subject stringclasses 1
value | question stringlengths 3 1.14k | options listlengths 5 5 | solution stringlengths 18 3.7k | answer stringclasses 5
values |
|---|---|---|---|---|
mathematics | Which of the following could be the sum of the reciprocals of two prime numbers? | [
"7/13",
"11/12",
"12/10",
"23/50",
"19/77"
] | 12/10 it is
6/5=(1/2) + (1/5)
Answer - C
The answer is: C | C |
mathematics | Two trains, each 160 m long, moving in opposite directions, cross other in 8 sec. If one is moving twice as fast the other, then the speed of the faster train is? | [
"26 km/hr",
"17 km/hr",
"60 km/hr",
"77 km/hr",
"96 km/hr"
] | Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(160 + 160)/8 = 3x => x = 40/3.
So, speed of the faster train = 80/3 = 80/3 * 18/5
= 96 km/hr.
Answer:E
The answer is: E | E |
mathematics | A, B and C invested Rs.6300, Rs.4200 and Rs.10500 respectively, in a partnership business. Find the share of A in profit of Rs.12100 after a year? | [
"3630",
"2879",
"289",
"279",
"2928"
] | 6300:4200:10500
3:2:5
3/10 * 12100 = 3630
Answer:A
The answer is: A | A |
mathematics | X does a work in 10 days. Y does the same work in 15 days. In how many days they together will do the same work? | [
"10",
"15",
"3",
"6",
"12"
] | X's 1day's work= 1/10
Y's 1 day's work=1/15
(X+Y)'s 1day's work= (1/10+1/15)=1/6
both together will finish the work in 6 days.
correct option is D
The answer is: D | D |
mathematics | There are 8 balls in a bucket, 4 balls are blue and 4 balls are red. If two ball chosen randomly , how many chances there are at least one blue ball will present? | [
"21",
"25",
"16",
"22",
"20"
] | Two ball will be chosen. At least 1 blue ball
Total ways = 8C2 = 28
Total without any blue ball = 4C2 = 6
Hence ways in which at least one blue will be present = 28 - 6 = 22
Correct option: D
The answer is: D | D |
mathematics | The distance from City A to City B is 120 miles. While driving from City A to City B, Cara drives at a constant speed of 30 miles per hour. Dan leaves City A 90 minutes after Cara. What is the minimum constant speed in miles per hour that Dan must exceed in order to arrive in City B before Cara? | [
"42",
"44",
"46",
"48",
"50"
] | The time it takes Cara to drive to City B is 120 / 30 = 4 hours.
Dan needs to take less than 2.5 hours for the trip.
Dan needs to exceed a constant speed of 120 / 2.5 = 48 miles per hour.
The answer is D.
The answer is: D | D |
mathematics | Envelopes can be purchased for $1.50 per pack of 100, $1.00 per pack of 50, or $0.03 each. What is the greatest number of envelopes that can be purchased for $6.30? | [
"426",
"430",
"443",
"410",
"486"
] | I think first we should see in what group envelopes value less, so that we can buy as many as we can with a specific amount of money:
-the 100 pack costs 1.5$, meaning 0.015$ per envelope
-the 50 pack costs 1$, meaning 0.02$ per envelope
-the single envelope costs 0.03$ per envelope
Thus, we have to buy as many 100 pac... | D |
mathematics | In 2008, the profits of Company M were 5 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 15 percent of revenues. The profits in 2009 were what percent of the profits in 2008? | [
"80%",
"105%",
"124%",
"240%",
"138%"
] | the profit 0f 2009 in terms of 2008 = 0.8*15/5*100=240%
D
The answer is: D | D |
mathematics | The cost of an item was reduced from its usual selling price of $23.99 to $18.99. Which of the following is closest to the percent decrease in the price of the item? | [
"17%",
"21%",
"24%",
"25%",
"42%"
] | The price decreased by 23.99 - 8.99 = $5.
$5 is a bit more than 20% of original price of $24.
Answer: B.
The answer is: B | B |
mathematics | John want to buy a $100 Trouser at the store, but he think it’s too expensive. Finally, it goes on sale for $20. What is the percent decrease? | [
"20%",
"30%",
"40%",
"70%",
"80%"
] | The is always the difference between our starting and ending points. In this case, it’s 100 – 20 = 80. The “original” is our starting point; in this case, it’s 100. (80/100)*100 = (0.8)*100 = 80%.
E
The answer is: E | E |
mathematics | what is rate of interest if principal.amount be 400,simple interest 180 and time 2year. | [
"10",
"12.5",
"25",
"22.5",
"14.5"
] | s.i=(p*r*t)/100
180=800r/100
r=180/8=22.5%
answer D
The answer is: D | D |
mathematics | What is the next number of the following sequence
10,8,18,16,34,32,.... | [
"44",
"66",
"55",
"77",
"48"
] | 10
10-2=8
8+10=18
18-2=16
16+18=34
34-2=32
32+34=66
answer will be 66
ANSWER:B
The answer is: B | B |
mathematics | 80% of a number is added to 120, the result is the same number. Find the number? | [
"600",
"288",
"1687",
"997",
"121"
] | (80/100) * X + 120 = X
2X = 1200
X = 600
Answer:A
The answer is: A | A |
mathematics | Vijay bought 160 shirts at the rate of Rs. 225 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 10%? | [
"282",
"229",
"277",
"285",
"261.25"
] | Total CP per shirt = 225 + 1400/160 + 1.75 + 320/160 = Rs. 237.5
SP = CP[(100 + profit%)/100]
= 237.5 * [(100 + 10)/100] = Rs. 261.25.
