subject stringclasses 1
value | question stringlengths 3 1.14k | options listlengths 5 5 | solution stringlengths 18 3.7k | answer stringclasses 5
values |
|---|---|---|---|---|
mathematics | In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 6, the dividend is: | [
"92",
"94",
"96",
"98",
"100"
] | Divisor = (5 * 6) = 30
= 10 * Quotient = Divisor
=> Quotient = 30/10 = 3
Dividend = (Divisor * Quotient) + Remainder
Dividend = (30 * 3) + 6 = 96.
C
The answer is: C | C |
mathematics | Ravi can do a piece of work in 11 days while Prakash can do it in 22 days. In how many days will they finish it together? | [
"5 7/3 days",
"7 1/3days",
"5 1/9 days",
"5 7/3 days",
"4 7/9 days"
] | 1/11 + 1/22 = 3/22
22/3 = 7 1/3 days
ANSWER:B
The answer is: B | B |
mathematics | Brittany's income is 12 percent more than Tina's income, and Tina's income is 15 percent less than Jean's income. What percent of Jean's income is Brittany's income? | [
"95.2%",
"91.2%",
"96.2%",
"94.2%",
"92.2%"
] | Jean's income = 100 (assume);
Tina's income = 85 (15 percent less than Jean's income);
Brittany's income = 95.2 (12 percent more than Tina's income).
Thus, Brittany's income (95.2) is 95.2% of Jean's income (100).
Answer: A
The answer is: A | A |
mathematics | It takes 6 beavers 10 hours to build a certain dam, working at a uniform rate. If three beavers start to build the same dam at 8:00 AM, and one beaver per hour is added beginning at 6:00 PM, at what time will the dam be complete? | [
"7:30 PM",
"8:00 PM",
"9:00 PM",
"10:00 PM",
"11:00 PM"
] | The rate of 1 beaver is 1/60.
The amount of work done by 3 beavers in 10 hours is 3/60 *10 = 30/60
In the next hour, 4 beavers do 4/60 for a total of 34/60.
In the next hour, 5 beavers do 5/60 for a total of 39/60.
In the next hour, 6 beavers do 6/60 for a total of 45/60.
In the next hour, 7 beavers do 7/60 for a total... | E |
mathematics | If (-6)^(2x) = 6^(7 + x) and x is an integer, what is the value of x ? | [
"5",
"4",
"3",
"8",
"7"
] | Since x is an integer, (-6)^2x is always positive.
So, 6^2x = 6^(7 + x)
2x = 7 + x
x = 7
Answer: E
The answer is: E | E |
mathematics | The ratio, by weight, of coffee to sugar to water in a pot of coffee is 5:2:15. The ratio is then altered so that the ratio of coffee to sugar is halved while the ratio of coffee to water is doubled. If the altered pot of coffee contains 12 grams of sugar, how many grams of water does it contain after alteration? | [
"22.5",
"20",
"17.5",
"15",
"12.5"
] | The new ratio of coffee to sugar is 2.5:2 = 5:4
The new ratio of coffee to water is 10:15.
The new ratio of coffee to sugar to water is 10:8:15.
If there are 12 grams of sugar, then there are (15/8)*12=22.5 grams of water.
The answer is A.
The answer is: A | A |
mathematics | What is the greatest possible straight line distance, in inches, between any two points on a rectangular box that is 5 inches wide, 3 inches long, and 4 inches high? | [
"2√5",
"5",
"5√2",
"10",
"50"
] | The maximum possible distance in a cuboid is the diagonal.
Diagonal length = sqrt(length^2 + breadth^2 + height^2) = sqrt(50)
= 5√2
(Option C)
The answer is: C | C |
mathematics | The radius of a semicircle is 7. What is the approximate perimeter of the semicircle? | [
"36",
"25",
"15",
"28",
"37"
] | perimeter of a circle =2pi*r
perimeter of a semicircle = pi*r + 2r
aprox perimiter = 3.14*7 + 2*7 = 35.98 approximately 36
answer A
The answer is: A | A |
mathematics | A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs , then the weight of the pipe is | [
"3.496 kg",
"3.696 kg",
"3.690 kg",
"9.696 kg",
"3.296 kg"
] | Explanation:
External radius = 4 cm,
Internal radius = 3 cm.
Volume of iron = =
Weight of iron = (462 x 8)gm = 3696 gm = 3.696 kg
Answer: B) 3.696 kg
The answer is: B | B |
mathematics | Find the compound ratio of (1:2), (2:3) and (3:4) is | [
"1:2",
"3:5",
"5:7",
"1:4",
"2:1"
] | Required ratio = 1/2 * 2/3 * 3/4 = 1/4 = 1:4
Answer is D
The answer is: D | D |
mathematics | A certain number of two digits is three times the sum of its digits and if 45 be added to it, the digits are reversed. Then number is | [
"21",
"23",
"27",
"72",
"57"
] | Sol.
Let the ten's digit be x and unit's digit be y.
Then, 10x + y = 3(x+y) ⇒ 7x - 2y = 0
10x + y + 45 = 10y + x ⇒ y - x = 5
Solving (i) and (ii), we get : x = 2 and y = 7.
∴ Required number = 27.
Answer C
The answer is: C | C |
mathematics | A man sold 20 articles for $60 and gained 20%. How many articles should he sell for $70 to incur a loss 20%? | [
"45",
"35",
"40",
"50",
"48"
] | Production cost per article: $60*(100%-20%) / 20 = $2.40
Required production costs for a loss of 20%: $70*(100% + 20%) = $84
Number of articles to be sold for $84 to incur a 20% loss: $84 / $2.40 = 35
Thus, solution B is correct.
The answer is: B | B |
mathematics | A person covered one-fourth of the total distance at 26 kmph and remaining distance at 24 kmph. What is the average speed for the total distance? | [
"21 (1/8)kmph",
"21 (1/3)kmph",
"21 (7/3)kmph",
"27 (1/3)kmph",
"21 (1/8)kmph"
] | Let the total distance be x km
total time taken = (x/4)/16 + (3x/4)/24 = x/64 + x/32 = 3x/64
Average speed = x/(3x/64) = 64/3kmph
= 21 (1/3)kmph.
