subject stringclasses 1
value | question stringlengths 3 1.14k | options listlengths 5 5 | solution stringlengths 18 3.7k | answer stringclasses 5
values |
|---|---|---|---|---|
mathematics | Grace packed 5 pairs of shoes, 3 pairs of pants, 8 shirts, and 3 jackets for her business trip. If an outfit consists of one of each item of clothing except shirts, of which she will wear 2, how many different outfits S can does Grace have available during her trip? | [
"2,520",
"1,260",
"620",
"360",
"120"
] | The idea is to multiply the number of possibilities for each item of clothing with the different items. For the shirts you essentially choose 2 out of 8 so you should use the combination forumla (don't know how to use math symbols here).
This gives you S=5 x 3 x 28 x 3 = 1'260. Hence, solution B is correct.
The answer ... | 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 50 paisa. If the share of Y is RS. 36, what is the total amount? | [
"115",
"116",
"117",
"118",
"156"
] | x:y:z = 100:45:50
20:9:10
9 --- 36
39 --- ? => 156
ANSWER:E
The answer is: E | E |
mathematics | The length of a rectangle is two - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 100 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 2 units? | [
"140 sq.units",
"158 sq.units",
"8 sq.units",
"607 sq.units",
"815 sq.units"
] | Given that the area of the square = 100 sq.units
=> Side of square = √100= 10 units
The radius of the circle = side of the square = 10 units
Length of the rectangle = 2/5 * 10 = 4 units
Given that breadth = 2 units
Area of the rectangle = lb = 4 * 2 = 8 sq.units
Answer: C
The answer is: C | C |
mathematics | From a group of 3 CATS and 3 DOGS, 4 animals are to be randomly selected. What is the probability that equal numbers of cats and dogs will be selected? | [
"1/5",
"2/5",
"4/5",
"3/5",
"1"
] | Using the first example, here is the probability of THAT EXACT sequence occurring:
CCDD = (3/6)(2/5)(3/4)(2/3) = 36/360 = 1/10
Each of the other 5 options will yield the exact SAME probability....
eg
CDCD = (3/6)(3/5)(2/4)(2/3) = 36/360 = 1/10
So we have 6 different options that each produce a 1/10 chance of occurring.... | D |
mathematics | A company can manufacture 1000 phones in a day. One-fifth of the phones produced are defective and one-quarter of all phones produced are rejected by quality control technician. If one-tenth of the nondefective phones are rejected by mistake, and if all the phones not rejected are sold, then what percent of the phones ... | [
"4%",
"16%",
"24%",
"2%",
"8%"
] | We have 20% defective and 80% non-defective; we have 25% rejected and 75% not rejected. We also know that 1/10 of the non-defective ones (8%) are rejected, so 72% sold. This means that we have 3% sold that are defective and 17% rejected that are defective. Overall, we have 3%/75% or 1 of every 25 that are sold (not rej... | A |
mathematics | A train running at the speed of 60 km/hr crosses a pole in 36 seconds. What is the length of the train? | [
"186 m",
"176 m",
"100 m",
"600 m",
"765 m"
] | Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train
= (Speed x Time) = (50/3 * 36) m
= 600 m.
Answer: D
The answer is: D | D |
mathematics | Train X and train Y pass one another traveling in opposite directions. Thirty minutes later they are 100 miles apart. If train X’s constant speed is 40 miles per hour greater than train Y’s, how far does train X travel during that time? | [
"28",
"40",
"60",
"72",
"80"
] | Let the rate of the Train Y be R
Then the rate of the Train X will be R+40 (given)
As per relative rate concept, the rate at which they are increasing the distance between them is R+(R+40) [add the rates] i.e. 2R+40
d=100 and t = 30 min i.e 30/60 hr
using RTD table, (2R+40) * 30/60 = 100 ==> R= 80 miles/hr
So the rate ... | C |
mathematics | Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank? | [
"18",
"10",
"12",
"11",
"17"
] | 4/12 + x/15
= 1
x = 10
Answer: B
The answer is: B | B |
mathematics | Juan is a gold medalist in athletics. In the month of May, if Juan takes 12 seconds to run y yards, how many seconds will it take him to run x yards at the same rate? | [
"10x/y",
"11x/y",
"9x/y",
"12x/y",
"13x/y"
] | velocity=distance/time;
since he ran at same rate both d tyms,
y/12=x/t
so t=12x/y
ANSWER:D
The answer is: D | D |
mathematics | The actual price of an article was Rs. 6000/- the successive discount on 10% and 20% then Finds the selling price | [
"Rs.3240/-",
"Rs. 4320/-",
"Rs.4230/-",
"Rs.4200/-",
"None of these"
] | Explanation:
Note: Selling price = MRP * (100 - d1)/100 * (100 - d2)/100 * -------------
MRP = 6000/- , d1 = 10, d2 = 20
Selling price = 6000 * (100 - 10)/100 * (100-20)/100 ==> 6000 * 90/100 * 80/100
=> 48 * 90 = Rs. 4320/-
Answer: Option B
The answer is: B | B |
mathematics | A rectangular grass field is 75 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m? | [
"Rs.1350",
"Rs.1327",
"Rs.1328",
"Rs.1397",
"Rs.1927"
] | Area = (l + b +2d) 2d
= (75 + 55 +2.5 * 2) 2*2.5 => 675
675 * 2 = Rs.1350
Answer: A
The answer is: A | A |
mathematics | Two numbers are respectively 20% and 50% more than a third number. The percentage that is first of the second is? | [
"77%",
"78%",
"79%",
"80%",
"81%"
] | I II III
120 150 100
150----------120
100-----------? => 80%
Answer:D
The answer is: D | D |
mathematics | A certain animal shelter has 28 cats and 46 dogs. How many dogs must be adopted and taken away from the animal shelter so that 70 percent of the animals in the shelter will be cats? | [
"6",
"12",
"28",
"34",
"40"
] | (28 + 46 - x)*0.7 = 28
x = 34.