Answer:E
The answer is: E | E |
mathematics | A retailer bought a machine at a wholesale price of $90 and later on sold it after a 10% discount of the retail price. If the retailer made a profit equivalent to 20% of the whole price, what is the retail price of the machine? | [
"81",
"100",
"120",
"135",
"160"
] | My solution: Wholesale Price= 90
Retail Price, be = x
He provides 10 % discount on Retail price= x-10 x/100
This Retail price = 20 % profit on Wholesale price
x-10 x/100 = 90+ 1/5(90)
x=120;
ANSWER:C
The answer is: C | C |
mathematics | 2 hours after train A leaves Lucknow a train B leaves the same stationtraveling in the same direction at an average speed of 36 km/hr. After traveling 6 hrsthe train B overtakes the train A. What is the average speed of the train A? | [
"22.5 km/hr",
"16 km/hr",
"27 km/hr",
"18 km/hr",
"None of these"
] | Explanation :
Total distance covered by B=36*6=216kmTotal time taken by A to cover same distance=2+6=8 hrsaverage speed of A=216/8=27 km/hr
Answer : C
The answer is: C | C |
mathematics | When four fair dice are rolled simultaneously, in how many outcomes will at least one of the dice show 3? | [
"233",
"671",
"287",
"279",
"171"
] | Explanation:
When 4 dice are rolled simultaneously, there will be a total of 6 x 6 x 6 x 6 = 1296 outcomes.
The number of outcomes in which none of the 4 dice show 3 will be 5 x 5 x 5 x 5 = 625 outcomes.
Therefore, the number of outcomes in which at least one die will show 3 = 1296 – 625 = 671
Answer: B) 671
The answer... | B |
mathematics | If 625^(-x) + 25^(-x) + 5^(-4x) = 15, what is the value of x? | [
"-4",
"-1/4",
"0",
"1/4",
"4"
] | We're told that 625^(-X) + 25^(-2X) + 5^(-4X) = 15. We're asked for the value of X.
Since each of the calculated terms MUST be positive (regardless of what the exponent is), we can use thebasesto our advantage.....
With Answer A, we'd have 625^4, which is MUCH BIGGER than 15 (and we'd be adding to that big number). Eli... | E |
mathematics | What is x if x + 2y = 10 and y = 1? | [
"A)10",
"B)8",
"C)6",
"D)4",
"E)2"
] | x = 10 - 2y
x = 10 - 2.
x = 8
Answer : B
The answer is: B | B |
mathematics | How many 7-digits number are Palindromic numbers? A Palindromic number reads the same forward and backward, example 1234321. | [
"100",
"610",
"729",
"9000",
"1000"
] | Take the task of building palindromes and break it intostages.
Stage 1: Select the 7th digit
We can choose 1, 2, 3, 4, 5, 6, 7, 8, or 9
So, we can complete stage 1 in 9ways
Stage 2: Select the 6th digit
We can choose 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9
So, we can complete stage 2 in10ways
Stage 3: Select the 5th digit
We c... | D |
mathematics | A can finish a work in 72days, B in 9days and C in 2days, B and C start the work but are forced to leave after 3 days. The remaining work was done by A in? | [
"30days",
"12days",
"6days",
"7days",
"8days"
] | B+C 1day work = 1/9 + 1/12 = 7/36
work done by B and C in 3days = 7/36 * 3 = 7/12
Remaining work = 1 - 7/12 = 5/12
1/24 work is done by A in 1day
5/12 work is done by A in 72*5/12 = 30days
Answer is A
The answer is: A | A |
mathematics | A bowl of fruit contains 10 apples and 23 oranges. How many oranges must be removed so that 50% of the pieces of fruit in the bowl will be apples? | [
"3",
"13",
"14",
"17",
"20"
] | Number of apples = 10
number of oranges = 23
let number of oranges that must be removed so that 50% of pieces of fruit in bowl will be apples = x
Total number of fruits after x oranges are removed = 10+(23-x) = 33-x
10/(33-x) = 5/10
=>20 = 33-x
=>x= 13
Answer B
The answer is: B | B |
mathematics | Ramu rides his bike at an average speed of 45 km/hr and reaches his desitination in four hours. Somu covers the same distance in five hours. If Ramu covered his journey at an average speed which was 9 km/hr less and Somu covered his journey at an average speed which was 10 km/hr more, then the difference in their times... | [
"65 minutes",
"66 min",
"56 minutes",
"69 minutes",
"46 minutes"
] | Distance travelled by Ramu = 45 * 4 = 180 km
Somu travelled the same distance in 5 hours.
His speed = 180/5 = 36 km/hr
Hence in the conditional case, Ramu's speed = 45 - 9 = 36 km/hr and Somu's speed = 36 + 10 = 46km/hr.
Therefore travel time of Ramu and Somu would be 5 hours and 3.9 hours respectively. Hence differenc... | B |
mathematics | If k is an integer and 121 < k^2 < 225, then k can have at most how many values? | [
"3",
"4",
"5",
"6",
"8"
] | given k is an integer
121 < k^2 < 225
11 < | k| < 15
K=-12,-13,-14,12,13,14
ANSWER:D
The answer is: D | D |
mathematics | Find the value of a/b + b/a, if a and b are the roots of the quadratic equation x2 + 10x +5 = 0? | [
"6",
"42",
"24",
"18",
"95"
] | a/b + b/a = (a2 + b2)/ab = (a2 + b2 + a + b)/ab
= [(a + b)2 - 2ab]/ab
a + b = -10/1 = -10
ab = 5/1 = 5
Hence a/b + b/a = [(-10)2 - 2(5)]/5 = 90/5 = 18.
