subject stringclasses 1
value | question stringlengths 3 1.14k | options listlengths 5 5 | solution stringlengths 18 3.7k | answer stringclasses 5
values |
|---|---|---|---|---|
mathematics | 5 3 -2 -5 -3 2....What is the sum of first thirty number sequence? | [
"0",
"1",
"2",
"3",
"4"
] | 5 3 -2 -5 -3 2 5 3 -2 -5 -3 2 5 3 -2 -5 -3 2 5 3 -2 -5 -3 2 5 3 -2 -5 -3 2
=> 50-50=0.
ANSWER:A
The answer is: A | A |
mathematics | Robert spent $120 in buying raw materials, $195 in buying machinery and 10% of the total amount he had as cash with him. What was the total amount? | [
"A)$150",
"B)$210",
"C)$350",
"D)$160",
"E)$200"
] | Let the total amount be x
then, (100-10)% of x = 120+195
90% of x = 315
90x/100 = 315
x = $350
Answer is C
The answer is: C | C |
mathematics | The breath of a rectangular landscape is 6 times its length. There is a playground in it whose area is 4200 square mtr & which is 1/7 th of the total landscape. What is the breath of the landscape? | [
"520",
"420",
"320",
"550",
"450"
] | Sol. 6x * x =7* 4200
x = 70
Length = 6* 70 = 420 B
The answer is: B | B |
mathematics | A side of beef lost 35 percent of its weight in processing. If the side of beef weighed 545 pounds after processing, how many pounds did it weigh before processing? | [
"191",
"355",
"737",
"838",
"1,560"
] | Let weight of side of beef before processing = x
(65/100)*x = 545
=> x = (545 * 100)/65 = 838
Answer D
The answer is: D | D |
mathematics | The sum of the mean, the median, and the range of the set {5,6,7} equals which one of the following values? | [
"18",
"14",
"16",
"12",
"10"
] | Here Mean => 5+6+7/3 => 6
median => 6
and range => 7-1 => 6
hence sum => 6+6+6=> 18
Answer: A
The answer is: A | A |
mathematics | At what rate percent on simple interest will a sum of money double itself in 30 years? | [
"3 1/3%",
"3 5/3%",
"3 1/9%",
"3 1/5%",
"3 1/7%"
] | P = (P*30*R)/100
R = 3 1/3%
Answer:A
The answer is: A | A |
mathematics | Kurt, a French painter, has 9 jars of paint: 4 jars of yellow paint, 2 jars of red paint, and 3 jars of brown paint. Kurt pours the contents of 3 jars of paint into a new container to make a new color, which he will name according to the following conditions:
The paint will be namedBrun Yif it contains 2 jars of brown ... | [
"5/42",
"37/42",
"1/21",
"4/9",
"5/9"
] | I get B.
Jaune Y = (4 choose 1)*(5 choose 2) = 4*10 = 40
Jaune X = (4 choose 2)*(5 choose 1) + (4 choose 3) = 6*5 + 4 = 34
Total combinations = 9 choose 3 = 84
Probability of Jaune MM = (40 + 34)/84 = 37/42.B
The answer is: B | B |
mathematics | In a mixture of 45 litres, the ratio of acid to base is 3 : 2. How much base must be added to make the ratio 9: 11? | [
"10 lts",
"15 lts",
"17 lts",
"20 lts",
"22 lts"
] | Let M = 3K,W = 2K
Thus, 3K + 2K = 45
=> K=9
=> acid = 27 litres and base = 18 litres.
Now suppose x litres of base is added to the mixture such that
27/(18 + X) = 9/11
=>162 +9X = 297
=> 9X = 135
=> X = 15
ANSWER:B
The answer is: B | B |
mathematics | The average age of A, B and C is 27 years. If the average age of A and C is 29 years, what is the age of B in years ? | [
"19",
"35",
"20",
"32",
"23"
] | Age of B = Age of (A + B + C) Γ’β¬β Age of (A + C) = 27 Γβ 3 Γ’β¬β 29 Γβ 2 = 81 Γ’β¬β 58 = 23 years
E
The answer is: E | E |
mathematics | How many seconds will a train 100 meters long take to cross a bridge 250 meters long if the speed of the train is 36 kmph? | [
"54 sec",
"35 sec",
"25 sec",
"45 sec",
"24 sec"
] | D = 100 + 250 = 350
S = 36 * 5/18 = 10 mps
T = 350/10 = 35 sec
Answer:B
The answer is: B | B |
mathematics | In a mixture of 60 liters, the ratio of milk and water is 2:1. What amount of water must be added to make the ratio of milk and water as 1:2? | [
"76 liters",
"86 liters",
"60 liters",
"34 liters",
"18 liters"
] | 2:1 --- 60
1:2
2:4
---------------
3
3 ----------- 60
3 ----------- ? => 60 liters
Answer:C
The answer is: C | C |
mathematics | The password for a computer account has to consist of exactly eight characters. Characters can be chosen from any of the following: letter of the alphabet, numerical digits from 0 to 9, a hyphen, or the exclamation mark. Upper-case letters (e.g., A) are considered different from lower-case letters (e.g., a), and charac... | [
"2^9",
"2^14",
"2^18",
"2^40",
"2^48"
] | 26 letters in the alphabet, 26*2 = 52 letters, since the password is case-sensitive. Accounting for possibilities of the other special characters we have;
26+26+10+1+1 = 64, or 2^6 possibilities per character of the password.
Total number of possible combinations: (2^6)^8 = 2^48
ANSWER:E
The answer is: E | E |
mathematics | A company produces 72000 bottles of water everyday. If a case can hold 9 bottles of water .How many cases are required by the company to hold its one day production | [
"2000",
"4500",
"5000",
"8000",
"9000"
] | Number of bottles that can be held in a case = 9.
Number of cases required to hold 72000 bottles = 72000/9=8000 cases.
So the answer is D =8000
The answer is: D | D |
mathematics | How many five letter combinations can be formed using the letters of the word CARTS? | [
"12",
"20",
"60",
"120",
"200"
] | The number of letters in the given word is four.