Answer: D.
The answer is: D | D |
mathematics | 45 men can complete a work in 18 days. Six days after they started working, 30 more men joined them. How many days will they now take to complete the remaining work? | [
"6.6",
"10",
"15",
"7.2",
"8"
] | 45*18 men can complete the work in 1 day
1 man's 1 day work = 1/810
45 men 6 days work = 6*1/18 = 1/3
remaining work = 1-1/3 = 2/3
75 men's 1 day's work = 75/810 = 5/54
2/3 work is done by them in 54/5 * 2/3 = 7.2 days
Answer is D
The answer is: D | D |
mathematics | A reduction of 15% in the price of wheat enables a house wife to obtain 3 kgs more for Rs.500, what is the reduced price for kg? | [
"Rs.10",
"Rs.15",
"Rs.20",
"Rs.25",
"Rs.30"
] | Explanation:
500*(15/100) = 75 ---- 3
? ---- 1 => Rs.25
Answer: D
The answer is: D | D |
mathematics | A rectangular box of volume V has width, depth and height in the ratio of 2:1:3 (in that order). What is the height as a function of V? | [
"(V/2)^(1/3)",
"(2V/6)^(1/3)",
"(9V/2)^(1/3)",
"(4V/3)^(1/3)",
"(4V/2)^(1/3)"
] | We are given width = 2, depth = 1, height = 3.
Then Volume V = Width x Depth x Height = 2*1*3 = 6
i.e. V = 6
The correct option should result in 3 (the height) on substituting the value of V=6.
Checking options with V=6:
A) (V/2)^(1/3) = (6/2)^(1/3) = 3^(1/3) INCORRECT ANSWER
B) (2V/6)^(1/3) = (12/6)^(1/3) = 2^(1/3) IN... | C |
mathematics | If 1st October is Sunday, then 1st November will be | [
"Saturday",
"Thursday",
"Wednesday",
"Tuesday",
"Monday"
] | Explanation:
Given that 1st October is Sunday
Number of days in October = 31
31 days = 3 odd days
(As we can reduce multiples of 7 from odd days which will not change anything)
Hence 1st November = (Sunday + 3 odd days) = Wednesday
Answer: Option C
The answer is: C | C |
mathematics | At a certain stage of a soccer tournament, the score ratio of teams A, B and C was 3:4:5. Eventually, the score ratio of A to B has doubled while the score ratio of A to C has halved. If the final score of team C was 40, what was the final score W of team B? | [
"1)8",
"2)10",
"3)20",
"4)40",
"5)80"
] | A to B = 3 : 4
So, on doubling we get 6 : 4
A to C = 3 : 5
So, on halving we get 1.5 : 5 or 3 : 10 or 6 : 20
So final ratio = 6 : 4 : 20.
If 20x = 40
4x = 8
Hence, answer is A
The answer is: A | A |
mathematics | A guy was asked to specify his age in years. He said, “Take my age 8 years hence, multiply it by eight and subtract eight times of my age 8 years ago and get the half of the result and you will know my age.” What was the age of that guy? | [
"18",
"55",
"63",
"64",
"70"
] | Current age of the guy = A years.
Then, 8 (A + 8) – 8 (A – 8) = A
(8A + 64) – (8A – 64) = A
A = 128/2 =64
D
The answer is: D | D |
mathematics | A car takes 6 hours to cover a distance of 288 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time? | [
"50 Kmph",
"60 Kmph",
"32 Kmph",
"70 Kmph",
"None"
] | Time = 6
Distence = 288
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 288/9 = 32 Kmph
C)
The answer is: C | C |
mathematics | Joe’s average (arithmetic mean) test score across 4 equally weighted tests was 35. He was allowed to drop his lowest score. After doing so, his average test score improved to 40. What is the lowest test score that was dropped? | [
"20",
"25",
"55",
"65",
"80"
] | The arithmetic mean of 4 equally weighted tests was 35. So what we can assume is that we have 4 test scores, each 35.
He dropped his lowest score and the avg went to 40. This means that the lowest score was not 35 and other three scores had given the lowest score 5 each to make it up to 35 too. When the lowest score wa... | A |
mathematics | If -1<x<0, what is the median M of these six numbers listed below
1/x^3,1/x^2, 1/x,x, x^2,x^3 | [
"1/x",
"x^2",
"x^2(x+1)/2",
"M=x(x^2+1)/2",
"x^2/2x"
] | My approach: Put any value between -1 and 0. you will get the answer. lets say 0.5. so the list will be as follows:
-8,-2,-0.5,-0.125 and last two numbers will be positive so need to see that.
median will be between -0.5 and -0.125.
So, (x^3+x)/2 (D).
