you select the 4 people, you have the following arrangement, PBRW (PBRW being the 4 prizes) but the same group of people can also be chosen aga... | D |
mathematics | 9.99 x 9.9 x 9 ÷ 9.9 ÷ 0.3 = ? | [
"276",
"299",
"310",
"3.33",
"365"
] | Explanation:
? = (9.99 x 9.9 x 9)/(9.9 x 0.9 x 0.3) = 3.33
Answer: Option D
The answer is: D | D |
mathematics | The difference between the place value and the face value of 6 in the numeral 856973 is | [
"5994",
"6973",
"973",
"1000",
"7000"
] | (Place value of 6) - (Face value of 6) = (6000 - 6) = 5994
ANSWER A
The answer is: A | A |
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 ? | [
"70",
"80",
"90",
"100",
"110"
] | Explanation:
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.
C)
The answer is: C | C |
mathematics | A clock loses a minute every three hours for 4 days and gains 2% in the subsequent 6 days. If it was set right on Friday at 11 AM, what will be the time at the end of 10 days? | [
"01:54:40 PM",
"01:56:24 PM",
"12:46:40 PM",
"11:54:24 AM",
"01:20:48 PM"
] | Loses 8 minutes each day.
so total loss = 4×8 = 32min
subsequent 6 days = 6×48×60 minutes
1% gain = ( 6×24×60)/100 = 172.8 minutes
so, total gain = 172.8 - 32 = 140.8 min = 140 + 0.8 min = 2 Hours 20 minutes + 0.4 × 60 seconds = 2 Hours 20 min + 48 seconds
10 days later the clock should be 2 Hours 20 min + 48 seconds
s... | E |
mathematics | The average age of husband, wife and their child 3 years ago was 21 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is | [
"22 years",
"40 years",
"50 years",
"55 years",
"None"
] | Solution
Sum of the present ages of husband, wife and child = (21x3+3x3) years
= 72 years.
Sum of the present ages of wife and child = (20x2+5x2) years
= 50 years.
∴ Husband's present age = (72 - 50) years
= 22 years.
Answer A
The answer is: A | A |
mathematics | There are 145 bananas lying in a shop which is to be divided equally among 12 candidates. Find the extra number of bananas lying with the shop owner after distribution. | [
"1",
"2",
"3",
"4",
"9"
] | 145 divided by 12 = 12x12+1. That is, 1 banana will be extra after distributing 12 bananas to each candidate (12 in number). Answer A.
The answer is: A | A |
mathematics | If the two-digit integers A and B are positive and have the same digits, but in reverse order, which of the following could be the sum of A and B? | [
"41",
"42",
"43",
"44",
"45"
] | A two-digit number "cd" can be expressed algebraically as 10c+d.
The sum of A + B = (10c+d)+(10d+c)=11(c+d).
The only answer that is a multiple of 11 is 44.
The answer is D.
The answer is: D | D |
mathematics | In what time will a train 100 meters long cross an electric pole, if its speed is 360 km/hr | [
"1 second",
"4.5 seconds",
"3 seconds",
"2.5 seconds",
"None of these"
] | Explanation:
First convert speed into m/sec
Speed = 360*(5/18) = 100 m/sec
Time = Distance/speed
= 100/100 = 1 second
Answer: A
The answer is: A | A |
mathematics | In how many ways can 3 hats be formed out of 3 blue hats and 10 red hats? | [
"12",
"302",
"1",
"250",
"286"
] | Total number of hats = 13
Possible number of formations = 13C3 = 286
Correct answer is E
The answer is: E | E |
mathematics | Ayush was born two years after his father's marriage. His mother is five years younger than his father but 20 years older than Ayush who is 15 years old. At what age did the father get married ? | [
"20years",
"21years",
"22years",
"23years",
"25years"
] | Explanation:
Ayush's present age = 15 years.
His mother's present age = (15 + 20) years = 35 years.
Ayush's father's present age = (35 + 5) years = 40 years.
Ayush's father's age at the time of Ayush's birth = (40 - 15) years = 25 years.