The number of five letter combinations that can be formed using these five letters is
= 5 * 4 * 3 * 2 * 1= 120.
Answer: D
The answer is: D | D |
mathematics | In filling a room with gas 100 m * 10 m * 10 m the volumes of gas will be? | [
"100 cu.m",
"1000 cu.m",
"10000 cu.m",
"100000 cu.m",
"10000000 cu.m"
] | 100 * 10 * 10 = 10000
ANSWER:C
The answer is: C | C |
mathematics | Suppose you want to buy three loaves of bread that cost $1.50 each
and a jar of peanut butter that costs $4. A jar of jelly is $2.75, but you
donβt need any jelly. You have $10. How much money will you have left
over? | [
"$1.50",
"$2.50",
"$3.50",
"$4.50",
"$5.50"
] | The jelly is extra information. 10.00 β 3 x 1.50 β 4.00 =
10.00 β 4.50 β 4.00 = 1.50.
You have $1.50 left.
correct answer A
The answer is: A | A |
mathematics | What is the height of the triangle?
I. The area of the triangle is 20 times its base.
II. The perimeter of the triangle is equal to the perimeter of a square of side 10 cm. | [
"I alone sufficient while II alone not sufficient to answer",
"II alone sufficient while I alone not sufficient to answer",
"Either I or II alone sufficient to answer",
"Both I and II are not sufficient to answer",
"Both I and II are necessary to answer"
] | EXPLANATION
I. A = 20 x B β1-div-1by2 x B x H = 20 x BβH = 40.
I alone gives the answer.
II gives, perimeter of the triangle = 40 cm.
This does not give the height of the triangle.
answer is (A).
The answer is: A | A |
mathematics | How many odd factors does 210 have? | [
"3",
"4",
"5",
"6",
"8"
] | Start with the prime factorization: 210 = 2*3*5*7
For odd factors, we put aside the factor of two, and look at the other prime factors.
set of exponents = {1, 1, 1}
plus 1 to each = {2, 2, 2}
product = 2*2*2 = 8
Therefore, there are 8 odd factors of 210. In case you are curious, they are {1, 3, 5, 7, 15, 21, 35, and 10... | E |
mathematics | A man has some hens and cows. If the number of heads be 48 and the number of feet equals 140, then the number of cows will be: | [
"30",
"23",
"24",
"26",
"22"
] | Explanation:
Let the number of hens be x and the number of cows be y.
Then, x + y = 48 .... (i)
and 2x + 4y = 140 x + 2y = 70 .... (ii)
Solving (i) and (ii) we get: x = 26, y = 22.
The required answer = 22.
Answer: E
The answer is: E | E |
mathematics | During the first two weeks of January, the total rainfall in Springdale was 35 inches. If the rainfall during the second week was 1.5 times the rainfall during the first week, what was the rainfall during the second week of January? | [
"5 inches",
"6 inches",
"9 inches",
"10 inches",
"21 inches"
] | Total rainfall in 2 weeks = 35 inches.
Assume the rainfall in second week = 1.x
Rainfall in first week = x
Total rainfall = 2.5x = 35 inches
x = 14 and 1.5x = 21
Rainfall during second week = 21 inches
Option E
The answer is: E | E |
mathematics | A project has three test cases. Three teams are formed to study the three different test cases. James is assigned to all three teams. Except for James, each researcher is assigned to exactly one team. If each team has exactly 7 members, then what is the exact number of researchers required? | [
"23",
"20",
"21",
"22",
"19"
] | alternatively, we have
7*3-2( because james is included in all the three teams)
=19
E
The answer is: E | E |
mathematics | X and Y invest Rs.21000 and Rs.17500 respectively in a business. At the end of the year, they make a profit of Rs.26400. What is the share of X in the profit? | [
"Rs.14400",
"Rs.26400",
"Rs.12000",
"Rs.12500",
"None of these"
] | Explanation :
Ratio of the investment = 21000 : 17500 = 210 : 175 = 42 : 35 = 6 : 5
Share of X in the profit = 26400 * (6/11) = 2400 * 6 = 14400 .. Answer : Option A
The answer is: A | A |
mathematics | 45 girls and 60 boys are present at a party. There are 17 girl-boy are in relationship among them. If a girl and a boy is selected at random, what is the probability that they will be a couple? | [
"1/200",
"1/100",
"90/2900",
"17/2700",
"1/20"
] | In how many ways we can select a girl and a boy from 45 lady and 60 gentlemen? In 45*60 = 2,700 ways.
We have a total of 17 couples so, the probability of selecting a couple is 17/2,700 = 17/2700.
Ans- D
The answer is: D | D |
mathematics | With a uniform speed a car covers the distance in 8 hours. Had the speed been increased by 3 km/hr, the same distance could have been covered in 7 1/2 hours. What is the distance covered? | [
"360 km",
"480 km",
"278 km",
"297 km",
"671 km"
] | Let the distance be x km. Then,
x/(7 1/2) - x/8 = 3
2x/15 - x/8 = 3 => x = 360 km.
Answer:A
The answer is: A | A |
mathematics | In the xy plane line m has the equation 4x + y = t. Line n passes through the origin and is perpendicular to line m. If point p has the coordinates (r, r+1) and is on both line n and m what is the value of r? | [
"-4/3",
"1/4",
"-4",
"3/4",
"4/3"
] | The equation of line m is y=-4x+t. Now, since line n is perpendicular to line m, then its slope is negative reciprocal of the slope of line m, so the slope of n is 1/4. Next, as line n passes through the origin (0, 0) and has the slope of 1/4 then its equation is y=1/4*x.
Point (r, r+1) lies on line n means that (r+1)=... | A |
mathematics | Subtracting 10% from X is the same as multiplying X by what number? | [
"12",
"90",
"26",
"27",
"18"
] | X - (10/100) X = X * ?