D)
The answer is: D | D |
mathematics | A man saves Rs. 200 at the end of each year and lends the money at 5% compound interest. How much will it become at the end of 3 years? | [
"Rs. 565.25",
"Rs. 635",
"Rs. 662.02",
"Rs. 666.50",
"Rs. 686.50"
] | Amount = [200(1 + 5/100)3 + 200(1 + 5/100)2 + 200(1 + 5/100)]
= [200 * 21/20(21/20 * 21/20 + 21/20 + 1)] = Rs. 662.02
ANSWER:C
The answer is: C | C |
mathematics | At Joel’s bookstore, the current inventory is 40% historical fiction. Of the historical fiction books, 40% are new releases, while 20% of the other books are new releases. What fraction of all new releases are the historical fiction new releases? | [
"4/25",
"8/23",
"2/5",
"8/14",
"2/3"
] | let there be 100 books in all
Historic fiction books = 40% of total = 40
Other books = 60
New historic fiction = 40% of 40 = 16
Other new books = 20% of 60 = 12
total new books = 28
fraction = 16/28 = 8/14
Ans: D
The answer is: D | D |
mathematics | An auction house charges a commission of 25% on the first $50,000 of the sale price of an item, plus 10% on the amount of of the sale price in excess of $50,000. What was the price of a painting for which the house charged a total commission of $24,000? | [
"$115,000",
"$165,000",
"$215,000",
"$240,000",
"$365,000"
] | Say the price of the house was $x, then 0.25*50,000+0.1*(x-50,000)=24,000 --> x=$165,000 (25% of $50,000 plus 10% of the amount in excess of $50,000, which is x-50,000, should equal to total commission of $24,000).
Answer: B.
The answer is: B | B |
mathematics | A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 18, what is the total amount? | [
"70",
"105",
"178",
"177",
"169"
] | x:y:z = 100:45:30
20:9:6
9 --- 18
35 --- ? => 70
Answer: A
The answer is: A | A |
mathematics | The cost of producing x tools by a company is given by
C(x) = 2000 x + 5500 (in $)
a) What is the cost of 100 tools? | [
"215500 $",
"205800 $",
"125900 $",
"226500 $",
"205500 $"
] | Solution
C(100) = 2000*100 + 5500 = 205500 $
Answer E
The answer is: E | E |
mathematics | Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 90 kmph and 72 kmph. After how much time will the trains meet? | [
"20/8 sec",
"20/9 sec",
"20/7 sec",
"22/7 sec",
"60/7 sec"
] | They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (90 + 72)*5/18 = 9*5 = 45 mps.
The time required = d/s = 100/45 = 20/9 sec.Answer:B
The answer is: B | B |
mathematics | A and B can together complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can B alone complete that work ? | [
"4 days",
"5 days",
"6 days",
"7 days",
"8 days"
] | Explanation:
(A+B)'s 1 day work = 1/4
A's 1 day work = 1/12
B's 1 day work =
(1/4−1/12)=3−1/12=1/6
So B alone can complete the work in 6 days
Option C
The answer is: C | C |
mathematics | Rahim bought 50 books for Rs.1000 from one shop and 40 books for Rs.800 from another. What is the average price he paid per book ? | [
"28",
"20",
"27",
"29",
"21"
] | Average price per book
= (1000+ 800) / (50 + 40)
= 1800 / 90
= Rs.20
Answer:B
The answer is: B | B |
mathematics | In a bag there are coins of 50 paisa, 25 paisa and one rupee in the proportion 10:8:2. If there are in all Rs.90, the number of 50 paisa coins is? | [
"120",
"110",
"90",
"80",
"100"
] | 10x 8x 2x
50 25 100
500x + 200x + 200x = 4200
900x = 9000
x = 10 => 10x = 100
Answer: E
The answer is: E | E |
mathematics | Working alone, machine X can manufacture 1,000 nails in 16 hours. Working together, machines X and Y can manufacture 1,000 nails in 5 hours. How many hours does it take machine Y to manufacture 1,000 nails working alone? | [
"3 9/17",
"5 1/3",
"7",
"7 3/11",
"8 4/7"
] | rate of machine x = 1000/16
(1000/16 + y)5=1000
y=200-125/2=275/2
275/2 * t = 1000
t=7 3/11
D. 7 3/11
The answer is: D | D |
mathematics | If there are 156 laborers in a crew, and on a certain day, 70 were present. Calculate the percentage that showed up for work? (round to the nearest tenth). | [
"45.9%",
"43.9%",
"42.9%",
"41.9%",
"44.9%"
] | 70/156*100=44.87
44.9%
correct answer E
The answer is: E | E |
mathematics | what comes next?
7, -35, -34, -3, 15, 16, 4 | [
"-20",
"-15",
"5",
"21",
"33"
] | 7*-5=-35, then -35+1=-34
-3*-5=15,then 15+1=16
so 4*-5=-20
ANSWER:A
The answer is: A | A |
mathematics | A tank is filled in eight hours by three pipes A, B and C. Pipe A is twice as fast as pipe B, and B is twice as fast as C. How much time will pipe B alone take to fill the tank? | [
"22",
"28",
"77",
"12",
"21"
] | 1/A + 1/B + 1/C = 1/8 (Given)
Also given that A = 2B and B = 2C
=> 1/2B + 1/B + 2/B = 1/8
=> (1 + 2 + 4)/2B = 1/8
=> 2B/7 = 8
=> B = 28 hours.Answer: B
The answer is: B | B |
mathematics | Which one of the following numbers is divisible by 11? | [
"4823718",
"8423718",
"8432718",
"4832718",
"4852718"
] | Explanation:
4832718 = (4+3+7+8) – (8+2+1) = 11
So, the given number is divisible by 11
Answer:D
The answer is: D | D |
mathematics | Positive integer x has y factors; 3x has 3 factors; Which of the following values can y take?
