subject stringclasses 1
value | question stringlengths 3 1.14k | options listlengths 5 5 | solution stringlengths 18 3.7k | answer stringclasses 5
values |
|---|---|---|---|---|
mathematics | How many integers Z are prime numbers in the range 200 < Z < 220? | [
"1",
"2",
"3",
"4",
"5"
] | My friend, every single odd number greater than can be written either as 4Z+1 or as 4Z+3. If you divide any odd number by 4, you will get a remainder of either 1 or 3. That's not a rule unique to prime numbers at all.
The 6Z+1 or 6Z-1 rule is basically every odd number that is not divisible by three, so it narrows the ... | A |
mathematics | A man swims downstream 76 km and upstream 48 km taking 4 hours each time; what is the speed of the current? | [
"3 kmph",
"1.5 kmph",
"3.5 kmph",
"6.5 kmph",
"7:3kmph"
] | Explanation:
76 --- 4 DS = 19
? ---- 1
48 ---- 4 US = 12
? ---- 1 S = ?
S = (19 - 12)/2 = 3.5
Answer: Option C
The answer is: C | C |
mathematics | Pipe A fills a swimming pool in 4 hours. Pipe B empties the pool in 6 hours. If pipe A was opened at 7:00 am and Pipe B at 8:00 am, at what time will the pool be full? | [
"16:00",
"18:00",
"19:00",
"20:00",
"17:00"
] | Pipe A fills the pool in 4 hrs.
1 hour's work : 1/4
Pipe B empties the pool in 6 hrs.
1 hour's work : 1/6
Together if they work, 1 hour's work = 1/4 -1/6 = 1/12
Given : Pipe A started at 7:00 a.m and Pipe B at 8:00 a.m
Pool filled after 1 hour by Pipe A : 1/4 or 3/12
After 8:00 a.m
Pool filled after 1 hour with both th... | E |
mathematics | A boy has 11 trousers and 12 shirts. In how many different ways can he select a trouser and a shirt? | [
"120ways",
"138ways",
"140ways",
"132ways",
"150ways"
] | The boy can select one trouser in 11 ways.
The boy can select one shirt in 12 ways.
The number of ways in which he can select one trouser and one shirt is 11 * 12
= 132 ways.
Answer: D
The answer is: D | D |
mathematics | A car started running at a speed of 28 km/hr and the speed of the car was increased by 2 km/hr at the end of every hour. Find the total distance covered by the car in the first 10 hours of the journey. | [
"37 km",
"76 km",
"25 km",
"15 km",
"30 km"
] | A
37 km
The total distance covered by the car in the first 10 hours = 28 + 30 + 32 + 34 + 36 + 38 + 40 + 42 + 44 + 46 = sum of 10 terms in AP whose first term is 28 and last term is 46 = 10/2 [28 + 46] = 370 km.
The answer is: A | A |
mathematics | A can do a piece of work in 20 days. B in 15 days A and C in 12 days. In how many days can A finish the work if he is assisted by B on one day and C on the next, alternately? | [
"9 days",
"8 days",
"5 days",
"54 days",
"2 days"
] | A + B = 1/20 + 1/15 = 7/60
A + C = 1/20 + 1/12 = 8/60
7/60 + 8/60 = 15/60 = 1/4
4 days * 2 = 8 days
Answer: B
The answer is: B | B |
mathematics | Eighteen years ago, a father was three times as old as his son. Now the father is only twice as old his son. Then the sum of the present ages of the son and the father is: | [
"53",
"108",
"77",
"107",
"109"
] | Explanation:
Let the present ages of the father and son be 2x and x years respectively.
Then, (2x - 18) = 3(x - 18) => x = 36
Required sum = (2x + x) = 108 years.
Answer: Option D
The answer is: D | D |
mathematics | Workers at a campaign office have 3000 fliers to send out. If they send out 1/5 of them in the morning and 1/4 of the remaining ones out during the afternoon, how many are left for the next day? | [
"1800",
"800",
"1100",
"1200",
"1900"
] | (1/5)*3000 = 600
Remaining = 3000-600 = 2400
(1/4) of remaining = (1/4)*2400 = 600
Remaining now = 2400-600 = 1800
Answer: Option A
The answer is: A | A |
mathematics | A tree increases annually by 1⁄5 th of its height. If its height today is 50 cm, what will be the height after 2 years? | [
"64 cm",
"84 cm",
"72 cm",
"64 cm",
"74 cm"
] | Explanation:
This problem is similar to the problems we saw in compound interest.
We can use the formulas of compound interest here as well.
Rate of increase = 1/5 × 100 = 20%
Height after 2 years = P(1+R/100)T
= 50(1 + 20/100)2 = 50(1 + 1/5)2
= 50(6/5)2 = (50 × 6 × 6)/(5 × 5) = 2 × 6 × 6 = 72 cm
Answer: Option C
The a... | C |
mathematics | A pair of articles was bought for $50 at a discount of 40%. What must be the marked price of each of the article? | [
"$25",
"$15",
"$29.65",
"$35.95",
"$45.62"
] | S.P. of each of the article = 50/2 = $25
Let M.P = $x
60% of x = 25
x = 25*.6 =$15
Answer is B
The answer is: B | B |
mathematics | In her backyard, Florry grows only yellow roses and white roses. Some of the rose bushes have flowers of both colors, and some have flowers of one color only. The number of rose bushes that have only yellow roses is 50% greater than the number of rose bushes that have only white roses. If there are yellow roses on 80% ... | [
"20",
"30",
"50",
"70",
"80"
] | let, the number of bushes with only yellow flowers be x
so, number of bushes with only yellow flowers will be 1.5x
if total number of bushes of flowers= T
then total number of bushes with yellow flowers= 0.8T
we can say that total number of bushes with yellow flowers+ bushes with only white flowers= total number of bus... | B |
mathematics | The total age of A and B is 11 years more than the total age of B and C. C is how many year younger than A | [
"A)11",
"B)12",
"C)13",
"D)14",
"E)15"
] | Explanation:
Given that A+B = 11 + B + C
=> A – C = 11 + B – B = 11
=> C is younger than A by 11 years
Answer: Option A
The answer is: A | A |
mathematics | Find out the square of a number which when doubled exceeds its one sixth by 11 ? | [
"36",
"25",
"19",
"26",
"17"
] | A
Let the number be p, then the square will be p^2
According to question:
2p = (p/6) + 11
=> 12p = p + 66
=> p = 6
p^2 = 6^2 = 36.