? = 90%
Answer:B
The answer is: B | B |
mathematics | How much 60% of 50 is greater than 40% of 30? | [
"18",
"91",
"11",
"17",
"12"
] | (60/100) * 50 β (40/100) * 30
30 - 12 = 18
Answer: A
The answer is: A | A |
mathematics | A taxi company charges $1.40 for the first quarter of a mile and fifteen cents for each additional quarter of a mile. What is the maximum distance someone could travel with $4.90? | [
"4 miles",
"4 1/4 miles",
"4 3/4 miles",
"5 1/2 miles",
"6 miles"
] | If we start out with $4.90 and have to spend $1.40 for the first quarter-mile, we will have $3.50 left to spend on quarter-mile intervals.
Since $3.50/$0.15 = 23.33, we can buy 23.33 more quarter-miles, and will travel 24.33 quarter miles in all:
24.33 Γ 1/4 = 6 miles.
The correct answer is choice (E).
The answer is: E | E |
mathematics | If $30,000 interest is invested in 10 percent simple annual interest for 2 years, which of the following represents the total amount of interest, in dollars, that will be earned by this investment in the 2 years? | [
"$6000",
"$4000",
"$5000",
"$3000",
"$2000"
] | 30000*10/100*2 = $6000
Answer : A
The answer is: A | A |
mathematics | Malar and Roja combined will complete a task in 35 days, but Malar alone can complete same work in 60 days. Calculate in how many days Roja can complete this work ? | [
"85 days",
"45 days",
"90 days",
"84 days",
"95 days"
] | Malar - 35 days =>1/35
Roja - 60 days =>1/60
Malar one day work = 1/35-1/60
=1/84
==>84 days
ANSWER D
The answer is: D | D |
mathematics | If difference between compound interest and simple interest on a sum at 10% P.a. for 2 years is Rs.150 then sum is | [
"s.15000",
"s.15100",
"s.15800",
"s.16000",
"s.16200"
] | p(r/100)^2=C.I-S.I
P(10/100)^2=150
15000
ANSWER:A
The answer is: A | A |
mathematics | How many seconds will a train 100 meters long take to cross a bridge 180 meters long if the speed of the train is 36 kmph? | [
"22 sec",
"27 sec",
"25 sec",
"24 sec",
"28 sec"
] | Explanation:
D = 100 + 180 = 280
S = 36 * 5/18 = 10 mps
T = 280/10 = 28 sec
Answer: Option E
The answer is: E | E |
mathematics | A cistern normally takes 6 hours to be filled by a tap but because of a leak, 2 hours more. In how many hours will the leak empty a full cistern ? | [
"20 hours",
"24 hours",
"26 hours",
"18 hours",
"None of these"
] | β΅ cistern fill in 6 hours.
β΄ in 1 hour, filled part = 1β6th
Now, due to leakage, filled part in 1 hour = 1β8th
Part of the cistern emptied, due to leakage in 1 hour
= 1β6 - 1β8 = 1β24th
β΄ The leakage will empty the full cistern in 24 hrs.
Answer B
The answer is: B | B |
mathematics | Jack and Dick work at a hospital with 4 other workers. For an internal review, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that Jack and Dick will both be chosen? | [
"A)1/3",
"B)1/4",
"C)1/15",
"D)3/8",
"E)2/3"
] | Total number of people = 6
Probability of selecting Jack first and then Dick is 1/6β1/5=1/30
Probability of selecting Dick first and then Jack is 1/6β1/5=1/30
Therefore probability of selecting Jack and Dick for the review is 1/30+1/30=1/15
Answer is C
The answer is: C | C |
mathematics | I buy coffee from 3 different shops at Rs.150,Rs.140,Rs.130 per kg and mix them in proportion 8:5:3.At what price per kg must I sell the mixture to make a profit of 25%? | [
"168.906",
"178.906",
"188.906",
"198.906",
"158.906"
] | total=16x kg, tot cp=2290x
sp should be=2862.5x
so sp/kg=178.906
ANSWER:B
The answer is: B | B |
mathematics | It takes printer A 4 more minutes more than printer B to print 40 pages. Working together, the two printers can print 50 pages in 6 minutes. How long will it take Printer A to print 100 pages? | [
"12",
"18",
"20",
"24",
"30"
] | If it takes 4 more minutes for A to print 40 pages than it takes B,
it takes 5 more minutes for A to print 50 pages than it takes B.
Thus if b is the number of minutes than B takes to print 50 pages,
we can write:
1/b+1/(b+5)=1/6 (since in 1 minute, they print 1/6th of the 50 page job)
6(2b+5)=b(b+5)
b^2-7b-30=0
(b-10)... | E |
mathematics | In a circuit board factory, all circuit boards that pass a verification process are certified. Every board that fails the verification process is indeed faulty, but 1/8 of those that pass are also faulty.
Approximately how many faulty circuit boards exist in a group of 400 circuit boards where 64 fail inspection? | [
"106",
"192",
"200",
"256",
"264"
] | Total of 400 boards. All that fail verification are indeed faulty. So the 64 are indeed faulty. 1/8 those that pass are also faulty.
From the 400 we know 64 fail. So 336 must pass. Of these 1/8 are faulty. 336 divided by 8 gives you 42.
What one must do now is to add to the 42 which were not detected the actually detec... | A |
mathematics | In 10 years,A will be 5 times as old as B was 10 years ago.If A is now 9 years older than B,the present age of B is : | [
"17.25 Years",
"29 Years",
"39 Years",
"49 Years",
"59 Years"
] | Solution
Let B's present age = x years.Then,A's present age =(x +9) years.
Γ’ΛΒ΄ (x + 9)+ 10 = 5 (x - 10) Γ’β‘β x + 19 = 5x- 50 Γ’β‘β 4x = 69.
x = 17.25
Answer A
The answer is: A | A |
mathematics | Robin is traveling from one end of a forest to the other. In order to find her way back, she is leaving morsels of bread in the following pattern: 2 morsels of RICE , 3 morsels of white, and 1 morsel of rye. The pattern repeats after she leaves the morsel of rye. If Robin drops 2,000 morsels of bread, what are the last... | [
"rye β wheat β wheat",
"RY-R-R",
"white β rye β wheat",
"white β white β white",
"white β white β rye"
] | Q is nothing BUT asking about remainder..
total morsels thrown before the pattern is repeated = 2+3+1 = 6..
so REMAINDER when 2000 is div by 6..