I. 1
II. 2
III. 3 | [
"I or II",
"I only is true",
"II only is true",
"II or III",
"I or III"
] | Squares have odd number of factors.The square which is a multiple of 3 is 9.
3 has factors 1,3 .
Therefore 2 factors
Answer C
The answer is: C | C |
mathematics | 1/0.05 is equal to | [
"25.5",
"2.5",
"25",
"20",
"None of these"
] | Explanation:
1/0.05 = (1 * 100)/5 = 100/5 = 20
Option D
The answer is: D | D |
mathematics | The area of a rectangular field is equal to 750 square meters. Its perimeter is equal to 110 meters. Find the width of this rectangle. | [
"5",
"10",
"15",
"20",
"25"
] | L * W = 750 : area , L is the length and W is the width.
2 L + 2 W = 110 : perimeter
L = 55 - w : solve for L
(55 - W) * W = 750 : substitute in the area equation
W = 25 and L = 30
correct answer E
The answer is: E | E |
mathematics | A and B put in Rs.300 and Rs.400 respectively into a business. A reinvests into the business his share of the first year's profit of Rs.210 where as B does not. In what ratio should they divide the second year's profit? | [
"39:40",
"39:48",
"39:43",
"39:46",
"39:42"
] | 3: 4
A = 3/7*210 = 90
390: 400
39:40
Answer: A
The answer is: A | A |
mathematics | The price of a cycle is reduced by 25 per cent. The new price is reduced by a further 50 per cent. The two reductions together are equal to a single reduction of | [
"45%",
"62.5%",
"35%",
"32.5%",
"30%"
] | Price = p
initially price reduced by 25% which means new price is 3/4P
Now on this new price further 50percent is reduced which means the new price is merely 50percent of 3/4P
==> (3/4)x(1/2)P = 3/8P is the new price after both deduction which is 37.5percent of the original value P. This implies this entire series of d... | B |
mathematics | Pipe A can fill a tank in 5 hours, pipe B in 10 hours and pipe C in 30 hours. If all the pipes are open, in how many hours will the tank be filled? | [
"2",
"2.2",
"3",
"3.5",
"4"
] | Part filled by A + B + C in 1 hour = 1/5 + 1/10 + 1/30 = 1/3
All the three pipes together will fill the tank in 3 hours.
ANSWER:C
The answer is: C | C |
mathematics | In how many ways letters of the word POLICIES be arranged? | [
"45326",
"28763",
"20160",
"45693",
"54823"
] | POLICIES has 8 letters, out of which I repeated 2 times. Hence total ways = 8! / 2! = 20160ways
C
The answer is: C | C |
mathematics | If the cost price of 12 pencils is equal to the selling price of 8 pencils, the gain percent is: | [
"30",
"40",
"50",
"60",
"70"
] | C
50%
Let C.P. of each pencil be $ 1.
Then, C.P. of 8 pencils = $8; S.P. of 8 pencils = $12.
Gain % = 4/8 * 100 = 50%
The answer is: C | C |
mathematics | The perimeter of a triangle is 22 cm and the inradius of the triangle is 3.5 cm. What is the area of the triangle? | [
"22",
"35",
"77",
"54",
"38"
] | Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 3.5 * 22/2
= 38.5 cm2
Answer:E
The answer is: E | E |
mathematics | Mr. loyd wants to fence his Square shaped land of 120Sqft each side.If a pole is laid every 10ft how many poles do he need? | [
"20",
"30",
"48",
"50",
"60"
] | If each side is 120 feet..then total perimeter is 120*4=480
poles every 10 feet hence no of poles= 480/10=48
ANSWER:C
The answer is: C | C |
mathematics | A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold? | [
"480",
"266",
"287",
"1661",
"211"
] | 1/x - 1/20 = -1/24
x = 120
120 * 4 = 480
Answer: A
The answer is: A | A |
mathematics | Can you replace the question mark with the number to complete the series, provided the pair of numbers exhibits a similar relationship?
? : 4623 :: 9 : 647 | [
"?= 17",
"18",
"13",
"10",
"20"
] | A
17
The relationship holds for below formula :
pow(x,3) - pow(x,2) - 1
=> 9*9*9 - 9*9 - 1
=> 729 - 81 - 1
=> 647
Similarly,
17*17*17 - 17*17 - 1
=> 4913 - 289 - 1
=> 4623
The answer is: A | A |
mathematics | If a farmer wants to plough a farm field on time, he must plough 120 hectares a day. For technical reasons he ploughed only 85 hectares a day, hence he had to plough 2 more days than he planned and he still has 40 hectares left. What is the area of the farm field and how many days the farmer planned to work initially? | [
"483",
"720",
"885",
"645",
"287"
] | Let x be the number of days in the initial plan. Therefore, the whole field is 120⋅x hectares. The farmer had to work for x+2 days, and he ploughed 85(x+2) hectares, leaving 40 hectares unploughed. Then we have the equation:
120x=85(x+2)+40
35x=210
x=6
So the farmer planned to have the work done in 6 days, and the area... | B |
mathematics | The jogging track in a sports complex is 1040 m in circumference. Kapil and his wife start from the same point and walk in opposite directions at 7.5 km/hr and 3.7 km/hr respectively. They will meet for the first time in? | [
"3.12 min",
"3.74 min",
"4.25 min",
"4.90 min",
"5.57 min"
] | Clearly, the two will meet when they are1040 m apart.