Answer : A
The answer is: A | A |
mathematics | The manager of a theater noted that for every 10 admissions tickets sold, the theater sells 3 bags of popcorn at 2.40 $ each, 4 sodas at 1.50 $ each and 2 candy bars at 1.00$ each. To the nearest cent, what is the average (arithmetic mean) amount of these snacks sales per ticket sold? | [
"1.48$",
"1.52$",
"1.60$",
"1.64$",
"1.70$"
] | For every 10 tickets amount of snacks sold is 3*2.40+4*1.5+2*1=$15.2, hence amount of the snacks sales per ticket is $15.2/10=~$1.52.
Answer: B.
The answer is: B | B |
mathematics | In how many different number of ways a Committee of 4 person of can be selected from 6 boys and 4girls such that at least 1 girl is included in the committee | [
"195",
"200",
"80",
"15",
"NONE OF THESE"
] | 1G 3B 2G 2B 3G B 4G
= (4C1*6C3)+(4C2*6C2)+(4C3*6C1)+4C4
= (4*20)+(6*150+(4*6)+1
= 80+90+24+1=195
Total 5M 3W
10C4=210
6C4=15
At least one girl = total - with out girl
At least one girl = 210-15=195
A)
The answer is: A | A |
mathematics | If two dice are thrown together, the probability of getting an even number on one die and an odd number on the other is? | [
"1/4",
"1/2",
"1/8",
"1/0",
"1/1"
] | The number of exhaustive outcomes is 36.
Let E be the event of getting an even number on one die and an odd number on the other. Let the event of getting either both even or both odd then = 18/36 = 1/2
P(E) = 1 - 1/2 = 1/2.
Answer: B
The answer is: B | B |
mathematics | Two pipes A and B can separately fill a cistern in 10 and 15 minutes respectively. A person opens both the pipes together when the cistern should have been was full he finds the waste pipe open. He then closes the waste pipe and in another 4 minutes the cistern was full. In what time can the waste pipe empty the cister... | [
"2 min",
"8 min",
"9 min",
"3 min",
"5 min"
] | 1/10 + 1/15 = 1/6 * 4 = 2/3
1 - 2/3 = 1/3
1/10 + 1/15 - 1/x = 1/3
x = 8
Answer: B
The answer is: B | B |
mathematics | A certain football coach allows his quarterback to call three plays in a row. If the quarterback can choose from 3 passing plays, 4 running plays, and 2 trick plays, how many different E arrangements of plays can be run, if the same play can’t be run more than once? | [
"24",
"125",
"243",
"504",
"729"
] | Number of E ways to choose the first play: 9
Second play: 8
Third:7
9*8*7= 504.D
The answer is: D | D |
mathematics | The membership of a committee consists of 3 science teachers, 4 Mathematics teachers, and 2 Social Studies teachers. If 2 committee members are to be selected at random to write the committee’s report, what is the probability that the two members selected will both be science teachers? | [
"1/12",
"1/3",
"2/9",
"1/14",
"1/24"
] | Probability of first member an science teacher = 3/9
Probability of second member an science teacher = 2/8
Probability of both being english teacher = 3/9 x 2/8 =1/12 (A)
The answer is: A | A |
mathematics | A gives B a start of 10 metres in a 100 metre race and still beats him by 1.25 seconds. How long does B take to complete the 100 metre race if A runs at the rate of 10 m/sec? | [
"8 seconds",
"10 seconds",
"16.67 seconds",
"12.5 seconds",
"None"
] | Solution:
A gives B a start of 10 metres in a 100 metre race. This means that when A runs 100 metres, B runs only 90 metres.
Despite that start, A beats B by 1.25 seconds.
As A is running at the speed of 10 m/sec, he will take 10 seconds to complete the 100 metre race. And B takes 10 + 1.25 = 11.25 seconds to cover 90 ... | D |
mathematics | One week, a certain truck rental lot had a total of 20 trucks, all of which were on the lot Monday morning. If 50% of the trucks that were rented out during the week were returned to the lot on or before Saturday morning of that week, and if there were at least 16 trucks on the lot that Saturday morning, what is the gr... | [
"18",
"16",
"12",
"14",
"8"
] | N - Not rented trucks; R - Rented trucks
N + R = 20
N + R/2 = 16
R = 8
E
The answer is: E | E |
mathematics | The average of 11 results is 45, if the average of first five results is 49 and that of the last seven is 52. Find the fifth result? | [
"114",
"116",
"117",
"118",
"119"
] | 1 to 11 = 11 * 45 = 495
1 to 5 = 5 * 49 = 245
5 to 11 = 7 * 52 = 364
5th = 245 + 364 – 495=114
ANSWER:A
The answer is: A | A |
mathematics | Arjun and Sajal are friends . each has some money. If Arun gives Rs. 30 to Sajal, the Sajal will have twice the money left with Arjun. But, if Sajal gives Rs. 10 to Arjun, the Arjun will have thrice as much as is left with Sajal. How much money does Sajal have? | [
"Rs 34",
"Rs 35",
"Rs 36",
"Rs 37",
"Rs 38"
] | If arun had x rs , and sejal had y rs, then
2*(x-30) = y+30 or 2x-60= y+30 or y= 2x-90
and
x+10 = 3*(y-10)= 3*(2x-90-10)=6x-300
or
5x=310
x= 310/5 = 62 Rs with Arjun
y= 2x-90 = Rs 34 with Sajal
ANSWER:A
The answer is: A | A |
mathematics | Which of these must the factor of the product of four consecutive even integers:-
1) 48
2) 64
3) 96
4) 192
5) 80 | [
"1,2 only",
"2,3 only",
"1,2,3 only",
"1,2,3,4 only",
"All of them"
] | 80 is not factor.... It has to have one 5.