1998 is EVEN and also div by 3, so remainder is 2..
Last 3 of morsels are 1998-1999-2000
so he uses the last of morsel of pattern in 1998 two of the first morsels of the patte... | B |
mathematics | Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 7 sec. What is the length of the fast train? | [
"27 7/6",
"27 7/5",
"27 7/2",
"350/9",
"27 7/1"
] | Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 7 = 350/9
= 350/9 m.
Answer:D
The answer is: D | D |
mathematics | The ratio of men to women in the Snyder community choir is 4 to 5. The ratio of men to women in the Leigh community choir is 5 to 6. If the two choirs merged, the ratio of men to women in the combined choir would be 22 to 27. If Snyder has 4 more men and 6 more women than Leigh, how many women are in the Snyder choir? | [
"20",
"24",
"30",
"32",
"34"
] | Use simultaneous equations / By combination
4x = 5y + 4
5x = 6y + 6
Multiply (1) by 6
Multiply (2) by -5
Get rid of y, and x = 6
Then 5x = 30
ANSWER:C
The answer is: C | C |
mathematics | Total value of the quantity sold for item C is what per cent of the total value of the quantity sold for Item E? | [
"30",
"60",
"100",
"80",
"90"
] | E
90
Total value of the quantity sold for item C = Rs(45 Γ 7.5 Γ 100)
= Rs 33750
Total value of the quantity sold for item E = Rs(15 Γ 25 Γ 100) = Rs 37500
β΄ Required percentage = 33750/37500X 100 = 90
The answer is: E | E |
mathematics | How many values of c in x^2 - 5x + c, result in rational roots which are integers? | [
"23",
"27",
"25",
"12",
"82"
] | Explanation:
By the quadratic formula, the roots of x2β5x+c=0x2β5x+c=0 are β(β5)Β±β52β4(1)(c)ββββββββββββ2(1)β(β5)Β±β52β4(1)(c)2(1) = 5Β±25β4cβββββββ25Β±25β4c2
To get rational roots, 25β4c25β4c should be square of an odd number. Why? because 5 + odd only divided by 2 perfectly.
Now let 25 - 4c = 1, then c = 6
If 25 - 4c = ... | C |
mathematics | If a, b, and c are integers and a*b^2/c is a positive even integer, which of the following must be true?
I. c is even
II. ab > 4
III. ab is even | [
"I only",
"III only",
"I and II",
"I and III",
"I, II, and III"
] | Two ways this can happen: 1- Even/ Even= Even or 2- Even/Odd= Even
So Ab MUST be even, with either A or B being even, Ab does not have to be positive, as B could be negative and once it is raised to 2 it becomes positive again, and of course, C could be Odd or Even as described above.
III only.letter B
The answer is: B | B |
mathematics | A set of consecutive positive integers beginning with 1 is written on the blackboard. A student came along and erased one number. The average of the remaining numbers is 35*7/17. What was the number erased? | [
"7",
"8",
"6",
"5",
"4"
] | Explanation :
Let the higher number be n and x be the number erased.
Then((n(n+1)/2)+x)/(n+1) = 35*7/17 = 602/17
Hence, n = 69 and x =7 satisfy the above conditions.
Answer : A
The answer is: A | A |
mathematics | A can complete a certain job in 7 days. B is 40% more efficient than A. In how many days can B complete the same job? | [
"5",
"6.25",
"7",
"7.5",
"4.8"
] | Let, Total Work Unit = 70 Units
A can finish in 7 days = 70 unit work
i.e. A can finish in 1 days = 10 unit work
i.e. B can finish in 1 days = 10+(40/100)*10 = 14 unit work
Days in which B will complete the work alone = 70/14 = 5 days
Answer: Option A
The answer is: A | A |
mathematics | Little John had $7.10. He spent $1.05 on sweets and gave to his two friends $1.00 each. How much money was left? | [
"$4.85",
"$4.15",
"$4.65",
"$4.55",
"$4.05"
] | John spent and gave to his two friends a total of
1.05 + 1.00 + 1.00 = $3.05
Money left
7.10 - 3.05 = $4.05
Answer :E
The answer is: E | E |
mathematics | If n = 2Γ3Γ5Γ7Γ11Γ13Γ15, then which of the following statements must be true?
I. n^2 is divisible by 600
II. n + 19 is divisible by 19
III. (n + 4)/2 is even | [
"I only",
"II only",
"I and III",
"III only",
"None of the above"
] | Statement I: 600 = (2^3)*(3)*(5^2) this is true.
Statement 2: this is NOT true.
Statement 3: (n+4)/2 = n/2 + 2, So this is true.
Hence option (C).
The answer is: C | C |
mathematics | If the speed of x meters per second is equivalent to the speed of Y mile per hour, what is y in terms of x? (1 mile = 1609.34 meter) | [
"1.21x",
"1.33x",
"2.23x",
"2.84x",
"3.13x"
] | x meters per second -->
--> 3,600x meters per hour(as there are 3,600 seconds in one hour);
--> 3,600x/1,609.34=2.236x miles per hour (as there are 1,609.34 meters in one mile).
Answer: C.
The answer is: C | C |
mathematics | A train 600 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is? | [
"298 m",
"268 m",
"700 m",
"267 m",
"181 m"
] | Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (600 + x)/60 = 65/3
x = 700 m.
Answer: C
The answer is: C | C |
mathematics | Two cars are traveling towards each other. If car A is traveling at a speed of 50 mph and car B is traveling 12% slower, how much time will it take the cars to meet if the initial distance between the two is 705 miles? | [
"Six hours and 30 minutes.",
"Seven hours and 30 minutes.",
"Eight hours and 20 minutes.",
"Nine hours and 15 minutes.",
"Ten hours and 20 minutes."