Answer:B
The answer is: B | B |
mathematics | Murali travelled from city A to city B at a speed of 40 kmph and from city B to city C at 60 kmph. What is the average speed of Murali from A to C given that the ratio of distances between A to B and B to C is 2 : 3? | [
"50 kmph",
"60 kmph",
"40 kmph",
"70 kmph",
"80 kmph"
] | A
Let the distances between city A to B and B to C be 2x km and 3x km respectively.
Total time taken to cover from A to C
= (2x)/40 + (3x)/60 = (6x + 6x)/120 = 12x/120 = x/10 Average speed = (2x + 3x)/(x/10) = 50 kmph.
The answer is: A | A |
mathematics | The numerator of a certain fraction is 8 less than the denominator. If 3 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes 3/4. Find the original fraction? | [
"24.5",
"28.5",
"30",
"Data inadequate",
"None of these"
] | Explanation:
Let C.P. be Rs. 100.
Then, S.P. = Rs. 123.50
Let marked price be Rs. x. Then, 95/100 x = 123.50
x = 12350/95 = Rs. 130
Now, S.P. = Rs. 130, C.P. = Rs. 100
Profit % = 30%.
Answer: Option C
The answer is: C | C |
mathematics | If 2^z is a factor of 27!, which of the following could be the value of z?
I. 22
II. 23
III. 24 | [
"I only",
"II only",
"I and II",
"I, II, and III",
"None"
] | 27! contains all numbers from 1 to 27. To find the factor with the highest power of 2, we count the number of multiples of 2, 4, 8 and 16.
Multiples of 2 = 13
Multiples of 4 = 6
Multiples of 8 = 3
Multiples of 16 = 1
Total count = 23
The answer is C.
The answer is: C | C |
mathematics | City I City II City III City IV City V City VI
City I
City II
City III
City IV
City V
City VI
In the table above, what is the least number of table entries that are needed to show the mileage between each city and each of the other five cities? | [
"14",
"15",
"13",
"12",
"11"
] | Easy way to go about this problem is we have 6*6 = 36 enteries in table the least number of enteries would be (36 - 6) /2 since 6 enteries represent the distances between same points .
Alternatively this can be solved as combination problem.
Correct Answer B
The answer is: B | B |
mathematics | What is the area of a square field whose diagonal of length 14 m? | [
"160 sq m",
"140 sq m",
"200 sq m",
"400 sq m",
"180 sq m"
] | d2/2 = (14 * 14)/2 = 140
ANSWER:B
The answer is: B | B |
mathematics | A man buys an article and sells it at a profit of 10%. If he had bought it at 10% less and sold it for Rs.55 less, he could have gained 15%. What is the cost price? | [
"197",
"375",
"846",
"278",
"268"
] | CP1 = 100 SP1 = 110
CP2 = 90 SP2 = 90 * (115/100) = 103.5
6.5 ----- 100
55 ----- ? => 846
Answer:C
The answer is: C | C |
mathematics | The perimeter of a square is equal to the perimeter of a rectangle of length 19 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places) | [
"22.78",
"23.54",
"23.5",
"24.55",
"25.93"
] | Let the side of the square be a cm.
Perimeter of the rectangle = 2(19 + 14) = 66 cm
Perimeter of the square = 66 cm
i.e. 4a =66
A = 16.5
Diameter of the semicircle = 16.5 cm
Circumference of the semicircle
= 1/2(∏)(16.5)
= 1/2(22/7)(16.5) = 25.93 cm to two decimal places
Answer: E
The answer is: E | E |
mathematics | In the third grade of Windblown School there are 108 students, one third of them failed the math test and 1/6 failed that literature test. At least how many students failed both tests? | [
"0.",
"6.",
"8.",
"10",
"12"
] | One third of them failed the math test = 1/3 of 108 = 36. Passed in math test = 82.
And 1/6 failed that literature test = 18.
It is a possible scenario that these 18 (failed in literature) were the ones who passed the math test. So in this case, no one failed in both.
Hence A.
The answer is: A | A |
mathematics | √[200√[200√[200……..∞]]] = ? | [
"200",
"10",
"1",
"20",
"2"
] | Let √[200√[200√[200……..∞]]] = x ; Hence √200x = x
Squaring both sides 200x = x² Þ x (x – 200) = 0
Þ x = 0 or x – 200 = 0 i.e. x = 200
As x cannot be 0, x = 200.
ANSWER:A
The answer is: A | A |
mathematics | If (1+f)g=g, which of the following must be true? | [
"f=-1 or g=0",
"f=0 or g=0",
"f=1 or g=1",
"f=-1 or g=-1",
"f=0 or g=1"
] | By only having fg=0, we cannot say answer is B as A and E options also satisfy the condition fg=0. ans B
The answer is: B | B |
mathematics | A, B and C enter into a partnership and their shares are in the ratio 1/2 : 1/3 : 1/4. After 2 months, A withdraws half of his capital and after 10 months, a profit of Rs. 378 is divided among them. What is B's share ? | [
"144",
"378",
"217",
"299",
"277"
] | Explanation:
Ratio of initial investments = 1/2 : 1/3 : 1/4 = 6 : 4 : 3.
Let their initial investments be 6x, 2x and 3x respectively.
A : B : C = (6x * 2 + 3x * 10) : (4x * 12) : (3x * 12) = 42 : 48 : 36 = 7 : 8 : 6.
B's share = = Rs. 144.