Answer is D
The answer is: D | D |
mathematics | If x < 0 and 0 < y < 1, which of the following has the greatest value H? | [
"x^2",
"(xy)^2",
"(x/y)^2",
"x^2/y",
"x^2*y"
] | Given, x < 0 and 0 < y < 1
Let, x = -2 and y = 1/2
A. x^2 = (-2)^2 =4
B. (xy)^2 = (-2*1/2)^2 =1
C. (x/y)^2 = {-2/(1/2)}^2 = (-4)^2 =16
D. x^2/y = (-2)^2 / (1/2) = 4*2 =8
E. x^2*y = (-2)^2*(1/2) =2
Answer: option C
The answer is: C | C |
mathematics | After the recall of defective by Telvin inc 2 years ago, its share price has since lost 12%. However, after the launch of its new product 1 year ago its stock price has appreciated by 6%, bringing its share price to $25. What was its share price 2 years ago? | [
"28",
"26.8",
"56.6",
"27.2",
"25.7"
] | -12+6-(12*6)/100=-6.72% net decrease
let initial price be Y
Y(1-6.72/100)=25
Y=25/0.9328 = ~26.8
Ans is B)
The answer is: B | B |
mathematics | At a certain conference, 42% of the attendees registered at least two weeks in advance and paid their conference fee in full. If 40% of the attendees who paid their conference fee in full did not register at least two weeks in advance, what percent of conference attendees registered at least two weeks in advance? | [
"18.0%",
"62.0%",
"79.2%",
"70.0%",
"82.0%"
] | Refer to the table in the attachment:
Let x= No. of members who have paid in Full
40 % members paid in full and did not register in advance = 0.4x
42 % registerd in advance and paid in full.
So if total No. of members = 100, then 42 members paid Full and registered in advance.
Hence total members who paid full amount =... | D |
mathematics | A 5" cube is painted in all its faces and then it is cut down into 1" blocks. How many 1" blocks
are there even without a single face being painted? | [
"16 blocks",
"20 blocks",
"27 blocks",
"36 blocks",
"64 blocks"
] | The unpainted blocks are the interior blocks.
These blocks form a 3" cube on the inside.
The number of unpainted blocks is 3*3*3 = 27 blocks.
The answer is C.
The answer is: C | C |
mathematics | If it is 6:27 in the evening on a certain day, what time in the morning was it exactly 2,879,277 minutes earlier? (Assume standard time in one location.) | [
"6:22",
"6:24",
"6:27",
"6:30",
"6:32"
] | 6:27 minus 2,879,277 in any way must end with 0.
The only answer choice which ends with 0 is D.
The answer is D.
The answer is: D | D |
mathematics | The current of a stream runs at the rate of 4 kmph. A boat goes 6 km and back to the starting point in 2 hours, then find the speed of the boat in still water? | [
"9",
"4",
"8",
"5",
"3"
] | S = 4
M = x
DS = x + 4
US = x - 4
6/(x + 4) + 6/(x - 4) = 2
x = 8
Answer:C
The answer is: C | C |
mathematics | Rachel and Sarah spent $8 for gasoline, $15.65 for their lunch, and $5 apiece for gifts for Grandma.
Grandma gave each of them $10. If the girls left home with a total of $50, how much do they have for
the return trip? | [
"$36.35",
"$26.35",
"$16.35",
"$46.35",
"$56.35"
] | $50 + $20 = $70 what they left with
plus $10 to each
$8 + $15.65 + $10 = $33.65 what they spent
(gifts are $5 + $5)
$70 - $33.65 = $36.35 left
correct answer A
The answer is: A | A |
mathematics | Integer x is equal to the product of all even numbers from 2 to 60, inclusive. If Q is the smallest prime number that is also a factor of x-1, then which of the following expressions must be true? | [
"0<y<4",
"4<y<10",
"10<y<20",
"20<y<30",
"y>30"
] | Q Smallest prime factor is greater than 29. So answer is E
The answer is: E | E |
mathematics | 20 throws of a die produces following results
SCORE -- NUMBER OF OCCURRENCES
---1-------------------4
---2-------------------3
---3-------------------5
---4-------------------2
---5-------------------2
---6-------------------4
What is the probability P that one more throw to this series will increase the mean score? | [
"1/6",
"1/3",
"1/2",
"2/3",
"5/6"
] | I get the mean as 67/20 --> 3.35. Thus in order to raise this mean we would need a 4,5,or 6.
Thus probability P is 1/2.C
The answer is: C | C |
mathematics | A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water? | [
"12.8 kmph",
"12.7 kmph",
"12.6 kmph",
"12.5 kmph",
"12.3 kmph"
] | Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.
Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7
Solving the equation, the speed of man in still water is 12.5 kmph.
Answer:D
The answer is: D | D |
mathematics | The number of new words that can be formed by rearranging the letters of the word 'RAM' is ? | [
"5",
"10",
"120",
"6",
"8"
] | Number of words which can be formed
= 3! - 1 = 6- 1
= 5.
Answer:A
The answer is: A | A |
mathematics | According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 12 - ounce cans of the concentrate are required to prepare 272 6-ounce servings of orange juice? | [
"25",
"34",
"50",
"67",
"100"
] | Orange juice concentrate: water::1:3
total quantity of orange juice = 272*6 = 1632 oz
so Orange juice concentrate: water :: 408 oz:1224 oz
no. of 12 oz can = 408 oz/12 oz = 34
Answer B, 34 cans
The answer is: B | B |
mathematics | What Is The Next Number
12 13 15 17 111 113 117 119 123 ? | [
"154",
"220",
"129",
"428",
"224"
] | C
129.