To be (7.5 + 3.7) = 11.2 km apart, they take 1 hour. THat is 60 minutes.
To be 1040m apart, they take
= (1040/11200 * 60) min
= 5.57 min.
Answer: E
The answer is: E | E |
mathematics | the sum of 2nd and 19th term of A.P. is equal to the sum of 8th , 15th and 12 th term . find the term which is 0 | [
"12",
"13",
"14",
"15",
"16"
] | t2 + t19 = t8 + t15 + t12
=> a+d + a+18d = a+7d + a+14d + a+11d
=> a + 13d = 0
=> t14 = 0 i.e. 14th term is zero.
ANSWER:C
The answer is: C | C |
mathematics | Two trains of equal length 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 seconds. The length of each train is: | [
"50 m",
"72 m",
"80 m",
"82 m",
"84 m"
] | Let the length of each train be x metres.
Then, distance covered = 2x metres.
Relative speed = (46 - 36) km/hr
(10 x (5/18) ) m/s = 25/9 m/s
2x/36 = 25/9
2x=100
x=50
ANSWER:A
The answer is: A | A |
mathematics | Gopi gives Rs. 90 plus one turban as salary to his servant for one year. The servant leaves after 9 months and receives Rs. 45 and the turban. Find the price of the turban. | [
"27",
"36",
"29",
"90",
"11"
] | Let the price of turban be x.
Thus, for one year the salary = (90 + x)
For 9 months he should earn 3434 (90 + x).
Now he gets one turban and Rs. 45.
Thus, 3434 (90 + x) = 45 + x or 270 + 3x = 180 + 4x or x = 90
Answer:D
The answer is: D | D |
mathematics | Sam invested Rs. 15000 @ 10% per annum for one year. If the interest is compounded half-yearly, then the amount received by Sam at the end of the year will be? | [
"16537.52",
"16537.29",
"16537.5",
"16537.2",
"16537.11"
] | P = Rs. 15000; R = 10% p.a. = 5% per half-year; T = 1 year
= 2 half-year
Amount = [15000 * (1 + 5/100)2]
= (15000 * 21/20 * 21/20)
= Rs.16537.50
Answer:C
The answer is: C | C |
mathematics | Look at this series: 1000, 200, 40, ... What number should come next? | [
"8",
"10",
"15",
"20",
"25"
] | 1000/5=200
200/5=40
40/5=8
ANSWER:A
The answer is: A | A |
mathematics | Mr. Jones sold two pipes at $1.20 each. Based on the cost, his profit one was 20% and his loss on the other was 20%. On the sale of the pipes, he: | [
"broke even",
"lost 10 cents",
"lost 4 cents",
"gained 10 cents",
"gained 4 cents"
] | 20 % profit on $ 1.20
= $ 20/100 × 1.20
= $ 0.20 × 1.20
= $ 0.24
Similarly, 20 % loss on $ 1.20
= $ 20/100 × 1.20
= $ 0.20 × 1.20
= $ 0.24
Therefore, in one pipe his profit is $ 0.24 and in the other pipe his loss is $ 0.24.
Since both profit and loss amount is same so, it’s broke even.
The answer is: A | A |
mathematics | In how many different number of ways 3 boys and 2 girls can sit on a bench? | [
"720",
"730",
"740",
"750",
"120"
] | npn = n!
5p5 = 5 × 4 × 3 × 2 × 1 = 120
E
The answer is: E | E |
mathematics | What is the area of square field whose side of length 13 m? | [
"225",
"662",
"169",
"882",
"21"
] | 13 * 13
= 169 sq m
Answer:C
The answer is: C | C |
mathematics | Cereal A is 10% sugar by weight, whereas healthier but less delicious Cereal B is 3% sugar by weight. To make a delicious and healthy mixture that is 4% sugar, what should be the ratio of Cereal A to Cereal B, by weight? | [
"2:9",
"2:7",
"1:6",
"1:4",
"1:3"
] | (10/100)A+(3/100)B = (4/100)(A+B)
6A =B
=> A/B = 1/6
Answer is C.
The answer is: C | C |
mathematics | If you multiply all the numbers on your mobile phone except 0 and 9, what is the answer? | [
"25869",
"48586",
"40320",
"58964",
"45698"
] | We have to multiply 1 to 8 to find the answer.
Therefore 1*2*3*4*5*6*7*8=40320
Answer is C
The answer is: C | C |
mathematics | A man sells a car to his friend at 11% loss. If the friend sells it for Rs.54000 and gains 20%, the original C.P.of the car was : | [
"Rs.25561.80",
"Rs.37500.80",
"Rs.50561.80",
"Rs.60000",
"None of these"
] | Explanation:
S.P = Rs.54,000. Gain earned = 20%
C.P = Rs.[100/120×54000]
=Rs. 45000
This is the price the first person sold to the second at at loss of 11%.
Now S.P = Rs.45000 and loss = 11%
C.P. Rs.[100/89×45000]= Rs.50561.80.