The answer is: D | D |
mathematics | A and B complete a work in 4 days. A alone can do it in 8 days. If both together can do the work in how many days? | [
"3.75 days",
"3.78 days",
"3.25 days",
"3.15 days",
"2.7 days"
] | 1/4 + 1/8 = 3/8
8/3 = 2.7 days
Answer: E
The answer is: E | E |
mathematics | Calculate the average of first 18 even numbers is? | [
"21",
"29",
"19",
"14",
"10"
] | Explanation:
Sum of 10 even numbers = 18 * 19 = 342
Average = 342/18 = 19
Answer: Option C
The answer is: C | C |
mathematics | On dividing 109 by a number, the quotient is 9 and the remainder is 1. Find the divisor. | [
"12",
"14",
"16",
"18",
"22"
] | d = (D-R)/Q
= (109 - 1)/9
= 108/9 = 12
A)
The answer is: A | A |
mathematics | A card game called “high-low” divides a deck of 52 playing cards into 2 types, “high” cards and “low” cards. There are an equal number of “high” cards and “low” cards in the deck and “high” cards are worth 2 points, while “low” cards are worth 1 point. If you draw cards one at a time, how many ways can you draw “high” ... | [
"1",
"2",
"3",
"4",
"5"
] | To get a 5, you need one high and three lows (you could have had 2 highs and one low, but the constraint is that you must have three low cards)
HLLL = 4!3! =4
4! is the number of ways you can arrange these four spaces. divide by 3! because you you repeat three low cards
ANS:D
The answer is: D | D |
mathematics | In a series of six consecutive odd numbers, the third number is 31. What is the fifth number? | [
"35",
"33",
"45",
"31",
"29"
] | Let the numbers be x, x + 1, x + 3, x + 5 and x + 7.
Given (x + 3) = 31
=> x = 28
The fifth number = x + 7 = 28 + 7 = 35.
Answer: A
The answer is: A | A |
mathematics | Find the length of the wire required to go 15 times round a square field containing 69696 m^2. | [
"15840",
"26480",
"15642",
"15640",
"15849"
] | a^2 = 69696 => a = 264
4a = 1056
1056 * 15 = 15840
Answer: A
The answer is: A | A |
mathematics | Ravi and Kumar are working on an assignment. Ravi takes 6 hours to type 32 pages on a computer, while Kumar takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages? | [
"7 hours 30 minutes",
"8 hours",
"8 hours 15 minutes",
"8 hours 25 minutes",
"7 hours 35 minutes"
] | Number of pages typed by Ravi in 1 hour = 32/6 = 16/3 .
Number of pages typed by Kumar in 1 hour = 40/5 = 8.
Number of pages typed by both in 1 hour = (16/3+ 8) = 40/3 .
Therefore Time taken by both to type 110 pages = ( 110 x 3/40 ) hours
= 8 1/4 hours (or) 8 hours 15 minutes.
Option C
The answer is: C | C |
mathematics | Two kinds of Vodka are mixed in the ratio 1:2 and 2:1 and they are sold fetching the profit 25% and 20% respectively. If the vodkas are mixed in equal ratio and the individual profit percent on them are increased by 4/3 and 5/3 times respectively, then the mixture will fetch the profit of | [
"18%",
"20%",
"21%",
"25%",
"Cannot be determined"
] | Answer: D.
The answer is: D | D |
mathematics | Find the C.I. on Rs. 15,625 for 9 months at 16% per annum compounded quarterly? | [
"Rs.1978",
"Rs.1979",
"Rs.1951",
"Rs.1968",
"Rs.1929"
] | P = Rs. 15625, n = 9 months = 3 quarters, R = 16% p.a. per quarter.
Amount = [15625 * (1 + 4/100)3]
= (15625 * 26/25 * 26/25 * 26/25)
= Rs. 17576 C.I.
= 17576 - 15625 = Rs. 1951.
Answer:C
The answer is: C | C |
mathematics | If a, b, and c are consecutive even positive integers, which of the following could be equal to a + b + c ? | [
"141",
"200",
"624",
"391",
"412"
] | The key to answering this question quickly is to realize that a+b+c is a multiple of BOTH 2 and 3. With that information, you can quickly eliminate answer choices. If you don't recognize those two Number Properties though, then you can still get to the correct answer (but it will require a bit more work).
We're told th... | C |
mathematics | If 20 liters of chemical X are added to 80 liters of a mixture that is 30% chemical X and 70% chemical Y, then what percentage of the resulting mixture is chemical X? | [
"32%",
"35%",
"38%",
"41%",
"44%"
] | The amount of chemical X in the solution is 20 +0.3(80) = 44 liters.
44 liters / 100 liters = 44%
The answer is E.
The answer is: E | E |
mathematics | A grocer has a sale of Rs 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs, 6500 ? | [
"4991",
"2367",
"1976",
"1627",
"1981"
] | Explanation:
Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs.[(6500 x 6) - 34009]
= Rs. (39000 - 34009)
= Rs. 4991.
Answer: A
The answer is: A | A |
mathematics | 15 + sqrt(- 6 + 8×5÷4) =? | [
"31",
"32",
"33",
"34",
"35"
] | According to order of operations, inner brackets first where 8x5÷4 is first calculated since it has a multiplication and a division.
8x5÷4 = 40÷4 = 10
Hence
15 + sqrt(- 6 + 8×5÷4) = 15+ sqrt(- 6 + 10)
= 15 + sqrt(4) = 15 + 16 = 31
correct answer A)31
The answer is: A | A |
mathematics | January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008 ? | [
"Monday",
"Tuesday",
"wednesday",
"Sunday",
"None of these"
] | Solution
The year 2007 is an ordinary year. So, it has 1 odd day.
1st day of the year 2007 was Monday.
1st day of the year 2008 will be 1 day beyond Monday.
Hence, it will be Tuesday. Answer B
The answer is: B | B |
mathematics | If a - b = 4 and a2 + b2 = 30, find the value of ab. | [
"A)7",
"B)12",
"C)15",
"D)18",
"E)20"
] | Explanation:
2ab = (a2 + b2) - (a - b)2
= 30 - 16 = 14
ab = 7
Answer: A
The answer is: A | A |
mathematics | A bullet train 220 m long is running with a speed of 59 kmph. In what time will it pass a man who is running at 7 kmph in the direction opposite to that in which the bullet train is going? | [
"23 sec",
"15 sec",
"12 sec",
"11 sec",
"16 sec"
] | C
12 sec
Speed of the bullet train relative to man = (59 + 7) kmph
= 66 *5/18 m/sec = 55/3 m/sec.