These are the first 10 prime numbers (2, 3, 5...) prefixed with a 1
The answer is: C | C |
mathematics | A room 5m 55cm long and 3m 74cm broad is to be paved with square tiles.Find the least number of square tiles required to cover the floor? | [
"122",
"123",
"828",
"122",
"176"
] | Area of the room=(544 * 374)
size of largest square tile= H.C.F of 544 & 374 = 34 cm
Area of 1 tile = (34 x 34)
Number of tiles required== [(544 x 374) / (34 x 34)] = 176
Answer: E
The answer is: E | E |
mathematics | At the start of an experiment, a certain population consisted of 3 animals. At the end of each month after the start of the experiment, the population size was double its size at the beginning of that month. Which of the following represents the population size at the end of 11 months? | [
"2^3",
"3^2",
"2(3^10)",
"3(2^11)",
"3(10^2)"
] | 3*2^n where n is the #of month --> 3*2^11 Answer (D)
The answer is: D | D |
mathematics | What is the greatest 6-digit number when divided by 7 ,8 , 9, and 10 leaves a remainder of 5, 6, 7, and 8 respectively? | [
"456788",
"678910",
"997479",
"997919",
"997920"
] | When you divide a positive integer by 10, the remainder will just be the units digit. We know the remainder is 8 when we divide by 10, so A is the only possible answer.
The answer is: A | A |
mathematics | k = 2^n + 5, where n is an integer greater than 1. If k is divisible by 9, which of the following MUST be divisible by 9? | [
"2^n - 8",
"2^n - 4",
"2^n",
"2^n + 4",
"2^n + 5"
] | Given: k, M and N are integers
If k is a divisor of both N and M, then k is a divisor of N+M (and N–M and M–N)
We're told that 9 is a divisor of 2^n + 5
We also know that 9 is a divisor of9.
So, applying the aboverule, 9 is a divisor of 2^n + 5 +9, and 9 is a divisor of 2^n + 5 -9 = 2^n-4
B
The answer is: B | B |
mathematics | 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work? | [
"2",
"1",
"7",
"6",
"4"
] | 1 women's 1 day work = 1/70
1 child's 1 day work = 1/140
(5 women + 10 children)'s 1 day work
= (5/10 + 10/140) = (1/14 + 1/14) = 1/7
5 women and 10 children will complete the work in 7 days.
Answer:C
The answer is: C | C |
mathematics | The cost price of 20 articles is the same as the selling price of x articles. If the profit is 25%, then the value of x is: | [
"15",
"16",
"18",
"25",
"24"
] | Explanation:
Let C.P. of each article be Re. 1 C.P. of x articles = Rs. x.
S.P. of x articles = Rs. 20.
Profit = Rs. (20 - x).
(20-X/X X100=25)
2000 - 100x = 25x
125x=2000
x=16
ANSWER IS B
The answer is: B | B |
mathematics | In the City 45% of the population lived in the East at the Beginning of the Year and the rest of the City lived in the West. During the Same Year, the population of City grew by 5.0%. If the population in the West grew by 2.5%, by how much did the population grow in the remaining side? | [
"5.9%",
"2.5%",
"5.0%",
"8.2%",
"7.5%"
] | Ratio of population in City = East:West :: 45%:45% = 1:1
Mean growth = 5%
West Growth: 2.5%
East Growth = ??
East-------------Average--------------West
? __(1n)_____5.0%_____(1n)_____2.5%
Since:
2.5+1n=5
n=2.5
Therefore:
East=5+1n
East=5+2.5
That is the population grew in East Side of the town is 7.5%
The answer is: E | E |
mathematics | If 2 < x < 7 and 8 << y < 9, then the lowest possible value for xy is | [
"between 60 and 70",
"between 0 and 60",
"0",
"between 0 and -70",
"less than -70"
] | If 2 < x < 7 and 8 << y < 9,
Say y = 8.9 (8<<y<9)
x = 6
So xy =53.4 which is less than 60.
Answer is B.
The answer is: B | B |
mathematics | A train passes a station platform in 36 sec and a man standing on the platform in 23 sec. If the speed of the train is 54 km/hr. What is the length of the platform? | [
"767 m",
"240 m",
"195 m",
"176 m",
"186 m"
] | Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 23 = 345 m.
Let the length of the platform be x m . Then,
(x + 345)/36 = 15 => x = 195 m.
Answer:C
The answer is: C | C |
mathematics | How many different subsets of the set {10, 14, 13, 24} are there that contain an odd number of elements? | [
"3",
"6",
"8",
"10",
"12"
] | Answer = C = 8
{10}
{14}
{13}
{24}
{10, 14, 13}
{14, 13, 24}
{10, 13, 24}
{10, 14, 24}
The answer is: C | C |
mathematics | UBA Capital recently bought Brand new vehicles for office use. UBA capital only went for Toyota and Honda and bought more of Toyota than Honda at the ratio of 4:6. If 40% of the Toyota bought and 60% of the Honda bought were SUV’s. How many SUV’s did UBA capital buy in the aforementioned purchase? | [
"66%",
"64%",
"68%",
"69%",
"52%"
] | let total no of Vehicles bought be 100, Toyota 40 and Honda 60, so total number of SUV's bought for Toyota and Honda respectively 40* 40/100=16 and 60* 60/100=36
so total 52 SUV's were bought out of 100 Vehicles bought..so required % is 52%
ANSWER:E
The answer is: E | E |
mathematics | The price of lunch for 15 people was $206.00, including a 15 percent gratuity for service. What was the average price per person, EXCLUDING the gratuity? | [
"$11.73",
"$12.48",
"$13.80",
"$14.00",
"$15.87"
] | Take the initial price before the gratuity is 100
The gratuity is calculated on the final price, so as we assumed the final bill before adding gratuity is 100 so gratuity is 15% of 100 is 15 so the total price of meals is 115 so the given amount i.e 206 is for 115 then we have to calculate for 100
for 115 206
for 100 x... | B |
mathematics | If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players? | [
"1123",
"1234",
"1452",
"1356",
"1365"
] | A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players.