Correct Option : C
The answer is: C | C |
mathematics | How many three digit numbers W are divisible by 78 or 91? | [
"17",
"19",
"20",
"21",
"22"
] | The answer will be 19.
Explanation:
78= 2*3*13 now multiples of 78, 156 ....780, now 1000-780 = 220 only two more muktiples of 78 can exists. So total number of 3 digit Multiples of 78 are 9+2=11
91= 13*7--Total number of three digit multiples --9
No remember we have a common multiples as well-- 13*7*6=91*6=546
So tota... | B |
mathematics | Six cards numbered from 1 to 6 are placed in an empty bowl. First one card is drawn and then put back into the bowl; then a second card is drawn. If the cards are drawn at random and if the sum of the numbers on the cards is 6, what is the probability that one of the two cards drawn is numbered 3 ? | [
"1/3",
"1/2",
"1/5",
"3/5",
"4/5"
] | (5,1) (1,5) (4,2) (2,4) (3,3) – only 5 possible scenarios for sum to be 6. One from this 5 has already happened.
From this five cases, only in one we have 3. So, the probability is 1 chances out of 5 that the one that occurred had 3: P=1/5.
Answer: C.
The answer is: C | C |
mathematics | A sum of money lent out at S.I. amounts to a total of $520 after 2 years and to $820 after a further period of 5 years. What was the initial sum of money that was invested? | [
"$340",
"$360",
"$380",
"$400",
"$420"
] | S.I for 5 years = $820 - $520 = $300
The S.I. is $60/year
S.I. for 2 years = $120
Principal = $520 - $120 = $400
The answer is D.
The answer is: D | D |
mathematics | A part of certain sum of money is invested at 9% per annum and the rest at 12% per annum, if the interest earned in each case for the same period is equal, then ratio of the sums invested is? | [
"4:2",
"4:8",
"4:3",
"4:0",
"4:9"
] | 12:9
= 4:3
Answer: C
The answer is: C | C |
mathematics | The average of five numbers is 27. If one number is excluded, the average becomes 25. The excluded number is? | [
"12",
"72",
"23",
"35",
"28"
] | Excluded number = (27 * 5) - (25 * 4)
= 135 - 100
= 35.
Answer: D
The answer is: D | D |
mathematics | A daughter lent $750 to her mother to help pay her rent. At the end of the month, the daughter received y dollars more than than the amount that was lent due to interest. The mother also gave her daughter an additional $5 for goodwill. In terms of y, what fraction of the total amount that the daughter received was the ... | [
"(5y-1)/(755-y)",
"5/(755+y)",
"5y/(755+y)-1",
"5y/(755+y)",
"5y"
] | The amount of money the daughter received was (750 + 5+ y) dollars. The $5 goodwill gift as a fraction of the amount received was, therefore, 5/(755+y).
Answer: B.
The answer is: B | B |
mathematics | P beats Q by 5 seconds in a race of 1000 m and Q beats R by 5 metres in a race of 100 m. By how many seconds does P beats R in a race of 1000 m? | [
"5 sec",
"7 sec",
"10 sec",
"Can't be determined",
"None of these"
] | Explanation :
If P takes t seconds to run 1000 m, then Q takes (t+5) sec.
In (t+5) sec Q runs 100 m whereas R runs only 950 m.
R runs 1000 m in (1000/950)x(t+5)sec.
P takes t seconds to cover 1000m , while R takes (20t/19+100/95)sec.
From the data given, we cannot determine t .
Answer : D
The answer is: D | D |
mathematics | John has 6 friends who want to ride in his new car that can accommodate only 5 people at a time (John plus 4 passengers). How many different combinations of 4 passengers can be formed from John's 6 friends? | [
"3",
"8",
"10",
"15",
"20"
] | 6C4 = 15
The answer is D.
The answer is: D | D |
mathematics | In 1990 the budgets for projects Q and V were $700,000 and $780,000, respectively. In each of the next 10 years, the budget for Q was increased by $30,000 and the budget for V was decreased by $10,000. In which year was the budget for Q equal to the budget for V ? | [
"1992",
"1993",
"1994",
"1995",
"1996"
] | Let the no of years it takes is x.
700+30x = 780-10x --> 40x = 80 and x=2.
Thus, it happens in 1992.
A.
The answer is: A | A |
mathematics | A shop that sells phone accessories had the following sales: 10 thousand earbuds at $10 each, 5300 phone cases at $12 each and 450 power banks at $50 each. What % of the shop's revenue is from power banks? | [
"11.1%",
"12.1%",
"10.1%",
"9.1%",
"13.1%"
] | Correct Answer: B
The company's total revenue from earbuds=10000*$10=$100000
The company's total revenue from phone cases=5300*$12=$63600
The company's total revenue from power banks=450*$50=$22500
The combined total of all sales=$186100
Therefore % of power banks sales=22500/186100*100= 12.1%
The answer is: B | B |
mathematics | In how many ways can you line up 7 wrestlers in a row if one of them, Houdidi, cannot be in the middle or at the either end? | [
"1,850",
"929",
"828",
"724",
"2,880"
] | Since Houdini cannot be placed in the middle or at either end (3 spots), then he can choose 4 spots to sit. The remaining 6 apples can be placed in in 6! ways. Thus the # of arrangements is 4*6! = 2,880.
Answer: E.