Time taken by the bullet train to cross the man = Time taken by it to cover 220 m at (55/3) m / sec
= (220 *3/55) sec = 12 sec
The answer is: C | C |
mathematics | The diameter of a garden roller is 1.4 m and it is 2 m long. How much area will it cover in 5 revolutions ? (use π = 22⁄7) | [
"40 m2",
"44 m2",
"48 m2",
"36 m2",
"None of these"
] | Required area covered in 5 revolutions
= 5 × 2πrh = 5 × 2 × 22⁄7 × 0.7 × 2 = 44 m2
Answer B
The answer is: B | B |
mathematics | Thirty percent of the members of a swim club have passed the lifesaving test. Among the members who havenotpassed the test, 5 have taken the preparatory course and 30 have not taken the course. How many members are there in the swim club? | [
"60",
"80",
"50",
"120",
"140"
] | 30% of the members have passed the test, thus 70% have not passed the test.
We also know that 30+5=42 members have not passed the test, thus 0.7*Total=35 --> Total=50.
Answer: C.
The answer is: C | C |
mathematics | A is twice as good a work man as B and together they finish the work in 10 days. In how many days A alone can finish the work? | [
"23",
"15",
"77",
"92",
"61"
] | WC = 2:1
2x + x = 1/10 => x = 1/30
2x = 1/15
A can do the work in 15 days.
Answer: B
The answer is: B | B |
mathematics | In a triangle XYZ, XZ is the longest side, length of which is 1 unit more than YZ, which again has length 1 unit more than XY. If area of the triangle is 10 and the shortest side is 3. What are the lengths of the three sides? | [
"1, 2, 5",
"3, 4, 5",
"4, 5, 6",
"7, 8, 9",
"5, 2, 4"
] | XY=3
YZ=1+XY = 4
XZ=1+YZ=5
B is the correct option.
The answer is: B | B |
mathematics | 4,25,121,289,? | [
"345",
"445",
"515",
"529",
"645"
] | Prime numbers- 2,3,5,7,11,13,17,19,23.....
Series - 2^2,5^2,11^2,17^2,23^2
Series- 4, 25, 121, 289, 529.
So next term in series is- 529.
ANSWER:D
The answer is: D | D |
mathematics | If a and b are integers and (2^a)(3^b) is a factor of 180^40, what is the largest possible value of ab? | [
"2a",
"5a",
"20a",
"40a",
"80a"
] | (2^a)(3^b) is a factor of 180^40
We need to find the largest possible value of ab.
We know that 180 = 2^2*5^1*3^2
Therefore 180^40 will have 2 powers of 3 in it.
Hence in (2^a)(3^b), b has to 2
Therefore value of ab = 2a
Correct Option: A
The answer is: A | A |
mathematics | What is the largest 4 digit number exactly divisible by 88? | [
"8844",
"9944",
"7744",
"6644",
"5544"
] | Largest 4 digit number = 9999
9999 ÷ 88 = 113, remainder = 55
Hence largest 4 digit number exactly divisible by 88
= 9999 - 55 = 9944
Answer is B.
The answer is: B | B |
mathematics | The instructions state that Cheryl needs 4/9 square yards of one type of material and 2/3 square yards of another type of material for a project. She buys exactly that amount. After finishing the project, however, she has 6/12 square yards left that she did not use. What is the total amount of square yards of material ... | [
"1/12",
"1/9",
"2/3",
"1 1/9",
"11/18"
] | total bought = 4/9+2/3
left part 6/12--->1/2
so used part 4/9+2/3-1/2=11/18
Ans E
The answer is: E | E |
mathematics | In how many different ways can the letters of the word "LEADING" be arranged in such a way that the vowels always come together. | [
"W8",
"789",
"279",
"277",
"191"
] | Answer:D
The answer is: D | D |
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. 54, what is the total amount? | [
"166",
"105",
"178",
"177",
"210"
] | x:y:z = 100:45:30
20:9:6
9 --- 54
35 --- ? => 210
Answer: E
The answer is: E | E |
mathematics | If a stationery store owner buys 50% more identically-priced calendars than she usually purchases, she will be given a 20% discount off the standard price. Her total cost would then be 120 times the dollar value of the standard price of one calendar. How many calendars does she usually purchase? | [
"40",
"80",
"100",
"120",
"140"
] | Let the Price is x per item
and the final number of items she bought is y items
So to buy y items , the cost will be .8x (80% of original price , since there is a 20% discount on it)
120*x = y*0.8*x
Solving we get y =150
now to get the discount she bought 50% more than what she usually buys
So the number of items she u... | C |
mathematics | Find the average of the series : 256,254,350, 1110,1200 ? | [
"129",
"308",
"634",
"207",
"174"
] | Average = (256+254+350+1110+1200) /5
= 3170/5
= 634
Answer: C
The answer is: C | C |
mathematics | In a graduating class, 40 percent of the students are male. In this class, 50 percent of the male students and 40 percent of the female students are 25 years old or older. If one student in the class is randomly selected, approximately what is the probability that he or she will be less than 25 years old? | [
"0.44",
"0.5",
"0.56",
"0.62",
"0.68"
] | Let x be the total number of students.
The number students who are younger than 25 is 0.5*0.4x+0.6*0.6x = 0.56x
The answer is C.