=. Required number of ways = 14C10 = 14C4
= 14!/4!x19! = 1365
E
The answer is: E | E |
mathematics | If |r|=−r, which of the following must be true? | [
"x≥0",
"r≤0",
"x2>x",
"x3<0",
"2x<x"
] | |r| =-r means absolute value of r is equal to negative of r. Since absolute value cannot be negative hence negative of r should result in a non negative number. It means r is a non positive number i.e. r<0. Answer is B
The answer is: B | B |
mathematics | Mr. Jones is the Chairman of a committee. In how many ways can a committee of 5 be chosen from 10 people given that Mr. Jones must be one of them? | [
"126",
"252",
"459",
"3024",
"4126"
] | Total Ways of choosing the committee = Total Ways of choosing 4 out of 9 candidates leaving Mr.Jones as one of the selected candidate in advance
Total Ways of choosing 4 out of 9 candidates = 9C4 = 9!/(5!*4!) = 126
Answer: option A
The answer is: A | A |
mathematics | If a and b are digits, and the number a99,99b/88 = an integer, what are the values of a and b? | [
"a = b = 7",
"a = b = 6",
"a = b = 3",
"a = b = 1",
"a = b = 2"
] | a99,99b, divisible by 88.
Factors of 88 = (8)(11)
Divisible by 8: if the last 3 digits of the number are divisible by 8.
99b/8 => 992/8 = 124 => b = 2
Divisibe by 11: subtract the last digit from the number, over and over again, as necessary. If the remaining number is divisible by 11, the original number is divisible ... | E |
mathematics | A man counted his animals, 80 heads and 260 legs (ducks and goats). how many goats are there? | [
"30",
"40",
"50",
"60",
"70"
] | let no of ducks=d and no of goat=g
d+g=80(heads)----------> eq 1
each duck has 2 legs and goat has 4 legs
2d+4g=260 and divide 2d+4g=260 by 2 we get d+2g=130 -----------> eq2
subtract eq1 from eq2
we get no of goats=50
ANSWER:C
The answer is: C | C |
mathematics | A bottle is 80% full. The liquid in the bottle consists of 60% guava juice and 40% pineapple juice. The remainder of the bottle is then filled with 70 lm of rum. How much guava is in the bottle? | [
"155 ml",
"158 ml",
"165 ml",
"168 ml",
"175 ml"
] | if the Bottle is 100ml:
we have 48% Guava, 32% Pineapple, and 20% Rum.
Now, is the bottle 20% of rum is represented by 70 ml. So, we have to find for the same bottle 48% guava is what ml?
therefore, Guava= (70*48)/20= 168 ml
ANSWER:C
The answer is: C | C |
mathematics | In the Hillside summer camp there are 50 children. 90% of the children are boys and the rest are girls. The camp administrator decided to make the number of girls only 5% of the total number of children in the camp. How many more boys must she bring to make that happen? | [
"50",
"45.",
"40.",
"30.",
"25."
] | Given there are 50 students , 90% of 50 = 45 boys and remaining 5 girls.
Now here 90% are Boys and 10% are Girls.
Now question is asking about how many boys do we need to add, to make the girls percentage to 5 or 5%..
If we add 50 to existing 45 then the count will be 95 and the girls number will be 5 as it.
Now boys a... | A |
mathematics | Express a speed of 18 kmph in meters per second? | [
"5 mps",
"10 mps",
"6 mps",
"7 mps",
"12 mps"
] | 18 * 5/18
= 5 mps
Answer:A
The answer is: A | A |
mathematics | A cuboid of dimension 24cm x 9cm x 8 cm is melted and smaller cubers are of side 3 cm is formed.find how many such cubes can be formed ? | [
"64",
"56",
"48",
"40",
"47"
] | Explanation:
Volume of cuboid = (24 x 9 x 8) cm = 1728 cu.cm
Volume of small cube = (3 x 3 x 3) cm = 27 cu.cm
So,
No. of small cubes formed = 1728/27 = 64.
ANSWER IS A
The answer is: A | A |
mathematics | If the average (arithmetic mean) of x, y, and 40 is 5 greater than the average of x, y, 40, and 60, find the average of x and y. | [
"100",
"110",
"120",
"140",
"150"
] | consider the statement "9 is 5 greater than 4": 9 = 4 + 5
similarly,
the average of x, y, and 40 = (the average of x, y, 40, and 60) + 5
(x+y+40)/3 = (x+y+40+60)/4 + 5
(x+y+40)/3 = (x+y+100)/4 + 5
get a common denominator on the right side
(x+y+40)/3 = (x+y+100)/4 + 20/4
(x+y+40)/3 = (x+y+100+20)/4
(x+y+40)/3 = (x+y+12... | A |
mathematics | Which of the following fractions is greater than 4/5 and less than 9/10?
1. 4/5 2. 9/10 3. 1/2 4.3/4 5. 3/5 6. 8/9 | [
"4/5",
"9/10",
"1/2",
"3/4",
"3/5"
] | 4/5= 0.80, 9/10 = 0.90, 1/2= 0.5, 3/4= 0.75, 3/5=0.66, 1/10= 0.1.
Clearly, 0.75 lies between 0.80 and 0.90.
Therefore, 3/4 lies between 4/5 and 9/10.
Answer is D.
The answer is: D | D |
mathematics | Equal amount of water were poured into two empty jars of different capacities, which made one jar 1/6 full and other jar 1/5 full. If the water in the jar with lesser capacity is then poured into the jar with greater capacity, what fraction of the larger jar will be filled with water? | [
"1/7",
"2/7",
"1/3",
"7/12",
"2/3"
] | Same amount of water made bigger jar 1/6 full, thenthe same amount of water(stored for a while in smaller jar) were added to bigger jar, so bigger jar is 1/6+1/6=2/6= 1/3 full.
Answer: C.
The answer is: C | C |
mathematics | Two trains are running in opposite directions in the same speed. The length of each train is 120 meter. If they cross each other in 12 seconds, the speed of each train (in km/hr) is | [
"42",
"36",
"28",
"20",
"15"
] | Explanation:
Distance covered = 120+120 = 240 m
Time = 12 s
Let the speed of each train = v. Then relative speed = v + v = 2v
2v = distance/time = 240/12 = 20 m/s
Speed of each train = v = 20/2 = 10 m/s
= 10 × 36/10 km/hr = 36 km/hr.