Answer: A) 144
The answer is: A | A |
mathematics | A baker filled with a measuring cup with 3/4 cup water. He poured 1/2 of the water into the batter, and then spilled 2/8 of the water on the floor. How much water will the baker needed to add what is left in the cup to have 50% more than what he started with? | [
"1/8 cup",
"3/8 cup",
"1/4 cup",
"1/2 cup",
"8/8 cup"
] | 3/4 is the original water in cup .half in batter.So left is 3/8 out which 2/8 is spilled out.So again left with 1/8.
so 50% more than what he started was = 3/4+1/2*(3/4)=9/8
Amount of water needed to add = 9/8 - 1/8=8/8
ANSWER:E
The answer is: E | E |
mathematics | A woman invested $1,000, part at 5% and the rest at 6%. Her total investment with interest at the end of the year was $1,054. How much did she invest at 5%? | [
"$500",
"$600",
"$700",
"$900",
"$950"
] | et x be the portion invested at 5% and
Let (1-x) be the rest which is invested at 6%
The question states that the return after 1 year is (1054/1000)-1 = 0.054 = 5.4%
We want to find the dollar amount invested in X
Using our defined variables, put together the equation and solve for x (the percentage of 1000 invested at... | B |
mathematics | How much time will an express train of length 200 m moving at a speed of 72 kmph take to cross another express train of length 300 m, moving at 36 kmph in the same direction? | [
"sec",
"sec",
"sec",
"sec",
"sec"
] | The distance to be covered = Sum of their lengths = 200 + 300 = 500 m.
Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps.
Time required = d/s = 500/10 = 50 sec.
Answer: A
The answer is: A | A |
mathematics | In what ratio must a grocer mix two varieties of pulses costing Rs.15 and Rs.20 per kg respectively so as to get a mixture worth Rs.16.50 per Kg? | [
"3 : 7",
"5 : 7",
"7 : 3",
"7 : 5",
"None"
] | Solution
Required ratio = 3.50 : 1.50 = 35 : 15 = 7 : 3.
Answer C
The answer is: C | C |
mathematics | Among the employees of a certain company, 52 percent of the employees are male and 48 percent are female. In this company 70 percent of the male employees are married and 50 percent of the female employees are married. If one employee in the company is randomly selected, approximately what is the probability that he or... | [
"0.3",
"0.4",
"0.5",
"0.6",
"0.7"
] | Total Males = 52
Total Female = 48
Total = 100
Not married Male = 30% = 15.6
Not marries Female = 50% = 24
Total = 39.6
Probability = 39.6/100 = .396 = approx .4
ANSWER:B
The answer is: B | B |
mathematics | If Rs. 595 be divided among A, B, C in such a way that A gets 2/3 of what B gets and B gets 1/4 of what C gets, then their shares are respectively? | [
"s.420",
"s.360",
"s.389",
"s.368",
"s.323"
] | (A = 2/3 B and B = 1/4 C) = A/B = 2/3 and B/C = 1/4
A:B = 2:3 and B:C = 1:4 = 3:12
A:B:C = 2:3:12
A;s share = 595 * 2/17 = Rs. 70
B's share = 595 * 3/17 = Rs. 105
C's share = 595 * 12/17 =Rs.420.
Answer:A
The answer is: A | A |
mathematics | What ratio must a shopkeepermix Peas and Soybean of Rs.16 and Rs. 25/kg, As to obtain a mixture of Rs.20 ? | [
"10 : 7",
"9 : 8",
"5 : 4",
"13 : 11",
"14 : 8"
] | Correct option: (C)
Use rule of alligation, to determine the ratio
The required ratio of Soybean and Peas = 5 : 4
The answer is: C | C |
mathematics | The population of a city is 160,000. If it increases at the rate of 6% per annum, then what will be its population 2 years hence? | [
"268942",
"186935",
"179776",
"167425",
"None of these"
] | Explanation:
Population after n years = P [1 + (R/100)]2
Population after 2 years = 160000 * [1 + 6/100]2 = (160000 x 53/50 x 53/50) = 179776
ANSWER: C
The answer is: C | C |
mathematics | 10x + 2y = -6
8x + y = 3
In the system of equations above, what is the value of x? | [
"-6",
"-4",
"-2",
"2",
"4"
] | 10x + 2y = -6 can be written as 5x + y = -3
Let's subtract the second equation from this equation.
-3x = -6
x = 2
The answer is D.
The answer is: D | D |
mathematics | What is the are of an equilateral triangle of side 16 cm? | [
"64√8 cm2",
"64√1 cm2",
"68√3 cm2",
"64√3 cm2",
"24√3 cm2"
] | Area of an equilateral triangle
= √3/4 S2
If S = 16, Area of triangle
= √3/4 * 16 * 16
= 64√3 cm2;
Answer: D
The answer is: D | D |
mathematics | A sun is divided among X, Y and Z in such a way that for each 2 rupees X gets, Y gets 80 paisa and Z gets 60 paisa. If the share of Y is RS. 40, what is the total amount? | [
"160",
"155",
"150",
"170",
"165"
] | x:y:z = 200:80:60
10:4:3
4 --- 40
17 --- ? => 170
Answer: D
The answer is: D | D |
mathematics | How many 4 digit numbers can be formed with the digits 0, 1, 2, 3, 4, 5, 6 and 5? | [
"a. 220",
"b. 249",
"c. 432",
"d. 216",
"e. 288"
] | Taking Question with it's same language as given
To make number divisible by 5, the unit digit should be either 0 or 5 only
Case 1: If unit digit is fixed as zero
With two6s The choice to fill the remaining three digits = 3C2 x 5 = 15
With all remaining 3 digits different, The choice to fill the remaining three digits ... | A |
mathematics | One-fourth of a number is greater than one-fifth of the number succeeding it by 1. Find the number. | [
"24",
"42",
"36",
"48",
"50"
] | number is 24
as 1/4 th of 24= 6
1/5 th of 25(24+1) =5
6=5+1
ANSWER:A
The answer is: A | A |
mathematics | An urn contains 5 red, 6 blue and 8 green balls. 3 balls are randomly selected from the urn, find the probability that the drawn ball are blue? | [
"20/969",
"20/875",
"21/876",
"3/512",
"2/9"
] | Sample space = no. of ways 3 balls were drawn from urn = 19C3 = 969
No. ways 3 blue balls were drawn from bag = 6C3 = 20
Probability = 20 / 969
Ans - A
The answer is: A | A |
mathematics | Two trains of length 200 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet? | [
"22 sec",
"77 sec",
"76 sec",
"20 sec",
"24 sec"
] | Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps.