The answer is: E | E |
mathematics | A 14 cm long wire is to be cut into two pieces so that one piece will be 2/5th of the other, how many centimeters will the shorter piece be? | [
"12",
"20",
"88",
"77",
"4"
] | 1: 2/5 = 5: 2
2/7 * 14 = 4
Answer: E
The answer is: E | E |
mathematics | A straight line is formed using two points A(3,3) and B(6,6). Another point P(x,y) lies between A and B such that AP/BP = 2. What are the coordinates of P? | [
"(7/2, 7/2)",
"(4, 4)",
"(21/5, 21/5)",
"(9/2, 9/2)",
"(5, 5)"
] | The equation of the straight line is y = x, so the x- and y-coordinates of P are the same.
The x, y coordinates are 2/3 of the distance from 3 to 6.
x = 3 + (6-3)*(2/3) = 3 + 2 = 5 = y
The answer is E.
The answer is: E | E |
mathematics | A train 360 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 160 m long? | [
"41.6 sec",
"11 sec",
"88 sec",
"19 sec",
"10 sec"
] | Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 160 = 520 m
Required time = 520 * 2/25 = 41.6 sec
Answer: A
The answer is: A | A |
mathematics | Barbara has 8 shirts and 12 pants. How many clothing combinations does Barbara have, if she doesn’t wear 2 specific shirts with 3 specific pants? | [
"126",
"120",
"101",
"112",
"115"
] | 8 shirts
9 pants
we can combine 2 shirts with (12-3) pants
2*9=18
we can combine the other shirts (6) with any pants (9)
9*12=54
Thus total :108+18=126 ANS:A
The answer is: A | A |
mathematics | John has 10 pairs of matched socks. If he loses 3 individual socks, what is the greatest number of pairs of matched socks he can have left? | [
"7",
"8",
"5",
"4",
"3"
] | Because we have to maximize the pair of matched socks, we will remove 1 pairs(2 socks) out of 10 pairs 1 sock from the 2th pair.
Thus the no of matching socks pair remaining = 10 - 2 = 8
Answer B
The answer is: B | B |
mathematics | A volume of 11780 l water is in a container of sphere. How many hemisphere of volume 4l each will be required to transfer all the water into the small hemispheres? | [
"2812",
"8231",
"2734",
"4222",
"2945"
] | a volume of 4l can be kept in 1 hemisphere
therefore, a volume of 11780l can be kept in (11780/4) hemispheres
ans.2945
ANSWER:E
The answer is: E | E |
mathematics | By the how much is two-fifth of 150 greater than three -fifths of 25? | [
"15",
"3",
"45",
"30",
"None of these"
] | Reqd no. = 2â„5 × 150 - 3â„5 × 25
= 60 - 15 = 45
Answer C
The answer is: C | C |
mathematics | If the sum of a number and its square is 342, What is the number? | [
"16",
"77",
"25",
"87",
"18"
] | Explanation:
Let the integer be x.
Then, x + x2 = 342
x2 + x - 342 = 0
(x + 19) (x – 18) = 0
x = 18
ANSWER: E
The answer is: E | E |
mathematics | A 300 meter long train running at the speed of 120 kmph crosses another train running in the opposite direction at the speed of 80 kmph in 9 seconds.What is the lenght of other train. | [
"210m",
"220m",
"230m",
"240m",
"200m"
] | Relative speeds=(120+80)km/hr
=200km/hr=(200*5/18)m/s=(500/9)m/s
let length of train be xm
x+300/9=500/9
x=200
Ans is 200m
ANSWER:E
The answer is: E | E |
mathematics | ((1^m)/(5^m))((1^16)/(4^16)) = 1/(2(10)^31)
What is m? | [
"17",
"18",
"34",
"31",
"36"
] | ((1^m)/(5^m))((1^16)/(4^16)) = 1/(2(10)^31)
((1/5)^m ) * ((1/2)^32) = 1/ (2 * (2*5)^31))
2^36 will cancel out,since 1 can be written as 1^35 ,So (1/5)^m= (1/5)^31
((1/5)^m ) * ((1/2)^32) = 1/[(2^32)*(5^31)]
So, m=31
Answer D
The answer is: D | D |
mathematics | At the end of three years what will be the compound interest at the rate of 10% p.a. on an amount of Rs.30000? | [
"9930",
"1879",
"2779",
"2672",
"2782"
] | A = 30000(11/10)^3
= 39930
= 30000
----------
9930
Answer: A
The answer is: A | A |
mathematics | How many digits will be there to the right of the decimal point in the product of 95.75 and .02554 ? | [
"5",
"6",
"7",
"8",
"9"
] | EXPLANATION
Sum of decimal places = 7.
Since the last digit to the extreme right will be zero (since 5 x 4 = 20), so there will be 6 significant digits to the right of the decimal point.
Answer B
The answer is: B | B |
mathematics | Before lunch, a painter can paint a wall at a rate of r square feet per minute. The same painter, after lunch and a cup of coffee, can paint the same wall at a rate r + 1 square feet per minute, and the same wall would be finished in 30 seconds less time. What is the value of r? | [
"1/3",
"3",
"1/2",
"1",
"2"
] | Convert 30 seconds to 1/2 minute
Equation: 1/r = 1/(r + 1) + 1/2
Plug options into the equation:
D fits: 1/1 = 1/(1 + 1) + 1/2
Answer: D
The answer is: D | D |
mathematics | The graphs of the two linear equations ax + by = c and bx - ay = c, where a, b and c are all not equal to zero, | [
"are parallel",
"intersect at one point but not perpendicular",
"intersect at two points",
"perpendicular",
"none of the above"
] | find the slopes of the two lines
a x + b y = c , slope m1 = - a / b
b x - a y = c , slope m2 = b / a
m1*m2 = (- a / b)(b / a) = - 1
The two lines are perpendicular
ANSWER : D
The answer is: D | D |
mathematics | Simplify: (4 – 5) – (13 – 18 + 2). | [
"5",
"4",
"-3",
"2",
"-1"
] | (4 – 5) – (13 – 18 + 2).