The answer is: C | C |
mathematics | If p+q=8z, then which of the following represents the average (arithmetic mean) of p, q, and z, in terms of z? | [
"2z+1",
"3z",
"5z",
"z/3",
"3z/2"
] | Pick any number like P=12, Q=12 and Z= 3 so that P+Q=8Z, now then the arithmetic mean will be (12+12+3)/3=9. Now, just look at the answers and put the value of Z there.
(A) 2.3+1=7, no.
(B) 3.3=9, it can be the answer, lets check us the other options
(C) 5.3=15, no
(D) 3/3=1 no
(E) (3.3)/2=9/2, no
so the answer will be... | B |
mathematics | One year ago the ratio of Yamini’s and Gamini’s ages was 6 : 7 respectively. Four years hence this ratio would become 7 : 8. How old is Gamini? | [
"35 years",
"30 years",
"31 years",
"Cannot be determined",
"None of these"
] | Y : G = 6 : 7; One year before
Y : G = 7 : 8; After 4 years
Now, 1 → 5
∴ 7 → 35
Therefore, the age of Gamini now is 35 + 1 = 36 years
Answer E
The answer is: E | E |
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? | [
"22 days",
"77 days",
"24 days",
"17 days",
"18 days"
] | B = 1/8 – 1/2 = 1/24 => 24 days
Answer: C
The answer is: C | C |
mathematics | Rectangular tile each of size 35cm by 30cm must be laid horizontally on a rectangular floor of size 1000cm by 210cm,such that the tiles do not overlap and they are placed with edges jutting against each other on all edges. A tile can be placed in any orientation so long as its edges are parallel to the edges of floor. ... | [
"600",
"400",
"200",
"500",
"100"
] | Area of tile = 35*30 = 1050
Area of floor = 1000*210 = 210000
No of tiles = 210000/1050 =200
So, the no of tile = 200
ANSWER:C
The answer is: C | C |
mathematics | FOG + FOG + FOG + FOG = 1468.
If F,O and G are digits in a three-digit number in the preceding equation the F + O + G = ? | [
"11",
"12",
"13",
"14",
"16"
] | given,FOG + FOG + FOG + FOG = 1468
4(FOG)=1468
=>FOG=367
Face value of F is:3
Face value of O is:6
Face value of G is:7
so F+O+G=3+6+7=16
ANSWER:E
The answer is: E | E |
mathematics | A sum of money is to be distributed among A, B, C, D in the proportion of 5:2:4:3. If C gets Rs. 1000 more than D, what is B's share? | [
"Rs.2029",
"Rs.2028",
"Rs.2000",
"Rs.2022",
"Rs.2021"
] | Let the shares of A, B, C and D be 5x, 2x, 4x and 3x Rs. respectively.
Then, 4x - 3x = 1000 => x = 1000.
B's share = Rs. 2x = 2 * 1000
= Rs.2000.
Answer: C
The answer is: C | C |
mathematics | Steve traveled the first 2 hours of his journey at 40 mph and the last 2 hours of his journey at 80 mph. What is his average speed of travel for the entire journey? | [
"53.33 mph",
"56.67 mph",
"60 mph",
"64 mph",
"66.67 mph"
] | Average Speed = Total distance/ Total time = (40 * 2 + 80 * 2)/(2 + 2) = 240/4 = 60
Answer: C
The answer is: C | C |
mathematics | If a(a + 2) = 35 and b(b + 2) = 35, where a ≠ b, then a + b = | [
"-5",
"-6",
"-7",
"-2",
"-10"
] | i.e. if a = 5 then b = -7
or if a = -7 then b = 5
But in each case a+b = 5-7 = -2
Answer: D
The answer is: D | D |
mathematics | Jane makes toy bears. When she works with an assistant, she makes 80 percent more bears per week and works 10 percent fewer hours each week. Having an assistant increases Jane’s output of toy bears per hour by what percent R? | [
"20%",
"80%",
"100%",
"180%",
"200%"
] | C.
Let's assume just Jane 40 bears per 40/hrs a week, so that is 1 bear/hr. With an assistant she makes 72 bears per 36 hours a week or 2 bears/hr ([40 bears * 1.8] / [40 hrs * .90]).
R=[(2 - 1)/1] * 100% = 100%.C
The answer is: C | C |
mathematics | If P/2 = Q/3 = R/4 then find P:Q:R | [
"1:2:3",
"2:5:7",
"6:4:9",
"5:7:2",
"2:3:4"
] | Let P/2 = Q/3 = R/4 = K
P = 2K
Q = 3K
R = 4K
P:Q:R = 2:3:4
Answer is E
The answer is: E | E |
mathematics | The majority owner of a business received 25% of the profit, with each of 4 partners receiving 25% of the remaining profit. If the majority owner and two of the owners combined to receive $50,000, how much profit did the business make? | [
"$80,000",
"$100,000",
"$120,000",
"$150,000",
"$200,000"
] | Let P be the total profit.
P/4 + 1/2*(3P/4) = P/4 + 3P/8 = 5P/8 = 50000
P = $80,000
The answer is A.
The answer is: A | A |
mathematics | A man buys an article and sells it at a profit of 20%. If he had bought it at 20% less and sold it for Rs.50 less, he could have gained 25%. What is the cost price? | [
"197",
"250",
"279",
"278",
"268"
] | CP1 = 100 SP1 = 120
CP2 = 80 SP2 = 80 * (125/100) = 100
20 ----- 100
50 ----- ? => 250
Answer:B
The answer is: B | B |
mathematics | By selling 16 pencils for a rupee a man loses 20%. How many for a rupee should he sell in order to gain 20%? | [
"28",
"25",
"24",
"23",
"21"
] | 80% --- 16
120% --- ?