] | since they are travelling towards each other, the total speed is 50 mph + 50*0.88 = 94 mph (0.88 since, the other car is 12% less than first one)
Distance to be covered is 705, so time taken = distance/speed = 705/94 = 7.5 hours or 7 hours and 30 mins.
Answer is B: Seven hours and 30 minutes.
The answer is: B | B |
mathematics | The average age of 'a' boys is βbβ years and of βnβ girls βcβ years. The average age of all together is? | [
"(ab β nc)/ (a + n) years",
"(ab + nc)/ (a - n) years",
"(ab + nc)/ (a + n) years",
"(ab β nc)/ (a - n) years",
"None of these"
] | (ab + nc) / (a+ n)
ANSWER:C
The answer is: C | C |
mathematics | A sum of money is divided among A, B, C & D in the ratio 3:5:8:9 respectively. If the share of D Rs.1872 more than the share of A, then what is the total amount of money of B & C together? | [
"Rs. 4000",
"Rs. 4056",
"Rs. 4060",
"Rs. 4100",
"Rs. 4150"
] | Sol. Share of B + C = -3 x (5 + 8) = Rs. 4056
B
The answer is: B | B |
mathematics | 252 can be expressed as a product of primes as : | [
"2 x 2 x 3 x 3 x 7",
"2 x 2 x 2 x 3 x 7",
"3 x 3 x 3 x 3 x 7",
"2 x 3 x 3 x 3 x 7",
"2 x 3 x 7 x 3 x 2"
] | 252 = 2 x 2 x 3 x 3 x 7.
answer :A
The answer is: A | A |
mathematics | A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months? | [
"18:11",
"18:16",
"18:10",
"18:14",
"14:11"
] | A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only.
A : B
8000*18 : (8000*4) + (4000*14)
14400 : 88000
A:B = 18:11
Answer: A
The answer is: A | A |
mathematics | The average age of 3 boys is 15 years and their ages are in the proportion 1:2:3. The age of the youngest boy is? | [
"10 years",
"12 years",
"15 years",
"18 years",
"7.5 years"
] | Total age of 3 boys = 15*3 = 45
ratio of their ages = 1:2:3
Age of the youngest = 45*1/6 = 7.5 years
Answer is E
The answer is: E | E |
mathematics | 0.0006688/0.0000150 x 19.85 = ? | [
"850",
"900",
"950",
"1000",
"2000"
] | Explanation :
? = 6688/150 x 19.85 = 45 x 20 = 900
Answer : Option B
The answer is: B | B |
mathematics | A group of workers was put on a job. From the second day onwards, one worker was withdrawn each day. The job was finished when the last worker was withdrawn. Had no worker been withdrawn at any stage, the group would have finished the job in 55% of the time. How many workers were there in the group? | [
"33",
"38",
"23",
"10",
"27"
] | Explanation:
It can be solved easily through option.
\inline \left ( 10+9+8+....+1 \right )=10\left ( 10\times \frac{55}{100} \right )
55 = 55 Hence correct
Alternatively:
\inline \frac{n(n+1)}{2}=n\times \frac{55n}{100}
=> n= 10
In Both cases total work is 55man-days.
Answer: D) 10
The answer is: D | D |
mathematics | When 33 is divided by the positive integer k, the remainder is 3, for how many different values of k is this true? | [
"1",
"2",
"3",
"4",
"5"
] | This means that 30 must be a multiple of k.
The factors of 30 are 1, 2, 3, 5, 6, 10, 15, and 30.
Out of these, k can be 5, 6, 10, 15, and 30.
The answer is E.
The answer is: E | E |
mathematics | A letter lock consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most | [
"200",
"215",
"220",
"230",
"240"
] | Since each ring consists of six different letters, the total number of attempts possible with the three rings is = 6 * 6 * 6 = 216. Of these attempts, one of them is a successful attempt.
Maximum number of unsuccessful attempts = 216 - 1 = 215
B
The answer is: B | B |
mathematics | At the store, Sam bought a shirt and a toaster. There was a 5% sales tax on each item, and with tax, Sam paid a total of K. If the price of the toaster before tax was T, what, in terms of K and T, is the price of the shirt before tax? | [
"0.95(K β T)",
"0.95K β T",
"0.95(K β 1.05T)",
"(K β T)/1.05",
"(K/1.05) β T"
] | 1.05S + 1.05T = K
1.05S = K - 1.05T
S = (K/1.05) - T
The answer is E.
The answer is: E | E |
mathematics | In a km race, A beats Bby 28 metres or 7 seconds. Find A's timeoverthe course | [
"4 min",
"3 min. 3sec",
"4 min.4 sec",
"5 min. 3 sec",
"4 min. 3 sec"
] | Clearly, B covers 28 m in 7 seconds.
:. B's time over the course = (278 x 1000) sec = 250 seconds.
:. A's time over the course = (250 - 7-) sec = 243 sec
= 4 min. 3 sec.
Option E
The answer is: E | E |
mathematics | In Solution P, the proportion of water to alcohol is 5:1. In Solution Q, the proportion of water to alcohol is 2:1. If the two solutions are combined, what is the concentration of alcohol in the new solution if the original solutions were mixed in equal amounts? | [
"21%",
"23%",
"25%",
"27%",
"29%"
] | Let V be the total volume of the new solution.
The amount of alcohol added from Solution P is (1/6)*V/2=(1/12)*V
The amount of alcohol added from Solution Q is (1/3)*V/2=(1/6)*V
The total amount of alcohol in the new solution is (1/12+1/6)*V=(1/4)*V
The alcohol concentration is 1/4=25%
The answer is C.