= -1-(13+2-18).
= -1-(15-18).
= -1-(-3).
= -1+3.
= 2.
correct answer D
The answer is: D | D |
mathematics | A store has 10 bottles of juice, including 5 bottles of apple juice. In the evening, 6 bottles of juice are sold one by one. What is the probability of selling 4 bottles of apple juice among the 6 bottles? Assume that every bottle has an equal chance of being bought. | [
"2/7",
"3/11",
"4/15",
"5/21",
"6/25"
] | The total number of ways to sell 6 bottles from 10 is 10C6 = 210.
The number of ways to sell 4 bottles of apple juice is 5C4*5C2 = 5*10 = 50
P(selling 4 bottles of apple juice) = 50/210 = 5/21
The answer is D.
The answer is: D | D |
mathematics | A is a positive integer. when a is divided by 4 the remainder is 3, and when divided by 9 the remainder is 1. what is the remainder if a is divided by 52? | [
"Between 1 and5, inclusive",
"Between 10 and15, inclusive",
"5",
"Between 8 and 12, inclusive",
"Between 4 and 8, inclusive"
] | Given the integer a
4a+3= 9a+5
Start 4a+3 -->7, 11, 15,...59,....
Of these only 55 fit the description 9a+5. The remainder when divided by 52 is 7. So answer is E).
Answer = E)
The answer is: E | E |
mathematics | Of the 65 cars on a car lot, 45 have air-bag, 30 have power windows, and 12 have both air-bag and power windows. How many of the cars on the lot have neither air-bag nor power windows? | [
"8",
"2",
"10",
"15",
"18"
] | Total -Neither = All Air bag + All Power Windows - Both
or 65 - Neither = 45 + 30 -12 = 63.
=> Neither = 2, hence B.
Answer : B
The answer is: B | B |
mathematics | Mangala completes a piece of work in 12 days, Raju completes the same work in 18 days. If both of them work together, then the number of days required to complete the work is? | [
"5.2 days",
"6.2 days",
"7.2 days",
"8.2 days",
"9.2 days"
] | If A can complete a work in x days and B can complete the same work in y days, then, both
of them together can complete the work in x y/ x+ y days.
That is, the required No. of days = 12 × 18/30 = 7.2 days.
C)
The answer is: C | C |
mathematics | A and B started a partnership business investing some amount in the ratio of 3 : 5. C joined then after 3 months with an amount equal to that of B. In what proportion should the profit at the end of one year be distributed among A, B and C? | [
"4 : 9 : 8",
"5 : 7 : 4",
"6 : 10 : 7.5",
"7 : 9: 4",
"5 : 4 : 8"
] | Let the initial investments of A and B be 3x and 5x.
A : B : C = (3x x 12) : (5x x 12) : (5x x 9) = 36 : 60 : 45
= 6 : 10 : 7.5.
ANSWER :C
The answer is: C | C |
mathematics | Which of the following is the lowest positive integer that is divisible by 4, 5, 6, 7, 8, 9, and 10? | [
"1680",
"1950",
"2230",
"2520",
"2870"
] | The number needs to be divisible by 2^2, 5, 2*3, 7, 2^3, 3^2, and 2*5.
The lowest positive integer is 7 * 2^3 * 3^2 * 5 = 2520
The answer is D.
The answer is: D | D |
mathematics | A student chose a number, multiplied it by 2, then subtracted 138 from the result and got 104. What was the number he chose? | [
"123",
"121",
"277",
"267",
"120"
] | Let xx be the number he chose, then
2⋅x−138=104 2⋅x−138=104
x=121
Answer:B
The answer is: B | B |
mathematics | Angelina walked 250 meters from her home to the grocery at a constant speed. She then walked 360 meters to the gym at double the speed. She spent 70 seconds less on her way from the grocery to the gym than on her way from home to the grocery. What was Angelina's speed, in meters per second, from the grocery to the gym? | [
"2",
"3",
"4",
"6",
"12"
] | let the speed be X...
so time taken from home to grocery= 250/x..
the speed to gym = 2x..
so time taken = 360/2x=180/x..
its given 250/x-180/x=70..
70/x=70..
x=1m/secs..
so grocery to gym=2*1=2m/s...
Answer : A
The answer is: A | A |
mathematics | Fred and Sam are standing 35 miles apart and they start walking in a straight line toward each other at the same time. If Fred walks at a constant speed of 2 miles per hour and Sam walks at a constant speed of 5 miles per hour, how many miles has Sam walked when they meet? | [
"5",
"9",
"25",
"30",
"45"
] | relative distance =35 miles
relative speed =2+5 =7 miles per hour
time taken =35/7=5 hours
distance travelled by sam =5*5=25 miles=C
The answer is: C | C |
mathematics | Before being simplified, the instructions for computing income tax in Country R were to add 2 percent of one's annual income to the average (arithmetic mean) of 100 units of Country R's currency and 1 percent of one's annual income. Which of the following represents the simplified formula for computing the income tax, ... | [
"50+A/200",
"50+3A/100",
"50+A/40",
"100+A/50",
"100+3A/100"
] | the simplified formula for computing the income tax, in Country R's currency, for a person in that country
annual income is A:50+A/40
ANSWER:C
The answer is: C | C |
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