Distance covered in passing each other = 200 + 280 = 480 m.
The time required = d/s = 480/20 = 24 sec.
Answer:E
The answer is: E | E |
mathematics | A shipment of 8 television sets contains 2 black-and-white sets and 7 color sets. If 2 television sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black-and-white set? | [
"1/7",
"1/4",
"5/14",
"11/28",
"13/28"
] | I get 1/4, which is not in the answer choices.
the probability of getting at least one b/w TV is 1-(the probability of getting 2 color TVs)
1-C(7,2)/C(8/2)=7/28=1/4
B
The answer is: B | B |
mathematics | A snail, climbing a 42 feet high wall, climbs up 4 feet on the first day but slides down 2 feet on the second. It climbs 4 feet on the third day and slides down again 2 feet on the fourth day. If this pattern continues, how many days will it take the snail to reach the top of the wall? | [
"20",
"26",
"32",
"39",
"51"
] | total transaction in two days = 4-2 = 2 feet
in 38 days it will climb 38 feet
on the 39th day , the snail will climb 4 feet , thus reaching the top
therefore , total no of days required =39
D
The answer is: D | D |
mathematics | How many seconds will a 400 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr? | [
"20",
"30",
"40",
"24",
"60"
] | Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 400 * 3/50 = 24 sec.
Answer: Option D
The answer is: D | D |
mathematics | Given three boxes I, II and III, each containing two coins. In box I, both coins are 1 rupee
coins, in box II, both are 2 rupee coins and in the box III, there is one 1 rupee and one 2 rupee coin.
A person chooses a box at random and takes out a coin. If the coin is of 1 rupee, what is the
probability that the other co... | [
"1/5",
"2/3",
"2/7",
"3/7",
"2/5"
] | Let E1, E2 and E3 be the events that boxes I, II and III are chosen, respectively.
Then P(E1) = P(E2) = P(E3) = 1/3
Also, let A be the event that ‘the coin drawn is of 1 rupee'
Then P(A|E1) = P(a 1 rupee coin from bag I) = 2/2 = 1
P(A|E2) = P(a 1 rupee coin from bag II) = 0
P(A|E3) = P(a 1 rupee coin from bag III) = 1/... | B |
mathematics | The area of a square field 3136 sq m, if the length of cost of drawing barbed wire 3 m around the field at the rate of Rs.1.50 per meter. Two gates of 1 m width each are to be left for entrance. What is the total cost? | [
"Rs.500",
"Rs.250",
"Rs.896",
"Rs.789",
"Rs.999"
] | Explanation:
a^2 = 3136 => a = 56
56 * 4 * 3 = 672 – 6 = 666 * 1.5 =Rs. 999
Answer : E
The answer is: E | E |
mathematics | The radius of a cone is 14 m, slant height is 20 m. Find the curved surface area? | [
"770",
"550",
"110",
"880",
"330"
] | Cone curved surface area = πrl
22/7 × 14 × 120 = 44 × 20 = 880 m(power2)
Answer is D.
The answer is: D | D |
mathematics | Which of the following leads to the correct mathematical solution for the number of ways that the letters of the word TIE could be arranged to create a three-letter code? | [
"3!",
"3! − (3! + 2!)",
"3! − (2!)",
"3!/(3! + 2!)",
"3!/(3! × 2!)"
] | TIE - three letters can be arranged in 3! ways
since 'there is no repetition'
3!
Ans. A) 3!
The answer is: A | A |
mathematics | If 8 < x < 9, and x^2 = (10 – y)(10 + y), which of the following is a possible value for y? | [
"–7",
"–6",
"3",
"4",
"5"
] | Given : 8<x<9=> 64<x^2<81
Given X^2 = 100-y^2
Therefore 64<100-y^2<81
-36<-y^2<-19 = 19<y^2<36
Only (E) y=5 => Y^2 = 25 satisfies the above equation.
The answer is: E | E |
mathematics | Two persons A and B can complete a piece of work in 30 days and 45 days respectively. If they work together, what part of the work will be completed in 4 days? | [
"2/5",
"1/6",
"1/4",
"1/9",
"2/9"
] | A's one day's work = 1/30
B's one day's work = 1/45
(A + B)'s one day's work = 1/30 + 1/45 = 1/18
The part of the work completed in 4 days = 4 (1/18) = 2/9.
ANSWER E
The answer is: E | E |
mathematics | A 300 m long train crosses a platform in 42 sec while it crosses a signal pole in 18 sec. What is the length of the platform? | [
"286 m",
"350 m",
"277 m",
"400 m",
"267 m"
] | Speed = 300/18 = 50/3 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/42 = 50/3
x = 400 m.
Answer:D
The answer is: D | D |
mathematics | A, B and C can do a piece of work in 24, 30 and 40 days respectively. They start the work together but C leaves 4 days before the completion of the work. In how many days is the work done? | [
"22 days",
"77 days",
"88 days",
"11 days",
"18 days"
] | x/24 + x/30 + x/40 = 1
x = 11 days
Answer:D
The answer is: D | D |
mathematics | Find the mean proportional between 64 & 81? | [
"A)59",
"B)61",
"C)63",
"D)72",
"E)67"
] | Formula = √a×b
A = 64 and B = 81
√64×81 = 8 × 9 = 72
D
The answer is: D | D |
mathematics | Let a,b,c and d be the result of rounding off 7382.196 to the nearest thousand, hundred, ten and one, respectively. Which of the following statements is true? | [
"d<c<b<a",
"d<c<a<b",
"a<d<c<b",
"c<d<b<a",
"a<c<d<b"
] | Soln:
7382.196..