Answer: B
The answer is: B | B |
mathematics | A can do a piece of work in 16 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work? | [
"18",
"77",
"66",
"55",
"12"
] | 8/16 + 6/x = 1
X = 12 days
Answer:E
The answer is: E | E |
mathematics | The owner of a local jewellery store hired three watchmen to guard his diamonds, but a thief still got in and stole some diamonds. On the way out, the thief met each watchman, one at a time. To each he gave 1/3 of the diamonds he had then, and 3 more besides. He escaped with 3 diamonds. How many did he steal originally... | [
"198",
"199",
"200",
"None of these",
"Cannot be determined"
] | Explanation :
Since, thief escaped with 3 diamond,
Before 3rd watchman, he had ( 3 + 3 ) x 3 = 18 diamonds.
Before 2nd watchman, he had ( 18 + 3 ) x 3 = 63 diamonds.
Before 1st watchman, he had ( 63 + 3 ) x 3 = 198 diamonds.
Answer : A
The answer is: A | A |
mathematics | The speed of a car is 90 km in the first hour and 60 km in the second hour. What is the average speed of the car? | [
"72 kmph",
"75 kmph",
"30 kmph",
"80 kmph",
"85 kmph"
] | Explanation:
S = (90 + 60)/2 = 75 kmph
ANSWER IS B
The answer is: B | B |
mathematics | Find the value of x in 8.5 – { 5 ½ – [7 ½ + 2.8]/x}*4.25/(0.2)^2 = 306 | [
"3.2",
"3.4",
"3.5",
"4.1",
"4.2"
] | 8.5-{5.5-(7.5+(2.8/x))}*(4.25/0.04) = 306
8.5-{5.5-{(7.5x+2.8)/x)}*(425/4) = 306
8.5-{(5.5x-7.5x-2.8)/x}*(425/4) = 306
8.5-{(-2x-2.8)/x}*106.25 = 306
8.5-{(-212.5x-297.5)/x} = 306
(306-221)x = 297.5 x =(297.5/85) = 3.5.
ANSWER C 3.5
The answer is: C | C |
mathematics | A work can be finished in 30 days by twenty women. The same work can be finished in fifteen days by 10 men. The ratio between the capacity of a man and a woman is | [
"1:3",
"4:1",
"2:3",
"2:1",
"2:4"
] | Work done by 20 women in 1 day = 1/30
Work done by 1 woman in 1 day = 1/(30×20)
Work done by 10 men in 1 day = 1/15
Work done by 1 man in 1 day = 1/(15×10)
Ratio of the capacity of a man and woman =1/(15×10) : 1/(30×20) = 1/150 : 1/600
= 1/1 :1/4 = 4:1
Option B
The answer is: B | B |
mathematics | Tough and Tricky questions: Functions. Let a be a positive integer. Let n#a equal n^(2a) if a is odd and n^(a) if a is even. Then (2#3) + (3#2) – (3#3) is equal to | [
"64",
"-656",
"128",
"512",
"1522"
] | Answer:
2^6 + 3^2 - 3^6 = 2^6 = -656
ANs B
The answer is: B | B |
mathematics | A bakery has 6 employees. It pays annual salaries of $16,000 to each of 2 employees, $18,000 to 1 employee, and $19,000 to each of the remaining 3 employees. Which number is closest to the average (arithmetic mean) annual salary of these employees? | [
"$17,200",
"$17,500",
"$17,800",
"$18,000",
"$18,400"
] | average = 2(16000)+(18000)+3(19000) / 6 = $17,833
The answer is C.
The answer is: C | C |
mathematics | A, B, C together started a business. A invested Rs.2000 for 5 months B invested Rs.8000 for 6 months and C Rs.14000 for 3 months. If they get a total profit of Rs.2500. Find the share of A? | [
"2999",
"3000",
"2777",
"2999",
"250"
] | 1*5:4*6:7*3
5: 24: 21
5/50 * 2500 = 250
Answer:E
The answer is: E | E |
mathematics | Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 10 meters and a circumference of 9 meters, and the interior of tank B has a height of 9 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B? | [
"75%",
"90%",
"100%",
"120%",
"125%"
] | The radius of tank A is 9/(2*pi).
The capacity of tank A is 10*pi*81 / (4*pi^2) = 405 / (2*pi)
The radius of tank B is 10 / (2*pi).
The capacity of tank B is 9*pi*100 / (4*pi^2) = 450 / (2*pi)
Tank A / Tank B = 405/450 = 9/10 = 90%
The answer is B.
The answer is: B | B |
mathematics | Jamshid and Irwin decided to make up their own version of basketball. In addition to being able to score 2-point baskets, they created ways to score 5-, 11-, and 13-point baskets. If at halftime the product of the point values of Irwin’s baskets was 2,420, how many 11-point baskets T did Irwin score? | [
"0",
"1",
"2",
"3",
"4"
] | First thing I noticed was that all these numbers are prime...
Prime factorization gives the following
Step 1:2*1210
Step 2:2*11*110
Step 4:2*11*11*10
Step 5:2*11*11*2*5
So he scored T=2 11-point baskets in my opinion.
Answer C
The answer is: C | C |
mathematics | Raman mixed 24 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction? | [
"Rs.129",
"Rs.120",
"Rs.189",
"Rs.178",
"Rs.126"
] | CP per kg of mixture = [24(150) + 36(125)]/(24 + 36)
= Rs. 135
SP = CP[(100 + profit%)/100]
= 135 * [(100 + 40)/100]
= Rs.189.