The answer is: C | C |
mathematics | A train 300 m long can cross an electric pole in 15 sec and then find the speed of the train? | [
"65 Kmph",
"70 Kmph",
"72Kmph",
"75 Kmph",
"78 Kmph"
] | Length = Speed * time
Speed = L/T
S = 300/15
S = 20 M/Sec
Speed= 20*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 72 Kmph
ANSWER:C
The answer is: C | C |
mathematics | Which of the following CANNOT be true if the sum of k consecutive integers is 0, where k β₯ 1 ?
I. The product of the k integers is positive
II. The smallest of the k integers is zero
III. The largest of the k integers is negative | [
"I only",
"II only",
"III only",
"I and III",
"I, II and III"
] | for the sum of k consecutive integers to be 0 we have at least k=1 as 0
or if k=3 then 1,0,-1
1) product will be 0 every time......Not True
2)as stated earlier if k=1 as 0 then 0 is the highest as well lowest number.....Could be True
3) largest number can only be 0 if K=1 or any +ve integer if K>1--------->largest inte... | D |
mathematics | David has d books, which is 3 times as many as Jeff and 2/3 as many as Paula. How many books do the three of them have altogether, in terms of d? | [
"5/6*d",
"7/3*d",
"17/2*d",
"7/2*d",
"9/2*d"
] | Although we could plug in a real value for d, the problem can be just as easily solved by setting up equations. However, letβs start by defining some variables. Since we are given that David has d books, we can use variable d to represent how many books David has.
number of books David has = d
number of books Jeff has ... | C |
mathematics | A and B complete a work in 6 days. A alone can do it in 10 days. If both together can do the work in how many days? | [
"8 days",
"12 days",
"15 days",
"16 days",
"3.75 days"
] | Explanation:
1/6 + 1/10 = 8/30 = 4/15
15/4 = 3.75 days
Answer E
The answer is: E | E |
mathematics | In a function they are distributing noble prize. In how many ways can 3 prizes be distributed among 8 boys when a boy gets any no. of prizes? | [
"55",
"512",
"510",
"540",
"70"
] | Ans.(B)
Sol. In this case, repetitions are allowed, so all the three prizes can be given in 8 ways, i.e. (8 x 8x 8) ways = 83 ways = 512 ways Or nr ways = 83 ways = 512 ways
The answer is: B | B |
mathematics | If a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land Tails up exactly once in 3 consecutive flips ? | [
"0.125",
"0.375",
"0.325",
"0.5",
"0.666"
] | Total number of ways in which H or T can appear in 3 tosses of coin is
= 2 * 2 * 2 = 8 ways
For 2 T and 1 TH
Thus probability is
= P(HTT) + P(TTH) + P(THT)
= 1/8 + 1/8 + 1/8
= 3/8
= .375
Answer :B
The answer is: B | B |
mathematics | Among the first 1 million numbers, 40 is a number that is pretty unique.
Can you find out why ? | [
"36",
"31",
"45",
"39",
"40"
] | E
40
The number 40 (Forty) is the only number in one million numbers whose letters are arranged in the order they are arranged in English alphabets as well.
The answer is: E | E |
mathematics | If the perimeter of a rectangular garden is 1200 m, its length when its breadth is 240 m is? | [
"338 m",
"778 m",
"200 m",
"276 m",
"360 m"
] | 2(l + 240)
= 1200 => l
= 360 m
Answer:E
The answer is: E | E |
mathematics | The circumferences of two circles are 264 meters and 352 meters. Find the difference between the areas of the larger and the smaller circles. | [
"388",
"277",
"4312",
"2887",
"2992"
] | Let the radii of the smaller and the larger circles be s m and l m respectively.
2βs = 264 and 2βl = 352
s = 264/2β and l = 352/2β
Difference between the areas = βl2 - βs2
= β{1762/β2 - 1322/β2}
= 1762/β - 1322/β
= (176 - 132)(176 + 132)/β
= (44)(308)/(22/7) = (2)(308)(7) = 4312 sq m.Answer: C
The answer is: C | C |
mathematics | After successive discounts of 20%, 10% and 5% a certain good is sold for Rs. 6600. Find the actual price of the good. | [
"s. 6000",
"s. 9000",
"s. 10800",
"s. 9649",
"s. 9980"
] | Let actual price was 100.
After three successive discount this will become,
100 ==20% discount => 80 ==10% discount => 72 ==5% discount = 68.4
Now Compare,
68.4 = 6600
1 = 6600/68.4
100 = (6600*100)/68.4 = Rs. 9649.
Answer: Option D
The answer is: D | D |
mathematics | For an agricultural experiment, 300 seeds were planted in one plot and 200 were planted in a second plot. If exactly 20 percent of the seeds in the first plot germinated and exactly 35 percent of the seeds in the second plot germinated, what percent of the total number of seeds germinated? | [
"12%",
"26%",
"29%",
"30%",
"60%"
] | In the first plot 20% of 300 seeds germinated, so 0.20 x 300 = 60 seeds germinated.
In the second plot, 35% of 200 seeds germinated, so 0.35 x 200 = 70 seeds germinated.
Since 60 + 70 = 130 seeds germinated out of a total of 300 + 200 = 500 seeds, the percent of seeds that germinated is (130/500) x 100%, or 26%.
Answer... | B |
mathematics | A and B together can do a piece of work in 8 days. If A alone can do the same work in 12 days, then B alone can do the same work in? | [
"24",
"30",
"35",
"12",
"10"
] | b=188-1/2 = 1/24
=>24 days
ANSWER A
The answer is: A | A |
mathematics | If x*y = xy β 2(x + y) for all integers x and y, then 2* (β3) = | [
"β16",
"β11",
"β4",
"4",
"16"
] | The quickest (rather only) way is to apply the given formula:
2*(-3) = 2*(-3) - 2 (2 + (-3) ) = -6 +2 = -4
Option (C)
The answer is: C | C |
mathematics | There are 5 periods in each working day of a school. In how many ways can one organize 4 subjects such that each subject is allowed at least one period? | [
"240",
"250",
"260",
"280",
"None of these"
] | 4 subjects can be arranged in 5 periods in 5P4 ways.
Remaining 1 period can be arranged in 4P1 ways.
Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.
Total number of arrangements = (5P4 x 4P1)/2! = 240
ANSWER:A
The answer is: A | A |
mathematics | An empty fuel tank to a car was filled with A type of petrol. When the tank was half empty, it was filled with B type of petrol. Again when the tank was half empty, it was filled with A type of petrol. When the tank was half empty again,it was filled | [
"50%",
"40%",
"33.5%",
"37.5%",
"None of these"
] | Now, amount of petrol A = Aβ4 + Aβ8 = 3Aβ8
β΄ required% = 3Aβ (8 Γ A) Γ 100 = 37.50%
Answer D
The answer is: D | D |
mathematics | Fox jeans regularly sell for $15 a pair and Pony jeans regularly sell for $18 a pair. During a sale these regular unit prices are discounted at different rates so that a total of $9 is saved by purchasing 5 pairs of jeans: 3 pairs of Fox jeans and 2 pairs of Pony jeans. If the sum of the two discounts rates is 50 perce... | [
"9%",
"10%",
"110%",
"120%",
"150%"
] | x discount on Pony jeans, (0.5-x) discount on Fox jeans.
Set the equation: 3*15(0.5-x)+2*18x=9 --> x=1.5=150%
Answer: E.
The answer is: E | E |
mathematics | What is the average (arithmetic mean) of all the multiples of ten from 10 to 170 inclusive? | [
"90",
"80",
"100",
"105",
"110"
] | 10 and 190 inclusive would mean there are 17 terms.
No need to add up all the terms and further divide by 17 since the terms are evenly spaced in ascending order from 10, 20, 30........170
The middle term is the average which is the tenth term = 80
B is the answer.
The answer is: B | B |
mathematics | A train 360 m long is running at a speed of 42 km/hr. In what time will it pass a bridge 140 m long? | [
"40 sec",
"29 sec",
"26 sec",
"27 sec",
"43 sec"
] | Speed = 42 * 5/18 = 35/3 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 3/35
= 43 sec
Answer:E
The answer is: E | E |
mathematics | A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train? | [
"150m",
"157m",
"750m",
"850m",
"350m"
] | Length of the train be βXβ
X + 150/15 = X + 250/20
4X + 600 = 3X + 750
X = 150m
Answer:A:
The answer is: A | A |
mathematics | The average weight of 49 students in a class is 52 kg. 5 of them whose average weight is 48 kg leave the class and other 5 students whose average weight is 54 kg join the class. What is the new average weight (in kg) of the class ? | [
"51 1β3",
"52 30/49",
"52 1β49",
"43.42",
"None of these"
] | Total weight of 49 students
= 49 Γ 52 = 2548 kg
Total weight of 5 students who leave
= 5 Γ 48 = 240 kg
Total weight of 5 students who join
= 5 Γ 54 = 270 kg
Therefore, new total weight of 49 students
= 2548 β 240 + 270 = 2578
β New average weight = 2578β49 = 52 30/49 kg
Answer B
The answer is: B | B |
mathematics | If equation |x/2| + |y/2| = 1 encloses a certain region on the coordinate plane, what is the area of this region? | [
"8",
"50",
"100",
"200",
"400"
] | The equation can be reduced to intercept form as |x/2| + |y/2| = 1, so these are lines in four quadrants with x and y intercept as 2, so it is a rhombus with diagonals of 4 each and hence area = 1/2*d1*d2 = 1/2*4*4= 8. Answer A.
The answer is: A | A |
mathematics | Buses leave town B at 3 pm and every 10 hours after that. Buses leave town C at 4pm and every 15 hours after that. If the buses follow this schedule beginning on a Monday, what is the earliest day D on which the buses leave at the same time. | [
"D=Tuesday",
"D=Wednesday",
"Thursday",
"Sunday",
"D=The busses will never leave at the same time"
] | The answer is E.
I think the best way to do it is to look at the times on a 24 hour clock. Town B busses start at 15:00, and Town C start at 16:00. If you think about it that way, then for Town B you'd add 10 hours each time, and the number will always end in a 5. Town C you'd add 15 hours each time, and the numbers wo... | E |
mathematics | At the end of year X, automobile installment credit accounted for 35% of all outstanding consumer installment credit. At that time automobile finance companies extended $40 billion of credit, or 1/3 of the automobile installment credit. How many billion dollars of consumer installment credit was outstanding at that tim... | [
"120",
"300",
"401.36",
"350.15",
"342.86"
] | System of Equations
a = (35/100) c
(1/3) a = 40 --> a = 120
Substitution
120 = (35/100) c
c = (100/35) 120
Answer
- 120/35 * 100
The Correct Answer is E.
- 342.86
The answer is: E | E |
mathematics | The present ages of three persons in proportions 5 : 6 : 4. Five years ago, the sum of their ages was 60. Find their present ages (in years). | [
"8, 20, 28",
"16, 28, 36",
"25,30,20",
"18, 24, 32",
"None of these"
] | Explanation:
Let their present ages be 5x, 6x and 4x years respectively.
Then, (5x - 5) + (6x - 5) + (4x - 5) = 60
15x-15 = 60
x = 5
Their present ages are 5x = 25 years, 6x = 30 years and 4x = 20 years respectively.
Answer: C
The answer is: C | C |
mathematics | The rate of increase of the price of sugar is observed to be three percent more than the inflation rate expressed in percentage. The price of sugar, on January 1, 1994, is Rs. 25 per kg. The inflation rate for the years 1994 and 1995 are expected to be 12% each. The expected price of sugar on January 1, 1996 would be | [
"33.06",
"34.1",
"34.2",
"24.6",
"None of these"
] | Explanation :
Increase in the price of sugar = (12+3)= 15%
Hence, price of the sugar on Jan 1, 1996
=> (25 * 115 * 115)/( 100 * 100 ) = Rs 33.06.