80/120 * 16 = 24
Answer:C
The answer is: C | C |
mathematics | A man rides at the rate of 50km/hr. But stops 30minutes to change horses at the end of every 25th kilometer. How long will he take to go a distance of 250 kilometers? | [
"5hr",
"6hr 30min",
"8hr 10min",
"7hr 20min",
"8hr"
] | speed of man = 50km/hr
number of rests = (250/25)-1 = 9
time taken for the man = (250/50)+9*(20/60) = 8 hr
Answer is E
The answer is: E | E |
mathematics | A train when moves at an average speed of 40 kmph, reaches its destination on time. When its average speed becomes 35 kmph, then it reaches its destination 15 minutes late. Find the length of the journey | [
"40km",
"50km",
"60km",
"70km",
"80km"
] | Difference between timings = 15 min =0.25hr.
Let the length of journey be x km.
Then,
x/35-x/40=0.25
8x - 7x = 70
x = 70km.
ANSWER:D
The answer is: D | D |
mathematics | It costs a publishing company 50,000 dollars to make books. The 50,000 is a fixed cost or a cost that cannot change. To help the publishing company sell the books, a marketing company charges 4 dollars for each book sold. If the company charges 9 dollars per book, how many books should they sell to break even? | [
"100",
"1000",
"10000",
"100000",
"None"
] | Let C be the cost of producing and selling x books
Let R be the revenue made for selling x books
R = selling price of 1 book × number of books sold
R = 9x
C = fixed cost + variable cost
variable cost = fee charged for 1 book × number of books sold
variable cost = 4x
C = 50000 + 4x
R = C
9x = 50000 + 4x
9x - 4x = 50000 ... | C |
mathematics | If nn is a positive integer and (n+1)(n+3)(n+1)(n+3) is odd, then (n+2)(n+4)(n+2)(n+4) must be a multiple of which one of the following? | [
"2",
"4",
"6",
"8",
"9"
] | (n+1)(n+3)(n+1)(n+3) is odd only when both (n+1)(n+1) and (n+3)(n+3) are odd. This is possible only when nn is even.
Hence, n=2mn=2m, where mm is a positive integer. Then,
(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)
=4 * (product of two consecutive positive integers,... | D |
mathematics | a, b, c, and d are positive consecutive even integers and a < b < c < d.
If the product of the highest and lowest numbers is six more than the sum of the middle numbers, what is the product of the smallest two numbers? | [
"2",
"4",
"8",
"12",
"20"
] | We know the numbers must be consecutive even numbers, from the list 2, 4, 6, 8, 10, 12, 14, 16, and so on.
The product ad is 6 more than the sum bc. By testing some possible ad products (even numbers separated by two other even numbers), we can quickly see that the numbers have to be quite small: 6x12 is 72, much highe... | C |
mathematics | The average of first five multiples of 4 is? | [
"6",
"8",
"9",
"5",
"12"
] | Average = 4(1 + 2 + 3 + 4 + 5)/5
= 60/5
= 12.
Answer:E
The answer is: E | E |
mathematics | If Rs. 64 amount to Rs. 83.20 in 2 years, what will Rs. 86 amount to in 4 years at the same rate percent per annum ? | [
"Rs. 114.80",
"Rs. 86.70",
"Rs. 55.40",
"Rs. 51.60",
"None"
] | Solution
P = Rs. 64,S.I. = Rs. (83.20 - 64) = Rs. 19.20, T= 2 years.
So, rate = (100x19.20/64x2)= 15%.
Now, P = Rs. 86, R = 15% ,T = 4 years.
∴ S.I. = Rs.(86x15x4/100) Rs. 51.60.
Answer D
The answer is: D | D |
mathematics | Beth received 4/12 of the votes cast in a certian election. What franction of the other votes cast would she have needed in order to have received 1/2 of the votes cast? | [
"1/5",
"2/7",
"3/10",
"7/20",
"2/8"
] | Let the total votes be 12. Beth received 2 votes, other votes 12-4=8. In order to have received 1/2 of the votes she needed 6 votes so 2 more, which is 2/8 of the other votes.
Answer: E.
The answer is: E | E |
mathematics | There was a person who smoked a lot .One day he decided to quit his habbit,but he had 27 cigarettes with him.So he started smoking them one by one ,to finish them. He had the habit of smoking only 2/3rd of it and leaving the rest butt. Latter he found out that by joining 3 butts he can form 1 cigarette. So ,tell how ma... | [
"30",
"40",
"50",
"60",
"45"
] | 27+9+3+1=40.
ANSWER:B
The answer is: B | B |
mathematics | The average expenditure of a labourer for 10 months was 85 and he fell into debt. In the next 4 months by reducing his monthly expenses to 60 he not only cleared off his debt but also saved 30. His monthly income is | [
"180",
"100",
"112",
"110",
"None of the above"
] | Income of 10 months = (10 × 85) – debt
= 850 – debt
Income of the man for next 4 months
= 4 × 60 + debt + 30
= 270 + debt
∴ Income of 10 months = 1120
Average monthly income = 1120 ÷ 10 = 112
Answer C
The answer is: C | C |
mathematics | If 2ab - c = 2a(b - c), which of the following must be true? | [
"a=0 and c=0",
"a=1/2 and b=2",
"b=1 and c=0",
"a=1 or b=0",
"a=1/2 or c=0"
] | 2ab - c = 2a(b - c)
=> 2ab - c = 2ab - 2ac
=> - c = - 2ac
=> c = 2ac
=> c - 2ac = 0
=> c (1 - 2a) = 0
Either c = 0 or 1 - 2a = 0 i.e. a = 1/2.