Nearest thousand 7000..a
Nearest hundred 7400..b
Nearest ten 7380..c
Nearest one 7382...D
a<c<c<b
ANSWER:E
The answer is: E | E |
mathematics | If x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year, the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $48. If $1500 is the total amount invested, how much is invested at 8 percent? | [
"a. $280",
"b. $566.67",
"c. $892",
"d. $1108",
"e. $1200"
] | 2 equations with 2 unknowns
10x / 100 - 8y / 100 = 48
and
x + y = 1500
Solving these 2 equations, x = 933.33 and y = 566.67
Answer B.
The answer is: B | B |
mathematics | Cheese, bologna, and peanut butter sandwiches were made for a picnic in a ratio of 5 to 7 to 8. If a total of 360 sandwiches were made, how many Cheese sandwiches
were made? | [
"15",
"30",
"90",
"42",
"48"
] | For deciding such task we should calculate all parts 5 + 7 + 8 = 20 parts
and we should calculate how many sandwiches holds 1 part:
360 / 20 = 18 sandwiches in one part
For cheese we have 5 parts so:
5 * 18 = 90
Answer is C
The answer is: C | C |
mathematics | A Prototype fuel-efficient car (P-Car) is estimated to get 70% more miles per gallon of gasoline
than does a traditional fuel-efficient car (T-Car). However, the P-Car requires a special type
of gasoline that costs 30% more per gallon than does the gasoline used by a T-Car. If the two
cars are driven the same distance,... | [
"16 2/3%",
"23.53 %",
"50%",
"60%",
"66 2/3 %"
] | Assumption
Miles/Gallon
T = 100
P = 170 ( 70% more)
$/gallon
T = 100
P = 130 (30% more)
Miles
100 for both
Cost = (Miles X $/ Gallon)/ M/gallon
T = 100
P = 76.47
Hence 100 - 76.47 = 23.53%
Ans B
The answer is: B | B |
mathematics | A certain factory produces buttons and buckles at a uniform weight. If the total weight of 2 buttons and 2 buckles is one third of 11 buckles and 3 buttons, then the weight of 3 buttons and 2 buckles is how many times that of 4 buckles and 6 buttons? | [
"7/15.",
"4/9.",
"6/11.",
"1/2.",
"8/15."
] | 2buttons + 2buckles = 1/3(11buckles + 3buttons)
6buttons + 6buckles = 11buckles + 3buttons
3buttons = 5buckles
Weight of 3buttons and 2buckles = 5buckles + 2buckles = 7buckles
Weight of 6buttons and 5buckles = 10buckles + 4buckles = 14buckles
(3buttons and 2buckles) = x * (6buttons and 5buckles)
7 = x*14
x = 7/14=1/2
A... | D |
mathematics | In a group of 25 factory workers, 18 have brown eyes. Six of the women do not have brown eyes. How many of the 11 men have brown eyes. | [
"10",
"9",
"8",
"7",
"4"
] | Total number of worker (M+W): 25
No. of men (M): 11 (Inferred fromHow many of the 11 men)
No. of women (W): 14
Total no. of workers who have brown eyes (B): 18
No. of women who do not have brown eyes: 6
Therefore, no. of women who have brown eyes: W - 6 = 14 - 6 = 8
Remaining 10 are men. (B - 8= 18 - 8= 10)
So 10 out o... | A |
mathematics | A password of a computer used three digits where they are from 0 and 9. What is the probability that the password solely consists of prime numbers and zero? | [
"1/32",
"1/16",
"1/8",
"2/5",
"1/2"
] | We have three digits can be used for password -0,2,3,5,7.
Assuming that the numbers can be repeated any number of times in the password, probability of selecting any one of them is 5/10 (out of 10 digits from 0-9)
So, 5/10 * 5/10 * 5/10 =1/8 (C)
The answer is: C | C |
mathematics | If 4a = 5b and ab ≠0, what is the ratio of a/5 to b/4? | [
"125/64",
"25/16",
"1",
"4/5",
"64/125"
] | A nice fast approach is the first find a pair of numbers that satisfy the given equation: 4a = 5b
Here's one pair: a =5 and b =4
What is the ratio of a/5 to b/4?
In other words, what is the value of (a/5)/(b/4)?
Plug in values to get: (a/5)/(b/4) = (5/5)/(4/4)
= 1/1
= 1
C
The answer is: C | C |
mathematics | In how many ways can 22 books on English and 20 books on Hindi be placed in a row on a shelf so that two books on Hindi may not be together? | [
"4586",
"5896",
"2415",
"1771",
"1881"
] | In order that two books on Hindi are never together, we must place all these books as under:
H E H E H E H….. H E H
Where H denotes the position of Hindi book and E that of English book.
Since there are 22 books on English, the number of places marked E are 23.
Now, 20 places out of 23 can be chosen in 23C20 = 23C3 = 2... | D |
mathematics | The banker's discount on Rs. 1600 at 15% per annum is the same as true discount on Rs. 1680 for the same time and at the same rate. The time is? | [
"4 months",
"6 months",
"8 months",
"9 months",
"1 months"
] | S.I. on Rs. 1600 = T.D. on Rs. 1680.
Rs. 1600 is the P.W. of Rs. 1680, i.e., Rs. 80 is on Rs. 1600 at 15%.
Time =(100 x 80/1600 x 15)year
=1/3 year = 4 months.
Answer:A
The answer is: A | A |
mathematics | At Jefferson Elementary School, the number of teachers and students (kindergarten through sixth grade) totals 510. The ratio of students to teachers is 16 to 1. Kindergarten students make up 1/8 of the student population and fifth and sixth graders account for 1/3 of the remainder. Students in first and second grades a... | [
"8 greater",
"17 fewer",
"28 fewer",
"36 fewer",
"44 fewer"
] | Soln>> from the given ratio of 16:1 u can derive that ter are 480 students
KG= 1/8* 480 =60
5th and 6th graders = 1/3 * 384= 128 (1/3 of remainder)
1st and 2nd grade = 1/4 * 480 =120 ( 1/4 of all students)
equal number of students in 3rd and 4th => 480 - 344= 136 and 136/2=68 each since equal number
(344 is the sum of ... | A |
mathematics | Integer x is equal to the product of all even numbers from 2 to 60, inclusive. If y 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"
] | x = the product of all even numbers from 2 to n, where n is any even integer value from 2 to 60 including.