Answer:C
The answer is: C | C |
mathematics | A veterinarian surveys 26 of his patrons. He discovers that 14 have dogs, 10 have cats, and 5 have fish. Four have dogs and cats, 3 have dogs and fish, and one has a cat and fish. If no one has all three kinds of pets, how many patrons have none of these pets? | [
"5",
"6",
"8",
"None of these",
"Cannot determined"
] | 7 + 4 + 0 + 3 + 1 + 5 + 1 + x = 26
21 + x = 26
x = 5 patrons have none of these animals
A)
The answer is: A | A |
mathematics | The area of a parallelogram is 98sq m and its altitude is twice the corresponding base. Then the length of the base is? | [
"8",
"9",
"7",
"6",
"5"
] | 2x * x = 98 => x= 7
Answer: C
The answer is: C | C |
mathematics | A man misses a bus by 40 minutes if he travels at 30 kmph. If he travels at 40 kmph, then also he misses the bus by 10 minutes. What is the minimum speed required to catch the bus on time? | [
"43 kmph",
"45 kmph",
"47 kmph",
"49 kmph",
"42 kmph"
] | B
Let the distance to be travelled to catch the bus be x km
x/30 - x/40 = 30/60 => (4x - 3x)/120 = 1/2 => x = 60 km
By traavelling 30 kmph time taken = 60/30 = 2 hours
By taking 2 hours, he is late by 40 min. So, he has to cover 60 km in at most speed = 60/(4/3) = 45 kmph.
The answer is: B | B |
mathematics | A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 15%. Staff are allowed a further 10% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ? | [
"0.75D",
"0.76D",
"0.765D",
"0.775D",
"0.805D"
] | Successive doscounts = - a - b +ab/100
Putting the values,
Total discount = -15 - 10 + 150/100 = -25 + 1.5 = 23.5% discount
Hence the final price of the dress = D - 0.235D = 0.765D
Correct Option: C
The answer is: C | C |
mathematics | 5 nouns, 5 verbs and 3 adjectives are written on blackboard.we can form sentence by choosing 1 from each available set without caring it makes sense or not.what is the number of ways of doing this?? | [
"360",
"390",
"420",
"450",
"540"
] | we have to choose one from each set. 1 from 5 nouns and 1 from 5 verbs and 1 from 3 adjectives.
then we have to arrange 3 different sets in 3! ways.
so,
5c1*5c1*3c1*3!=450
ANSWER:D
The answer is: D | D |
mathematics | Find a sum for first 4 prime number'ss? | [
"18",
"12",
"30",
"17",
"36"
] | Required sum = (2 + 3 + 5 + 7) = 17
Note: 1 is not a prime number
Option D
The answer is: D | D |
mathematics | A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 100 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger? | [
"28 sec",
"16 sec",
"34 sec",
"18 sec",
"17 sec"
] | Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 100 = 340 m.
Time taken = 340/10 = 34 sec.
Answer:C
The answer is: C | C |
mathematics | Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 4 hours and 10 hours respectively. The ratio of their speeds is | [
"4 : 9",
"4 : 3",
"4 : 12",
"4 : 8",
"5 : 2"
] | Let us name the trains as A and B. Then, (A's speed) : (B's speed) = b : a = 10 : 4 = 5 : 2.
Answer: E
The answer is: E | E |
mathematics | The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 190 kmph. Find the speed of the boat in still water and the speed of the stream? | [
"10",
"99",
"77",
"55",
"65"
] | Speed of the boat in still water = (60+190)/2 = 125 kmph. Speed of the stream
= (190-60)/2
= 65 kmph.
Answer: E
The answer is: E | E |
mathematics | If you have 8 New Year greeting cards and you want to send them to 3 of your friends, in how many ways can this be done? | [
"336",
"720",
"340",
"670",
"None"
] | Solution
We have to find number of permutations of 3 objects out of 8 objects. This number is 8P3=8(8-1)(8-2)=8*7*6=336
Answer A
The answer is: A | A |
mathematics | A salesman’s terms were changed from a flat commission of 5% on all his sales to a fixed salary of Rs.1000 plus 2.5% commission on all sales exceeding Rs. 4,000. If his remuneration as per new scheme was Rs. 500 more than that by the previous schema, his sales were worth? | [
"s. 14,000",
"s. 12,000",
"s.16,000",
"s. 40,000",
"s. 50,000"
] | [1000 + (X-4000) * (2.5/100)] - X * (5/100) = 600
X = 16000
ANSWER:C
The answer is: C | C |
mathematics | What is the area of a square field whose diagonal of length 18 m? | [
"120 sq m",
"250 sq m",
"200 sq m",
"180 sq m",
"100 sq m"
] | d2/2 = (18 * 18)/2 = 180
ANSWER:D
The answer is: D | D |
mathematics | A clock is set right at 12 noon on Monday. It losses 1/2% on the correct time in the first week but gains 1/4 on the true time during the second week. The time shown on Monday after two weeks will be | [
"12:25:12",
"11:34:48",
"12:50:24",
"12:24:16",
"None of these"
] | Solution: Time lost over two weeks = 25% a week time(given that 1/2% clock loses in first week and in the second week it gains 1/4% on true time)
A week = 168 hours
Hence, clock lost = 0.42 hours = 25.2 minutes or 25 minute 12 seconds.
Thus, correct time = 12:25:12.
Answer: Option A
The answer is: A | A |
mathematics | 7% of the total quantity of rice is lost in grinding when a country has to import 6 million tonnes, but when only 7 3/4% is lost, it can import 3 million tonnes. Find the quantity of rice grown in the country. | [
"200",
"300",
"400",
"450",
"560"
] | Let x be the total grown quantity of wheat. According to the question
(7%of x)+ 64 31 %of x)+3 7x 31x => 100+ 6 = 400 + 3 1200 x = — 400 million tonnes rice grown
C
The answer is: C | C |
mathematics | the first flight out of Phoenix airport had a late departure. If the next three flights departed on-time, how many subsequent flights need to depart from Phoenix on-time, for the airport's on-time departure rate to be higher than 90%? | [
"6",
"7",
"9",
"10",
"11"
] | We need on-time departure rate to be higher than 9/10, so it should be at least 10/11 which means that 10 out of 11 flights must depart on time. Since for now 3 out of 4 flights departed on time then 10−3=7 subsequent flights need to depart on-time.