Hence, E
The answer is: E | E |
mathematics | Solve the given two equations and find the inequality of X and Y. (a) x^4- 227= 398 and (b) y^2 + 321=346 | [
"If x>y",
"If x>=y",
"If x < y",
"If x<=y",
"x=y or relationship cannot be established"
] | Solution:-
X=+5,-5 and Y= +5,-5
Comparing, we get X=Y, XY.
Therefore, no relationship can be established between X and Y.
E
The answer is: E | E |
mathematics | Aishwarya’s mom was 28 years of age at the time of her birth, while her mom was 20 years old when her 2 years younger sister was born. The variance between the parents ages is : | [
"10 years",
"11 years",
"15 years",
"9 years",
"4 years"
] | A
6 years
Mom’s age when Aishwarya’s sister was born = 20 years.
Dad’s age when Aishwarya’s sister was born = (28 + 2) years = 30 years.
Needed Variance = (30 – 20) years = 10 years.
Answer is A
The answer is: A | A |
mathematics | John makes $65 a week from his job. He earns a raise andnow makes $70 a week. What is the % increase? | [
"7.69%",
"16.66%",
"17.8%",
"19%",
"21%"
] | Increase = (5/65)*100 = (1/13)*100 = 7.69%.
A
The answer is: A | A |
mathematics | The perimeter of a triangle is 44 cm and the in radius of the triangle is 2.5 cm. What is the area of the triangle? | [
"76",
"88",
"66",
"55",
"35"
] | Area of a triangle = r * s
Where r is the in radius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 44/2 = 55 cm2
Answer:D
The answer is: D | D |
mathematics | If xy ≠ 0 and x^2y^2 − xy = 30, which of the following could be y in terms of x?
I. 6/x
II. -5/x
III. 3/x | [
"I only",
"II only",
"I and II only",
"I and III",
"II and III"
] | (x^2)(y^2) – xy - 30 = 0
(xy – 6)(xy + 5) = 0
xy – 6 = 0 or xy + 5 = 0
xy = 6 or xy = -5
Since we need y in terms of x, we can isolate y in both of our equations.
y = 6/x or y = -5/x
Answer: C
The answer is: C | C |
mathematics | What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad? | [
"814 tiles",
"800",
"100",
"200",
"456"
] | Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm.
Area of each tile = (41 x 41) cm2.
Required number of tiles = (1517 x 902)/41 x 41 = 814.
Answer:A
The answer is: A | A |
mathematics | If 20 men can build a wall 66 meters long in 6 days, what length of a similar can be built by 86 men in 8 days? | [
"49",
"39",
"29",
"19",
"None of them"
] | Let the required length be x meters
More men, More length built (Direct Proportion)
Less days, Less length built (Direct Proportion)
Men 20: 35
Days 6: 3 : : 56 : x
Therefore (20 x 6 x x)=(35 x 3 x 56)= x=(35 x 3 x 56)/120=49
Hence, the required length is 49 m.
Answer is A.
The answer is: A | A |
mathematics | Solve(0.76 × 0.76 × 0.76 − 0.008)/(0.76 × 0.76 + 0.76 × 0.2 + 0.04) | [
"0.56",
"0.71",
"0.45",
"0.67",
"0.71"
] | Option 'A'
The answer is: A | A |
mathematics | Approximately what percentage of the world’s forested area is represented by Finland given that Finland has 53.42 million hectares of forested land of the world’s 8.076 billion hectares of forested land. | [
"0.0066%",
"0.066%",
"0.66%",
"6.6%",
"66%"
] | Since 1 billion is 1000 million
Soc changing all quantities to million
Finland forest area =53.42 million hect.
Worlds's forest area =8.076 billion hect.
% =53.42*100/8.076*1000 =0.66%
Answer C
The answer is: C | C |
mathematics | The price of sugar is increased by 20%. If the expenditure is not allowed to increase, the ratio between the reduction in consumption and the original consumption is : | [
"1:3",
"1:4",
"1:6",
"1:5",
"None"
] | Explanation:
Reduction in consumption
=(20/120×100)%=50/3%
Reduction in consumption/Original consumption=(50/3×1/100)
=1/6=1:6
Correct Option: C
The answer is: C | C |
mathematics | How many 1/12s are there in 37 1/2? | [
"350",
"450",
"500",
"650",
"700"
] | Required number = (75/2)/(1/12)
= (75/2 x 12/1)
= 450.
ANSWER:B
The answer is: B | B |
mathematics | The digit in units place of the product 81 x 82 x ..... x 89 is | [
"0",
"2",
"6",
"8",
"9"
] | Sol.
Required digit = unit digit in (1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9) = 0.
Answer A
The answer is: A | A |
mathematics | The ratio of the cost price and the selling price is 4:5. The profit percent is? | [
"17",
"56",
"25",
"28",
"12"
] | Let C.P. = Rs. 4x. Then, S.P. = Rs. 5x
Gain = (5x - 4x) = Rs. x
Gain % = (x * 100)/ 4x = 25%.