If x = 2, x - 1 = 2! -1
If x = 2x4, x - 1 = 2! (2^2) - 1
If x = 2x4x6, x - 1 = 3! (2^3) - 1
If x = 2x4x6x8, x - 1 = 4! (2^4) - 1
.
.
.
.
If x = 2x4x6x.......x60, x - 1 = 30! (2^30) - 1
Lets find y, a smallest prim... | E |
mathematics | A WNBA player just signed a new contract in which she will earn a 5% increase in base pay from last year to this year. Last year, she did not have a performance bonus; but this year, she will have the opportunity to earn up to a $40,000 performance bonus. If she earns the full performance bonus, her new effective salar... | [
"2,120,000",
"2,140,000",
"2,180,000",
"2,240,000",
"2,260,000"
] | let x = last year's salary
the new base pay + 40,000 = the new effective pay
(1+.05)*x + 40,000 = (1+.07)*x
1.05x + 40,000 = 1.07x
40,000 = .02x
2,000,000 = x
thus the new salary = (1+.07)*2,000,000 = 2,140,000
B
The answer is: B | B |
mathematics | If we multiply the digits of a number until we get a single digit, then which is the only two digit number which require multiplication of digits more than 3 times? | [
"77",
"67",
"87",
"97",
"57"
] | 77 =7*7 =49
49 =4*9 =36
36 =3*6 =18
18 =1*8 =8
ANSWER:A
The answer is: A | A |
mathematics | Cream costs twice as much as skim milk. A certain brand of milk is 1/5 cream and 4/5 skim milk. What fraction of the cost of this brand is due to the cream? | [
"1/3",
"2/3",
"1/4",
"3/4",
"2/5"
] | Let x be the cost of the skim milk in the mixture.
The cost of the cream is (1/4)*x*2 = x/2.
The total cost is x+x/2 = 3x/2 and the fraction due to the cream is (x/2) / (3x/2) = 1/3
The answer is A.
The answer is: A | A |
mathematics | Set S consists of all prime numbers less than 10. If two numbers are chosen from et S at random, what is the probability that the product of these numbers will be greater than the product of the numbers which were not chosen? | [
"1/3",
"2/3",
"1/2",
"7/10",
"4/5"
] | Prime integers below 10: 2, 3, 5, 7
Total outcomes: Number of ways you can choose 2 from 4 = 4C2=6pairs4C2=6pairs
No. of ways for Event: Pairs that will have products greater than product of pairs not selected i.e. (3,5), (3,7), (5,7) =3pairs=3pairs
Probability = number of ways/Total outcomes =3/6=1/2=3/6=1/2
Hence cho... | C |
mathematics | Rahul's mother is the only daughter of Monika's father. How is Monika's husband related to Rahul ? | [
"Uncle",
"Father",
"Grandfather",
"Brother",
"SISTER"
] | Explanation:
Clearly, the only daughter or Monika's father is Monika herself
So, Rahul's mother is Monika
Thus, Monika's husband is the father of Rahul.
Answer: B) Father
The answer is: B | B |
mathematics | If money is invested at r percent interest, compounded annually, the amount of the investment will double in approximately 54/r years. If Joe's parents invested $5,000 in a long-term bond that pays 6 percent interest, compounded annually, what will be the approximate total amount of the investment 18 years later, when ... | [
"$20000",
"$15000",
"$12000",
"$10000",
"$9000"
] | Since investment doubles in 54/r years, then for r=6 it'll double in 54/6=~9 years (we are not asked about the exact amount so such an approximation will do). Thus after 18 years investment will become $5,000*2=$10,000 .
Answer: D.
The answer is: D | D |
mathematics | What is the sum of the prime factors of 121 and the prime factors of 7434 | [
"27",
"67",
"57",
"37",
"47"
] | The prime factors of 7434are 3*3*2*7
The prime factors of 121 are 11*11
3+3+2+7+11+11 = 37. D is the correct answer
The answer is: D | D |
mathematics | A 270 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train? | [
"230 m",
"240 m",
"260 m",
"320 m",
"520 m"
] | Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 270)/9 = 500/9 => x = 230.
ANSWER:A
The answer is: A | A |
mathematics | A mixture of 70 litres of milk and water contains 10% water. How many litres of water should be added to the mixture so that the mixture contains 12 1/2% water? | [
"2 litres",
"3 litres",
"5 litres",
"7 litres",
"8 litres"
] | Quantity of milk in the mixture = 90/100 (70) = 63 litres.
After adding water, milk would form 87 1/2% of the mixture.
Hence, if quantity of mixture after adding x liters of water,
(87 1/2) / 100 x = 63 => x = 72
Hence 72 - 70 = 2 litres of water must be added.
Answer:A
The answer is: A | A |
mathematics | A train 360 m long is running at a speed of 60 km/hr. In what time will it pass a bridge 140 m long? | [
"40 sec",
"30 sec",
"26 sec",
"27 sec",
"34 sec"
] | Speed = 60 * 5/18 = 50/3 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 3/50
= 30 sec
Answer: B
The answer is: B | B |
mathematics | The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 25%, then the cost price of the article is: | [
"500",
"277",
"222",
"448",
"111"
] | Explanation:
110% of S.P. = 616
S.P. = (616 * 100)/110 = Rs. 560
C.P = (100 * 560)/125 = Rs. 448
Answer:D
The answer is: D | D |
mathematics | Three numbers are in the ratio 3:5:7. The largest number value is 42. Find difference between Smallest & largest number is? | [
"20",
"24",
"26",
"28",
"30"
] | == 3:5:7
Total parts = 15
= The largest number value is 42
= The largest number is = 7
= Then 7 parts -----> 42 ( 7 * 6 = 42 )
= smallest number = 3 & Largest number = 7
= Difference between smallest number & largest number is = 7 - 3 = 4
= Then 4 parts -----> 24 (4 * 6 = 24)
B
The answer is: B | B |
mathematics | Twenty four men can do a work in 35 days. How many men are required to complete the work in 21 days? | [
"22",
"40",
"277",
"26",
"12"
] | We have M1 D1 = M2 D2
So, 24 * 35 = M2 * 21 => M2 = 40.