Answer : A
The answer is: A | A |
mathematics | Set S has a mean of 10 and a standard deviation of 1.5. We are going to add two additional numbers to Set S. Which pair of numbers would decrease the standard deviation the most? | [
"{2, 10}",
"{9, 11}",
"{10, 18}",
"{7, 13}",
"{16, 16}"
] | answer B,C, and E mean is not 10 therefore not accepted . D mean is 10 but S.D is more. therefore accepted
answer is B mean is 10 and S.D decreases minimum.
B
The answer is: B | B |
mathematics | A shopkeeper bought 600 oranges and 400 bananas. He found 15% of oranges and 5% of bananas were rotten. Find the percentage of fruits in good condition? | [
"92.5%",
"89.0%",
"85.2%",
"96.8%",
"78.9%"
] | Total number of fruits shopkeeper bought = 600 + 400 = 1000
Number of rotten oranges = 15% of 600
= 15/100 Γ 600
= 9000/100
= 90
Number of rotten bananas = 5% of 400
= 20
Therefore, total number of rotten fruits = 90 + 20= 110
Therefore Number of fruits in good condition = 1000 - 110 = 890
Therefore Percentage of fruit... | B |
mathematics | Each writer for the local newspaper is paid as follows: a dollars for each of the first z stories each month, and a + b dollars for each story thereafter, where a > b. How many more dollars will a writer who submits z + a stories in a month earn than a writer who submits z+ b stories? | [
"(a β b)( a + b + z)",
"a β b",
"a^2 β b^2",
"z( a β b)",
"az + bz β az"
] | total earned for z+a stories =a + a(a+b)
total earned for z+b stories =a+ b(a+b)
difference = a+a(a+b) -a -b(a+b)
=(a+b)(a-b) =a^2-b^2
answer is C
The answer is: C | C |
mathematics | A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 16 miles per hour. the cyclist stopswaits for the hiker 5 min after passing her while the hiker continues to walk at her constant rate. how many minutes must the cycli... | [
"6 2/3",
"15",
"20",
"25",
"26 2/3"
] | Here is how I did it:
The cyclist travels 16 miles in 60 mins, so in 5 mins he will travel [(16*5)/60] miles, which equals 4/3 miles in 5 mins.
Now the hiker travels 4 miles in 60 mins. To travel 4/3 miles, he will take [(60*4/3)/4] = 20 mins.
hence 20-5=15 mins
B
The answer is: B | B |
mathematics | The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 5300, what is the length of the plot in metres? | [
"333",
"200",
"288",
"276",
"1999"
] | Let length of plot = L meters, then breadth = L - 20 meters
and perimeter = 2[L + L - 20] = [4L - 40] meters
[4L - 40] * 26.50 = 5300
[4L - 40] = 5300 / 26.50 = 200
4L = 240
L = 240/4= 60 meters.
Answer: B
The answer is: B | B |
mathematics | After decreasing 24% in the price of an article costs Rs.912. Find the actual cost of an article? | [
"1218",
"2777",
"1200",
"2688",
"1991"
] | CP* (76/100) = 912
CP= 12 * 100 => CP = 1200
Answer: C
The answer is: C | C |
mathematics | If g and s are positive integers such that (2^g)(4^s) = 16, then 2g + s = | [
"2",
"3",
"4",
"5",
"6"
] | lets get the eq into simplest orm..
(2^g)(4^s) = 16..
(2^g)(2^2s) = 2^4..
or g+2s=4..
since g and s are positive integers, only g as 2 and s as 1 satisfy the Equation..
so 2g+s=2*2+1=5..
D
The answer is: D | D |
mathematics | A group of 55 adults and 70 children go for trekking. If there is meal for either 70 adults or 90 children and if 28 adults have their meal, find the total number of children that can be catered with the remaining food. | [
"33",
"54",
"18",
"17",
"01"
] | Explanation:
As there is meal for 70 adults and 28 have their meal, the meal left can be catered to 42 adults.
Now, 70 adults = 90 children
7 adults = 9 children
Therefore, 42 adults = 54 children
Hence, the meal can be catered to 54 children.
ANSWER: B
The answer is: B | B |
mathematics | A room is 18 meters long, 15 meters wide 12 meters in height. The longest possible rod which can be placed in the room is | [
"25.28 meters",
"24.28 meters",
"23.28 meters",
"26.28 meters",
"20.28 meters"
] | Square root of 18^2+15^2+12^2...(Diognal) which is square root of 639 that lies 25<β639<26. Hence the answer should be A
The answer is: A | A |
mathematics | Jonathanβs grandparents lend $10,000 to Jonathan at a simple annual interest rate of 10%. He pays them back 5 years later. How much do they receive? | [
"10,000β0.1^5",
"10,000β0.5",
"10,000β1.5",
"10,000β1.1^5",
"(10,000β0.1)^5"
] | Let the principal be $1
So Interest for the $1 for 5 years at 10% Pa is -
1β5β10/100 => 0.50
Now Principal is $1 and Interest is $ 0.50 , so Amount to be returned is - $1 + $0.50 => $1.50
So, for $ 10,000 , amount to be returned is 10,000 * 1.50; Answer is (C)
The answer is: C | C |
mathematics | A pupil's marks were wrongly entered as 73 instead of 45. Due to that the average marks for the class got increased by half. The number of pupils in the class is : | [
"56",
"80",
"20",
"25",
"26"
] | Let there be x pupils in the class.
Total increase in marks = (X*1/2) = X/2.
X/2 = (73 - 45)
=> X/2 = 28
=> X = 56.
ANSWER:A
The answer is: A | A |
mathematics | If X is the sum of first 50 positive even integers and Y is the sum of first 50 positive odd integers, what is the value of x-y? | [
"0",
"25",
"50",
"75",
"100"
] | First even minus first odd = 2-1 = 1;
The sum of first 2 even integers minus the sum of first 2 odd integers = (2+4)-(1+3) = 2;
The sum of first 3 even integers minus the sum of first 3 odd integers = (2+4+6)-(1+3+5) = 3;
...
We can see the patterns here, so the sum of first 50 positive even integers minus the sum of f... | C |
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