Answer: C
The answer is: C | C |
mathematics | The average of five integers is 71, and none of these integers is greater than 100. If the average of three of the integers is 76, what is the least possible value of one of the other two integers? | [
"5",
"15",
"20",
"21",
"27"
] | When it comes to averages, we know thataverage value = (sum of n values)/n
We can rewrite this into a useful formula:sum of n values = (average value)(n)
The average of five integers is 71
So, the sum of ALL 5 integers = (71)(5) =355
The average of three of the integers is 65
So, the sum of the 3 integers = (76)(3) =22... | E |
mathematics | P and Q started a business investing Rs, 85,000 and Rs. 15,000 respectively. In what ratio the profit named after 2 years bo divided between P and Q respectively ? | [
"17:9",
"17:3",
"17:2",
"17:1",
"17:0"
] | P : Q = 85000 : 15000 = 86 : 15 = 17 : 3
Answer: B
The answer is: B | B |
mathematics | In March, Kurt ran an average of 2 miles an hour. If by June he had increased his pace by 10 seconds per mile, then which of the following expresses the number of hours it would take Kurt to complete one mile in June? | [
"3590/60^2",
"2410/60^2",
"1790/60^2",
"3586/60",
"60^2/3590"
] | Kurt ran at an average of 2 miles/hour in march. So to run 1 mile he would take 1/2 hours = (60 * 60)/2 seconds = 1800 seconds.
If he increases his speed by 10 seconds, he will complete a mile in 1790 seconds. Converting in hours = 1790/(60 * 60) = 1790/(60^2)
ANSWER: C
The answer is: C | C |
mathematics | If x is an integer, which of the following is a possible value of K=(x^2 +2x – 7)/9? | [
"-2.4",
"0.268",
"1.166 repeating",
"4.555 repeating",
"8.125"
] | x is an integer, which of the following is a possible value of K=(x^2 +2x – 7)/9?
Used process of elimination
A. -2.4
when this is multiplied by 9, x is not an integer
B. 0.268
when this is multiplied by 9, x is not an integer
C. 1.166 repeating
when this is multiplied by 9, x is not an integer
D. 4.555 repeating
E. 8.... | D |
mathematics | There are 35 students in a hostel. If the no. of students increases by 2, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess? | [
"s. 234.50",
"s. 239.50",
"s. 242.50",
"s. 248.50",
"s. 249.50"
] | Suppose the average join the mess , total expenditure = 35x + 42
Now, the average expenditure = (35x + 42)/ (35 + 2) = x – 1
or, 35x + 42 = 37x – 37
or, x = 39.50
Thus the original expenditure of the mess = 35 x 39.5 =1382.50
Therefore x-1 = 38.5
hence 42 x 38.5 = 1617
1617-1382.50 = Rs. 234.50
A
The answer is: A | A |
mathematics | I. a^2 - 9a + 20 = 0,
II. 2b^2 - 5b - 12 = 0 to solve both the equations to find the values of a and b? | [
"a < b",
"a ≤ b",
"the relationship between a and b cannot be established",
"a > b",
"a ≥ b"
] | I. (a - 5)(a - 4) = 0
=> a = 5, 4
II. (2b + 3)(b - 4) = 0
=> b = 4, -3/2 => a ≥ b
Option E
The answer is: E | E |
mathematics | The largest four-digit number which when divided by 4, 7 or 13 leaves a remainder of 3 in each case,is : | [
"8739",
"9831",
"9834",
"9893",
"8976"
] | Solution
Greatest number of 4 digits is 9999. L.C.M. of 4, 7, and 13 = 364.
on dividing 9999 by 364, remainder obtained is 171.
So, greatest number of 4 digits divisible by 4,7, and 13 = (9999 - 171) = 9828.
Hence, required number = (9828 + 3) = 9831.Answer B
The answer is: B | B |
mathematics | If n = 3 x 4 x p, where p is a prime number greater than 3, how many different positive non-prime divisors does n have, excluding 1 and n? | [
"Six",
"Seven",
"Eight",
"Nine",
"Ten"
] | N=Xa∗Yb where X and Y are prime,
then number of factors of N are given by the formula (a+1)(b+1) { Notice I have simply increased the powers of X and Y by one and then multiplied them. Also Make sure X and Y are DISTINCT primes)
So, in your question, n = 3 x 4 x p, where p is prime.
I can n=31∗22∗p^1
or number of facto... | B |
mathematics | Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 20 seconds. Find the length of the faster train? | [
"270",
"277",
"200",
"257",
"271"
] | Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps.
Distance covered in 27 sec = 20 * 10 = 200 m.
The length of the faster train = 200 m.
Answer: C
The answer is: C | C |
mathematics | Together, Andrea and Brian weigh p pounds; Brian weighs 8 pounds more than Andrea. Brian and Andrea's dog, Cubby, weighs p/4 pounds more than Andrea. In terms of p, what is Cubby's weight in pounds? | [
"p/2 - 10",
"3p/4 - 4",
"3p/2 - 5",
"5p/4 - 10",
"5p - 5"
] | Together, Andrea and Brian weigh p pounds --> A + B = p.
Brian weighs 10 pounds more than Andrea --> B = A + 8 --> A + (A + 8) = p --> A = (p - 8)/2 = p/2 - 4.
Brian and Andrea's dog, Cubby, weighs p/4 pounds more than Andrea --> C = A + p/4 = (p/2 - 4) + p/4 = 3p/4 -4.
Answer: B.
The answer is: B | B |
mathematics | In a division sum, the remainder is 0. As student mistook the divisor by 12 instead of 21 and obtained 35 as quotient. What is the correct quotient ? | [
"0",
"12",
"13",
"20",
"25"
] | 12*35=420
420%21=20
ANSWER:D
The answer is: D | D |
mathematics | How many two-digit whole numbers yield a remainder of 1 when divided by 10 and also yield a remainder of 1 when divided by 6? | [
"None",
"One",
"Two",
"Three",
"Four"
] | The possible number N can be written as follow:
N = Multiple of LCM(6,10) + 1st such number
N = 30x + 1
Possible values = 1, 31, 61, 91
Answer : 3 such 2 digit number.
ANSWER:D
The answer is: D | D |
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