Answer:B
The answer is: B | B |
mathematics | A train 360 m long is running at a speed of 72 km/hr. In what time will it pass a bridge 140 m long? | [
"40 sec",
"29 sec",
"25 sec",
"27 sec",
"34 sec"
] | Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 1/20
= 25 sec
Answer: C
The answer is: C | C |
mathematics | Kiran started a business investing Rs. 20,000. After 4 months, Sanket joined with a capital of Rs. 12000. At the end of the year, they earn a profit of Rs. 14,000. Find what will be the share of Sanket in the profit? | [
"Rs. 4000",
"Rs. 4007",
"Rs. 4001",
"Rs. 4002",
"Rs. 4047"
] | Explanation:
Kiran : Sanket = (20000 * 12) : (12000 * 8) = 5 : 2
Sanket's share = Rs. 14,000 * (2/7) = Rs. 4000
ANSWER: A
The answer is: A | A |
mathematics | The surface area of a sphere is same as the curved surface area of a right circular cylinder whose height and diameter are 6 cm each. The radius of the sphere is | [
"3 cm",
"4 cm",
"6 cm",
"8 cm",
"None"
] | Solution
4Î R2 = 2Î 3x6
⇒ R2 = (3x6/2)
⇒ 9
⇒ R = 3 cm.
Answer A
The answer is: A | A |
mathematics | At a certain conference, 150 students spoke one or more of the following languages: Spanish, English, and French. If 51 students spoke Spanish, 90 spoke English, 65 spoke French, and 32 spoke only 2 languages, how many students spoke three different languages? | [
"7",
"9",
"12",
"15",
"18"
] | 150=51+90+65-32-2x
x=12
C. 12
The answer is: C | C |
mathematics | How much time will a train of length 200 m moving at a speed of 72 kmph take to cross another train of length 300 m, moving at 36 kmph in the same direction? | [
"50 sec",
"25 sec",
"40 sec",
"65 sec",
"60 sec"
] | Explanation:
The distance to be covered = Sum of their lengths = 200 + 300 = 500 m.
Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps.
Time required = d/s = 500/10 = 50 sec.
ANSWER IS A
The answer is: A | A |
mathematics | An bus covers a certain distance at a speed of 250 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of? | [
"1520 km/hr",
"1250 km/hr",
"1256 km/hr",
"1231 km/hr",
"1220 km/hr"
] | Distance = (250 x 5) = 1250 km.
Required speed = 1250km/hr.
B
The answer is: B | B |
mathematics | If a motorist had driven 1 hour longer on a certain day and at an average rate of 4 miles per hour faster, he would have covered 70 more miles than he actually did. How many more miles would he have covered than he actually did if he had driven 2 hours longer and at an average rate of 10 miles per hour faster on that d... | [
"100",
"120",
"140",
"150",
"160"
] | Case 1:
let rate = R, Time = T, and Distance =D
so D=RT
Case 2:
(D+70)=(R+4)(T+1)
Case 3:
(D+X)=(R+10)(T+2)
X=140
Ans C
The answer is: C | C |
mathematics | The ratio 6 : 5 expressed as a percent equals | [
"12.5%",
"40%",
"120%",
"125%",
"None"
] | Solution
6 : 5 = 6/ 5
= (6/5 x 100)%.
= 120 %.
Answer C
The answer is: C | C |
mathematics | if Juan takes 12 seconds to run y yards, how many seconds will it take him to run x yards at the same rate? | [
"11x/y",
"11y/x",
"x/11y",
"12x/y",
"xy/11"
] | Answer is D
The rate of running hards: 12 minutes per y hards.
Thus the time for running x hards = x hards * 12 minutes/y hards = 12x/y
The answer is: D | D |
mathematics | 8k8
+ k88
--------
1,6r6
If k and r represent non-zero digits within the integers above, what is r? | [
"6",
"7",
"8",
"9",
"17"
] | 8k8
k88
--------
16r6
Trial and error or just plug-in method might be the shortest way to solve this problem. Though you can narrow down the possible values of k to just two: 7 and 8 --> 8**+7**=16** or 8**+8**=16** (k can not be less than 7 or 9, as the result won't be 16**). After that it's easy to get that k=7 and r... | A |
mathematics | Company C produces toy trucks at a cost of $5.00 each for the first 100 trucks and $3.50 for each additional truck. If 500 toy trucks were produced by Company C and sold for $20.00 each, what was Company C’s gross profit? | [
"$7,250",
"$8,500",
"$8,100",
"$8,250",
"$8,600"
] | Cost of 500 trucks: (100 * 5 ) + (400 * 3.5) = 500 + 1400 =$ 1900
Revenue : 500 * 20 = $10000
Profit: 10000 - 1900 = $ 8100
Option C is correct
The answer is: C | C |
mathematics | At present, the ratio between the ages of Arun and Deepak is 4:5. After 5 years, Arun's age will be 25 years. What is the age of Deepak at present? | [
"18",
"20",
"25",
"23",
"22"
] | Let the present ages of Arun and Deepak be 4x and 3x years respectively.
Then, 4x + 5 = 25 => x = 5
Deepak's age = 5x = 25 years.
Answer: C
The answer is: C | C |
mathematics | If n = 3p, where p is a prime number greater than 2, how many different positiveevendivisors does n have, including n ? | [
"Two",
"Three",
"Four",
"Six",
"Eight"
] | This is an interesting question because we are immediately given the option to insert any prime number we wish for p. Since this is a problem-solving question, and there can only be one correct answer, we can select any value for p, as long as it is a prime number greater than 2. We always want to work with small numbe... | B |
mathematics | Find the ones digit of 73^353 | [
"3",
"5",
"6",
"7",
"9"
] | The units digit of 73^353 will be the same as the units digit of 3^353.