Therefore Ayush's father's age at the time of marriage = (25 - 2) years = 23 years... | D |
mathematics | A train 240 m in length crosses a telegraph post in 16 seconds. The speed of the train is? | [
"50",
"54",
"52",
"56",
"58"
] | Explanation:
speed= Distance/ Time
S = 240/16 * 18/5 = 54 kmph
Answer:B
The answer is: B | B |
mathematics | What number has a 5:1 ratio to the number 9? | [
"45",
"50",
"88",
"52",
"12"
] | 5:1 = x: 9
x = 45
Answer: A
The answer is: A | A |
mathematics | Rs.705 is divided amongst A, B, C so that 3 times A's share, 5 times B's share and 4 times C's share are all equal. Find B's share? | [
"177",
"150",
"180",
"716",
"616"
] | A+B+C = 705
3A = 5B = 4C = x
A:B:C = 1/3:1/5:1/4
= 20:12:15
12/47 * 705
= Rs.180
Answer: C
The answer is: C | C |
mathematics | If e is a positive integer, Which of the following options must be divisible by 2? | [
"(e−1)*e*(e+1)",
"e^2*(e−5)",
"e^2*(e−5)",
"(e^2−2)",
"e(e+2)^3"
] | option A) (e−1)*e*(e+1) which represents the product of three consecutive integers
the product of 3 consecutive integers is divisible by both 2 and 3.
Answer is A
The answer is: A | A |
mathematics | Find the L.C.M of 20,50,100 | [
"400",
"200",
"600",
"800",
"1000"
] | 20=2^2*5 50=2*5^2 100=2^4*5^2
L.C.M=2^4*5^2=400
Answer=(A)
The answer is: A | A |
mathematics | The third proportional to 1 and 5 is? | [
"8",
"27",
"24",
"25",
"3"
] | (5*5)/1 = 25
Answer:D
The answer is: D | D |
mathematics | Lisa is buying candy at the grocery store, and has $15 on hand. M&M's are $4.50, Snickers are $6.00, Reese's are $5.50, and Milky Way's are $7.25. Of the following, which of the 5 options could Lisa buy to have $4.00 leftover for a Coffee at Starbucks?A | [
"2 M&M's (9)",
"2 Snickers (12)",
"2 Reese's (11)",
"2 Milky Way's (14.50)",
"A & C"
] | The correct answer must be the Sum of 2 correct candies with a remainder of at least $4
A=(2*4.50+4) = $13 ($15 on hand is enough)
B=(2*6+4) =$16 ($15 on hand is not enough)
C=(2*5.50+4) = $15 (exactly enough on hand)
D=(2*7.25+4) = $18.50 ($15 on hand is not enough)
E= A & C (Total of both candies and $4 coffee is $15... | E |
mathematics | Bob finishes the first half of an exam in one-thirds the time it takes him to finish the second half. If the whole exam takes him an hour, how many minutes does he spend on the first half of the exam? | [
"20",
"24",
"27",
"30",
"40"
] | Many times, it is easiest to think of problems like this conceptually (as opposed to formulaically). Conceptually, if the first half of the exam takes 1/3's the time of the second half (3/3's), we can see that the hour the entire exam took to finish can be broken down into fifth's. (Another way to look at this problem ... | D |
mathematics | A house seller can deduct 5 percent from the total sales value. If he has sold 5 houses, and the price of two houses is between $100,000 and $250,000, one of them is $300,000 house, two houses are between $500,000 and 750,000, what is the range of his revenue? | [
"800",
"850",
"875",
"880",
"900"
] | (1) 2(100)+300+2(500) = 1500
1500*0.95=1425 (Revenue considering the minimum values with the discount)
(2) 2(250)+300+2(750) = 2300 (Revenue considering the maximum values without the discount)
So, the the revenue range could be = 2300 - 1425 = 875
C
The answer is: C | C |
mathematics | Find the cost of fencing around a circular field of diameter 20 m at the rate of Rs.1.50 a meter? | [
"287",
"94.2",
"156",
"158",
"267"
] | 2 * 22/7 * 10 = 62.8
62.8 * 1 1/2 = Rs.94.2
Answer: B
The answer is: B | B |
mathematics | Calculate how many ways a woman who has 4 bags and 6 books can put the books in her bag? | [
"4296",
"4056",
"4016",
"4096",
"3096"
] | First books can be put in 4 ways, similarly second, third , forth, fifth and sixth book also can be put in 4 ways.