Answer: B
The answer is: B | B |
mathematics | By selling a house for Rs.45000, it was found that 1/8 of the outlay was gained, what ought the selling to price to have been in order to have lost 5 p.c? | [
"38008",
"38000",
"38029",
"380219",
"38012"
] | CP + CP/8 = 45000
CP = 40000
SP = 40000*(95/100) = 38000
Answer:B
The answer is: B | B |
mathematics | If a man travels f miles an hour for t hours and r miles an hour for k hours, what is his average rate in miles per hour for the entire distance traveled? | [
"ft + rk",
"(ft + rk)/2",
"t/f + k/r",
"(ft + rk)/(t + k)",
"(ft + rk)/(t - k)"
] | Average Speed = Total Distance /Total Time Taken
Total Distance travelled in t hours = ft
Total Distance travelled in s hours = rk
Total Time taken = t+k
Therefore , Average Speed = (ft+tk)/(t+k)
Answer D
The answer is: D | D |
mathematics | A man is trying 2 different pairs of pants &6 different shirts. How many combinations of 1 pair of pants &1 shirt are possible? | [
"10",
"12",
"16",
"19",
"21"
] | Use a tree diagram to illustrate the possible selections. In the diagram, use P1 and P2 to represent the pants and S1, S2, S3, S4, S5, and S6 to represent the shirts.
Using the Fundamental Counting Principle, 2 × 6 = 12 outfits are possible.
B
The answer is: B | B |
mathematics | Find the least number which when divided by 33 and 8 leaves a remainder of 2 in each case. | [
"266",
"268",
"270",
"272",
"274"
] | The least number which when divided by different divisors leaving the same remainder in each case
= LCM(different divisors) + remainder left in each case.
Hence the required least number
= LCM(33, 8) + 2 = 266.
ANSWER:A
The answer is: A | A |
mathematics | There are 8 students. 4 of them are men and 4 of them are women. If 4 students are selected from the 8 students. What is the probability R that the number of men is equal to that of women? | [
"R=18/35",
"16/35",
"14/35",
"13/35",
"12/35"
] | METHOD-1:
Favorable outcomes (i.e. No. of Men= No. of Women =2) = 4C2 * 4C2 = 6*6 = 36
Total ways of selecting 4 out of 8 Students = 8C4 = 8! / (4! * 4!) = 70
Probability = 36/70 = 18/35
A
METHOD-2:Also see the mistake done by the person who posted this question
Probability of First selected person being Man = 4/8
Prob... | A |
mathematics | In a village there are 150 men and 90 women in present time.if in next year population will be P=(a^2 +b^2)^1/2 , and in every year men are reduces 12%.what is population of after 2 year. | [
"139",
"141",
"142",
"143",
"144"
] | next year total population=[150^2+90^2]^.5=174.92=175
man decreased by 11% so total man =150*.88=132
women will be= 175-132=43
so population after two years= [135^2+43^2]^.5=138.8=139
so population after two year= 139
ANSWER:A
The answer is: A | A |
mathematics | IF x is an integer greater than 6, then all the following must be divisible by 3 EXCEPT | [
"3x^3",
"x(x+1)(x+2)",
"9x",
"9x^2",
"x+3"
] | *any number multiplied by 3, will be divided by 3
for option E if we put value x=7, 7+3=10 is not divisible by 3
Answer : E
The answer is: E | E |
mathematics | A jet plane is rising vertically with a velocity of 10 m/s. It has reached a certain height when the pilot drops a coin, which takes 4 sec to hit the ground. Assuming that there is no resistance to the motion of the coin, the height of the place and the velocity of the coin on impact with the ground are: | [
"38.4 m, 28.7 m/s",
"38.4 m, 29.2 m/s",
"26.5 m, 13.5 m/s",
"26.5 m, 28.7 m/s",
"26 m"
] | The coin will move up with the initial velocity of 10 m/s till it comes to rest. Time taken is given by:
0=10−9.8t
⇒t=10/9.8 sec.
Time taken to reach the ground from the highest point:
=4−10/9.8
=29.2/9.8 sec
Velocity of coin on impact
=0+9.8×(29.2/9.8)
=29.2 m/s
If 'h' is the height from which the coin dropped.... | B |
mathematics | In how many ways can 3 postcards can be posted in 5 postcards? | [
"50",
"120",
"125",
"130",
"100"
] | First card can go into any of the five boxes, Second can go into any of the five boxes.
Third card also can go into any of the five boxes
Number of ways=5*5*5=125 ways
Answer:C
The answer is: C | C |
mathematics | What is the probability of rolling a total of 5 with a single roll of two fair six-sided dice, each with the distinct numbers 1 through 6 on each side? | [
"1/12",
"1/6",
"2/7",
"1/3",
"1/9"
] | Totalsample spacefrom two fair six-sided dice is 36.
There are six possible ways to be 5 i.e. (1+4), (2+3), (3+2), (4+1)
So, total probability is 4/36 or 1/9.
Answer is E.
The answer is: E | E |
mathematics | In an examination 35% of the students passed and 546 failed. How many students appeared for the examination? | [
"A)540",
"B)400",
"C)700",
"D)650",
"E)840"
] | Let the number of students appeared be x
then, 65% of x = 546
65x/100 = 546
x = 546*100/65 = 840
Answer is E
The answer is: E | E |
mathematics | Two musicians, Maria and Perry, work at independent constant rates to tune a warehouse full of instruments. If both musicians start at the same time and work at their normal rates, they will complete the job in 120 minutes. However, if Perry were to work at twice Maria’s rate, they would take only 20 minutes. How long ... | [
"1 hr 20 min",
"1 hr 45 min",
"2 hr",
"2 hr 20 min",
"1 hr"
] | Sol:
Lets Perry Rate be P and Rate of Maria be M
(rate)*(time)= Work or rate = work/time
first equation=> P+M = 1/120
converting it to hrs P+M= 1/(60/120) => 2
second equation => M+2M =>1/20
converting it to hrs 3M=1/(20/60) =>1/(1/3) =>3
therefore M= 1 and P=1
Rate of Perry = 1
time= work/rate (work = 1 job)
Time= 1 h... | E |
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