3^1=3 --> the units digit is 3;
3^2=9 --> the units digit is 9;
3^3=27 --> the units digit is 7;
3^4=81 --> the units digit is 1;
3^5=243 --> the units digit is 3 AGAIN;
...
So, as you can see the units digit repeats in blocks of 4: {3, 9, 7, 1}, {... | A |
mathematics | A train covers a distance of 54 km in 15 min. If it takes 8 sec to pass a telegraph post, then the length of the train is? | [
"470",
"480",
"490",
"500",
"510"
] | Speed = (54/15 * 60) km/hr = (216 * 5/18) m/sec = 60 m/sec.
Length of the train = 60 * 8 = 480 m.
Answer: Option B
The answer is: B | B |
mathematics | For all positive integers m and v, the expression m Θ v represents the remainder when m is divided by v. What is the value of (( 88 Θ 33 ) Θ 17 ) - ( 90 Θ (33 Θ 17)) ? | [
"0",
"1",
"2",
"3",
"4"
] | (( 88 Θ 33 ) Θ 17 )
The remainder of 88 divided by 33 is 22;
The remainder of 22 divided by 17 is 5;
( 98 Θ (33 Θ 17))
The remainder of 33 divided by 17 is 16;
The remainder of 98 divided by 16 is 2.
5 - 2 = 3.
Answer: D.
The answer is: D | D |
mathematics | A sum of money at simple interest amounts to Rs. 815 in 3 years and to Rs. 854 in 4 years. The sum is: | [
"Rs. 650",
"Rs. 690",
"Rs. 698",
"Rs. 700",
"Rs. 740"
] | S.I. for 1 year = Rs. (854 - 815) = Rs. 39.
S.I. for 3 years = Rs.(39 x 3) = Rs. 117.
Principal = Rs. (815 - 117) = Rs. 698.
Answer: Option C
The answer is: C | C |
mathematics | At a tanning salon, customers are charged $10 for their first visit in a calendar month and $4 for each visit after that in the same calendar month. In the last calendar month, 100 customers visited the salon, of which 30 made a second visit, and 10 made a third visit. All other customers made only one visit. If those ... | [
"$1220",
"$1160",
"$1300",
"$1340",
"$1880"
] | I get B. This question seems too straightforward for 600+. Am I missing something?
100 first-time visits --> 100(10) = $1000
30 + 10 = 40 subsequent visits --> 40(4) = $160
Total revenue: 1000+ 160 = $1160
The answer is B.
The answer is: B | B |
mathematics | A is thrice as good as B in work. A is able to finish a job in 60 days less than B. They can finish the work in - days if they work together. | [
"18 days",
"22 ½ days",
"24 days",
"26 days",
"23 days"
] | If A completes a work in 1 day, B completes the same work in 3 days
Hence, if the difference is 2 days, B can complete the work in 3 days
=> if the difference is 60 days, B can complete the work in 90 days
=> Amount of work B can do in 1 day= 1/90
Amount of work A can do in 1 day = 3 × (1/90) = 1/30
Amount of work A an... | B |
mathematics | The area of a sector of a circle of radius 5 cm formed by an arc of length 3.5 cm is? | [
"0.35 cm2",
"17.5 cm2",
"8.75 cm2",
"55 cm2",
"50 cm2"
] | Explanation:
(5 * 3.5)/2 = 8.75
ANSWER IS C
The answer is: C | C |
mathematics | In a rectangular axis system, what is the area of a parallelogram with the coordinates: (4,4), (7,4), (5,9), (8,9) ? | [
"21.",
"28.",
"5.",
"49.",
"52."
] | Delta x will give us the dimension of one side of the parallelogram = 5-4= 1 unit
Delta y will give us the dimension of the other side of parallelogram = 9-4=5 unit
Area of parallelogram = 1*5 = 5
ANSWER IS C
The answer is: C | C |
mathematics | The ratio of the ages of Mini and Minakshi is 4 : 3. The sum of their ages is 21 years. The ratio of their ages after 8 years will be | [
"2 : 3",
"20 : 17",
"5 : 4",
"3 : 5",
"6 : 11"
] | Let Mini’s age = 4x and Minakshi’s age = 3x
Then 4x + 3x = 21
x = 3
Mini’s age = 12 years
And Minakshi’s age = 9 years
Ratio of their ages after 8 years = (12 + 8) : (9 + 8) = 20 : 17
ANSWER:B
The answer is: B | B |
mathematics | Jill works as a waitress at the local diner where she earns an hourly wage of $4.00 per hour and a standard tip rate of 15% of the cost of the orders she serves. If she worked three 8-hour shifts this week and averaged $40 in orders per hour, how much did Jill earn this week? | [
"280",
"300",
"240",
"350",
"400"
] | Jill earns 4 dollars/hour and the hourly tip is (3/20)*40.
Jill thus earns 4*8+8*2*3 per day(or 4(8)+6(8)=10(8)=80).
Jill has worked for 3 days -> 80*3=240.
This matches answer choice C.
The answer is: C | C |
mathematics | By selling a bicycle for Rs. 2,850, a shopkeeper gains 14%. If the profit is reduced to 8%, then the selling price will be: | [
"Rs. 2,600",
"Rs. 2,700",
"Rs. 2,800",
"Rs. 3000",
"NOne"
] | Solution: Let Cost Price was X.
X + 14% of X = 2850
X + 14X/100 = 2850
X + 0.14X = 2850
1.14X = 2850
X = 2500.
So, Cost Price = Rs. 2500.
Now, Selling Price When profit remains at 8%,
= 2500 + 8% of 2500
= Rs. 2700.
Short-Cut
CP of bicycle = 100/114*2850 = Rs. 2500;
SP for a profit of 8% = 108/100*2500 = Rs. 2700.
Answ... | B |
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