So total number of ways = 4 x 4 x 4 x 4 x 4 x 4 = 4096
D
The answer is: D | D |
mathematics | Three partners A, B, C in a business invested money such that 3(A’s capital) = 2(B’s capital) = 5(C’s capital) then, The ratio of their capitals is | [
"63 : 45 : 34",
"63 : 54 : 34",
"36 : 54 : 28",
"63 : 45 : 35",
"10 : 15 : 6"
] | Explanation:
Let 3(A’s capital) = 2(B’s capital) = 5(C’s capital) = Rs.x
Then, A’s capital = Rs x/3, B’s capital = Rs. x/2 and C’s capital = Rs. x/5.
A : B : C = x/3 : x/2 : x/5
10 : 15 : 6
Answer: Option E
The answer is: E | E |
mathematics | The average weight of a group of boys is 30 kg. After a boy of weight 35 kg joins the group, the average weight of the group goes up by 1 kg. Find the number of boys in the group originally ? | [
"4",
"5",
"6",
"7",
"9"
] | Let the number off boys in the group originally be x.
Total weight of the boys = 30x
After the boy weighing 35 kg joins the group, total weight of boys = 30x + 35
So 30x + 35 + 31(x + 1) = > x = 4.
Answer: A
The answer is: A | A |
mathematics | After a storm deposits 120 billion gallons of water into the city reservoir, the reservoir is 60% full. If the original contents of the reservoir totaled 240 billion gallons, the reservoir was approximately what percentage full before the storm? | [
"40%",
"48%",
"54%",
"58%",
"65%"
] | When the storm deposited 120 billion gallons, volume of water in the reservoir = 240 + 120 = 360 billion gallons
If this is only 60% of the capacity of the reservoir, the total capacity of the reservoir = 360/0.6 = 600 billion gallons
Therefore percentage of reservoir that was full before the storm = (240/600)*100 = 40... | C |
mathematics | When positive integer n is divided by 3, the remainder is 1. When n is divided by 8, the remainder is 5. What is the smallest positive integer p, such that (n + p) is a multiple of 15? | [
"1",
"2",
"5",
"19",
"20"
] | When positive integer n is divided by 3, the remainder is 1 i.e., n=3x+1
values of n can be one of {1, 4, 7, 10, 13, 16, 19, 22..............49, 52, 59..................}
Similarly,
When n is divided by 8, the remainder is 5..i.e., n=7y+5
values of n can be one of {5, 13, 21, 29, 37, 45, 53, 61........}
combining both ... | B |
mathematics | A rectangular field is to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required ? | [
"34",
"40",
"68",
"88",
"None of these"
] | Solution
We have : l = 20 ft and lb = 680 sq. ft. So, b = 34 ft.
∴ Length of fencing = (l + 2b) = (20 + 68) ft = 88 ft. Answer D
The answer is: D | D |
mathematics | 70,76, 74,85,90,105,105,130,130,130
The list consists of the times in seconds that it took each of the 10 school children to run a distance of 400 mts . If the standard deviation of the 10 running times is 22.4, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviatio... | [
"1",
"2",
"3",
"4",
"5"
] | How many of the 10 running times are more than one SD below the meanmeans how many data points from given 10 are less thanmean-1SD.
We are given that SD=22.4, so we should find mean --> mean=100 --> there are only 3 data points below 100-22.4=77.6, namely 70 75, and 74.
Answer: C.
The answer is: C | C |
mathematics | If the arithmetic mean of seventy five numbers is calculated, it is 35. If each number is increased by 5, then mean of new number is? | [
"22",
"40",
"28",
"21",
"27"
] | A.M. of 75 numbers = 35
Sum of 75 numbers = 75 * 35 = 2625
Total increase = 75 * 5 = 375
Increased sum = 2625 + 375 = 3000
Increased average = 3000/75
= 40.
Answer: B
The answer is: B | B |
mathematics | What is the next number of the following sequence
108,58,50,8,? | [
"40",
"50",
"30",
"42",
"35"
] | 108-58=50
58-50=8
50-8=42
therefore next no. is 42
ANSWER:D
The answer is: D | D |
mathematics | March 11, 2003 is a Tuesday. What will be the day on which march 11 2004 comes?? | [
"Thursday",
"Friday",
"Saturday",
"Sunday",
"Monday"
] | 2004 is a leap year that means 29 days in feb.
so march 11,2003 to march 11, 2004 will be 366 days.
366/7=52 weeks + 2 days. Hence Thursday
ANSWER:A
The answer is: A | A |
mathematics | A candidate appearing for an examination has to secure 35% marks to pass paper I. But he secured only 42 marks and failed by 23 marks. What is the maximum mark for paper I? | [
"110",
"120",
"186",
"140",
"150"
] | he secured 42 marks nd fail by 23 marks so
total marks for pass the examinatn=65
let toal marks x
x*35/100=65
x=186
ANSWER:C
The answer is: C | C |
mathematics | A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 7 inches wide on each side, the total area would have been (M + 264) square inches. What is the perimeter of the photograph, in inches? | [
"8",
"12",
"16",
"20",
"24"
] | Let x and y be the width and length of the photograph.
(x+2)(y+2)=M and so (1) xy + 2x + 2y + 4 = M
(x+14)(y+14)=M and so (2) xy + 14x + 14y + 196 = M+264
Let's subtract equation (1) from equation (2).
12x + 12y + 192 = 264
2x + 2y = 12, which is the perimeter of the photograph.
The answer is B.
The answer is: B | B |
mathematics | If n + 15 is a positive odd integer, which of the following must be true about the sum of the next four integers? | [
"It is a multiple of 3",
"It is a multiple of 4",
"It is a prime number",
"It is a multiple of 5",
"It is a multiple of 2"
] | n+15 is a positive odd integer. This means n will be an odd integer
The next 4 integers would be: n + 15, n + 16, n + 17, n + 18
Sum = 4n + 56
This sum will always be even.
Option B
The answer is: B | B |
mathematics | A piece of work can finish by a certain number of men in 100 days. If however, there were 10 men less, it would take 10 days more for the work to be finished. How many men were there originally? | [
"75",
"82",
"100",
"110",
"120"
] | Originally let there be x men.
Less men, more days (Indirect)
:. (x-10): x : : 100 :110 or x-10/x = 100/110
or 11x-110 = 10x or x =110
So, originally there were 110 men.
ANSWER:D
The answer is: D | D |
mathematics | Some articles were bought at 6 articles for Rs. 5 and sold at 5 articles for Rs. 6. Gain percent is: | [
"30%",
"32%",
"34%",
"35%",
"44%"
] | Suppose, number of articles bought = L.C.M. of 6 and 5 = 30.
C.P. of 30 articles = Rs.5/6x30= Rs. 25.
S.P. of 30 articles = Rs.6/5x 30= Rs. 36.
Gain % = 11/25x 100% = 44%.
Answer is E.
The answer is: E | E |
mathematics | Which of the following equations describes a line that is perpendicular to y=x+5? | [
"y = x − 5",
"y = −1 − x",
"y = 5x",
"y = 5x+1",
"y = 1/x + 5"
] | Two perpendicular lines have slopes that are inverse reciprocals of each other.
The slope of y=x+5 is 1 so the slope of a perpendicular line will be -1.
The answer is B.
The answer is: B | B |
mathematics | A man has Rs. 160 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 ? | [
"30",
"60",
"75",
"90",
"105"
] | Answer : A
Let number of notes of each denomination be x.
Then, x + 5x + 10x = 160
16x = 160
x = 10.
Hence, total number of notes = 3x = 30.
The answer is: A | A |
mathematics | In a box there are 5 red balls and 6 blue balls. What is the probability of drawing at least one red ball when drawing 3 consecutive balls randomly? | [
"201/202",
"164/165",
"256/259",
"98/103",
"115/217"
] | P(at least one red) = 1 - P(no red, so 3 blue) = 1- 3/11*2/10*1/9 = 164/165.
Answer is B
The answer is: B | B |
mathematics | The probability that B can shoot a target two out of two times is 0.5. What is the probability that the target will be missed by B immediately after such two shots? | [
"0.25",
"0.5",
"0.75",
"0.4",
"0.8"
] | Suppose there are total 'x' shots.
B shoots 2 out of 2 times. means out of x shots (x>2) B shots 2 out of 2 ----> B shots at least 2 out of x.
therefore, 2/x = 0.5 (given)
the target will be missed by B immediately after such two shots : this means he can shot just twice ...the third shot cannot happen which means he m... | B |
mathematics | Eric, Nick and Archi make contributions to the Society Of Nature Protection in the ratio of 5:3:2.5. If altogether they contribute 5145 Nis, how much more money does Nick contribute than Archi? | [
"128 Nis",
"212 Nis",
"234 Nis",
"245 Nis",
"288 Nis"
] | Normalising the fraction from 5:3:2.5 to 10:6:5 (Eric: Nick:Archi)
Given Nick contributes one unit more than Archi and one unit of 5145/(10+6+5) = 245
Answer is D: 245 Nis
The answer is: D | D |
mathematics | A boy was asked to multiply a number by 25. He instead multiplied the next number by 52 and got the answers 324 more than the correct answer. The number to be multiplied was | [
"10",
"12",
"15",
"25",
"14"
] | Let the number be x.
Then, 52 x - 25 x = 324
‹=› 27 x = 324
x= 12.
Answer :B
The answer is: B | B |
mathematics | Excluding stoppages, the speed of a bus is 54 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour? | [
"9",
"10",
"12",
"20",
"22"
] | Due to stoppages, it covers 9 km less.
Time taken to cover 9 km = (9/54 x 60) min = 10 min.
Answer:B
The answer is: B | B |
mathematics | Jerry received a 10% raise each month for two consecutive months. What was his starting salary if after the two raises his salary is $1452? | [
"$1,200",
"$1,300",
"$1,331",
"$1,380",
"$1,403"
] | S * 1.1 * 1.1 = 1452 so,
S = 1200
Answer: A
The answer is: A | A |
mathematics | A grocer has a sale of Rs. 7435, Rs. 7920, Rs. 7855, Rs. 8230 and Rs. 7560 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 7500? | [
"500",
"2000",
"5000",
"6000",
"7000"
] | Total sale for 5 months = Rs. (7435 + 7920 + 7855 + 8230 + 7560) = Rs. 39000.
Required sale = Rs. [ (7500 x 6) - 39000 ]
= Rs. (45000 - 39000)
= Rs. 6000
Answer: Option D
The answer is: D | D |
mathematics | Souju's age is 125% of what it was 10 years ago, but 83 1/3% of what it will be after 10 years. What is her present age? | [
"50 years",
"62 years",
"56 years",
"60 years",
"76 years"
] | Let the age before 10 years =x. Then,
125x/100=x+10
⇒125x=100x+1000
⇒x=1000/25=40
Present age =x+10=40+10=50
ANSWER:A
The answer is: A | A |
mathematics | Let y = 2m + x^2 and m = 5x + 5. If m^2 =100, then which of the following can be a value of 2y + 3m? | [
"83",
"63",
"93",
"73",
"53"
] | m^2 = 100 => m=10
10= 5x+5 => x=1
y= 2*10+1^2 = 21
2y+3m = 2*21+3*10 = 93
Answer : C
The answer is: C | C |
mathematics | The C.P of 15 books is equal to the S.P of 18 books. Find his gain% or loss%? | [
"16 2/3% loss",
"100/3% loss",
"50/3% profit",
"100/3% loss",
"None of these"
] | Explanation:
15 CP = 18 SP
18 --- 3 CP loss
100 --- ? => 16 2/3% loss
ANSWER IS A
The answer is: A | A |
mathematics | There are between 90 and 100 cards in a collection of cards. If they are counted out 3 at a time, there is 1 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection? | [
"91",
"93",
"95",
"97",
"99"
] | The numbers with the form 4n+1 are 93 and 97.
Only 97 has the form 3k+1.
The answer is D.
The answer is: D | D |
mathematics | 1+3=2 2+3=10 3+3=30 4+3=68 5+3=?? | [
"110",
"120",
"130",
"140",
"150"
] | 1^3+3-2=2,
2^3+3-1=10,
3^3+3-0=30,
4^3+3+1=68,
5^3+3+2=130
ANSWER:C
The answer is: C | C |
mathematics | The result when a number subtracted from 100 is the same as the number added to 40. what is the number? | [
"70",
"65",
"80",
"140",
"60"
] | Answer
Let the number be x.
Then, x - 40= 100- x
⇒ 2x = 100+ 40= 140
⇒ 2x = 140
∴ x = 70
Correct Option: A
The answer is: A | A |
mathematics | 1500 is increased by 20%. Find the final number. | [
"1500",
"1800.",
"1900",
"1700",
"1660"
] | Final number = Initial number + 20%(original number) = 1500 + 20%(1500) = 1500 + 300 = 1800.
Answer B
The answer is: B | B |
mathematics | The sum of a number and its square is 1406. What is the number? | [
"1409",
"1402",
"1221",
"1406",
"8828"
] | Explanation:
By option Verification 37 + 37 × 37 = 1406
Answer: D
The answer is: D | D |
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