subject stringclasses 1
value | question stringlengths 3 1.14k | options listlengths 5 5 | solution stringlengths 18 3.7k | answer stringclasses 5
values |
|---|---|---|---|---|
mathematics | A group of 4 students bought movie tickets in one row next to each other. If Bob and Lisa are in this group, what is the probability that Bob and Lisa will each sit next to only one of the three other students from the group? | [
"5.55%",
"16.67%",
"15.75%",
"20.45%",
"25%"
] | The question basically asks about the probability that Bob and Lisa sit at the ends.
The total # of sitting arrangements is 4!.
Desired arrangement is either BYZL or LYZB. Now, YZ can be arranged in 2! ways, therefore total # of favorable arrangements is 2*2!.
P=(favorable)/(total)=(2*2!)/4!=1/6.
Answer: B.
The answer ... | B |
mathematics | If a and b are positive integers, and a=5b+20, the greatest common divisor of a and b CANNOT be | [
"2",
"4",
"5",
"6",
"10"
] | If b is 2, 4, 5, or 10, then GCD of a and b is 2, 4, 5, and 10 respectively. So, by POE the answer must be D.
Still: if b is a multiple of 6, then a is 20 greater than a multiple of 6, so not a multiple of 6, so both of them cannot be divisive by 6.
Answer: D.
The answer is: D | D |
mathematics | If the average (arithmetic mean) of 8 consecutive odd integers is 414, then the least of these integers is | [
"a) 407",
"b) 518",
"c) 519",
"d) 521",
"e) 525"
] | A very helpful rule to know in arithmetic is the rule that in evenly spaced sets, average = median. Because the average will equal the median in these sets, then we quickly know that the median of this set of consecutive odd integer numbers is 414.
There are 8 numbers in the set, and in a set with an even number of ter... | A |
mathematics | A bat is bought for Rs.400 and sold at a gain of 20% find its selling price | [
"Rs.500/-",
"Rs.480/-",
"Rs.430/-",
"Rs.490/-",
"Rs.500/-"
] | 100 % ------> 400 (100 * 4 = 400)
120 % ------> 480 (120 * 4 = 480)
Selling price = Rs.480/-
B
The answer is: B | B |
mathematics | A 90 cm long wire is to be cut into two pieces so that one piece will be 2/7th of the other, how many centimeters will the shorter piece be? | [
"A)73",
"B)20",
"C)83",
"D)21",
"E)52"
] | Explanation:
1: 2/7 = 7: 2
2/9 * 90 = 20
Answer: Option B
The answer is: B | B |
mathematics | if 5+6+4=010530
and 2+4+8=021040
and 3+5+9=021155
and 4+6+7=020954....
then 2+7+5=?????? | [
"051070",
"051770",
"051074",
"151070",
"071070"
] | if 5+6+4=010530
and 2+4+8=021040
and 3+5+9=021155
and 4+6+7=020954....
then 2+7+5=??????
051070
ANSWER:A
The answer is: A | A |
mathematics | The smallest number which when diminished by 7, is divisible by 12, 16, 18, 21 and 28 is | [
"2333",
"1015",
"2683",
"2693",
"1113"
] | Explanation:
Required Number = (L.C.M of 12, 16, 18,21,28)+7
= 1008 + 7
= 1015
Answer: B) 1015
The answer is: B | B |
mathematics | A basketball team composed of 12 players scored 100 points in a particular contest. If none of the individual players scored fewer than 7 points, what is the greatest number of points T that an individual player might have scored? | [
"7",
"13",
"16",
"21",
"23"
] | General rule for such kind of problems:
to maximize one quantity, minimize the others;
to minimize one quantity, maximize the others.
Thus to maximize the number of points of one particular player minimize the number of points of all other 11 players.
Minimum number of points for a player is 7, so the minimum number of... | E |
mathematics | A team scored a total of 126 points. If each player on the team scored at least 14 points, then what is the greatest possible number of players on the team? | [
"A)6",
"B)7",
"C)8",
"D)9",
"E)10"
] | 126/14=9 plus remainder.
The answer is D.
The answer is: D | D |
mathematics | A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey? | [
"8",
"4",
"3",
"2",
"6"
] | M = 45
S = 1.5
DS = 6
US = 3
AS = (2 * 6 * 3) /9 = 4
Answer: B
The answer is: B | B |
mathematics | Find the number of square tiles to cover the floor of a room measuring 4.5 m * 9.5 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms? | [
"422",
"576",
"429",
"428",
"413"
] | Floor area to be covered by tiles = 4 * 9 = 36
tiles area = 0.25 * 0.25 =0.0625
No. of tiles = 36/0.0625 = 576
Answer : B
The answer is: B | B |
mathematics | Reena took a loan of Rs. 1400 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest? | [
"8.55%",
"5.55%",
"4.55%",
"6.55%",
"7.55%"
] | Let rate = R% and time = R years.
Then, (1400 * R * R) / 100 = 432
14R2 = 432
R2 = 30.8 => R = 5.55
ANSWER:B
The answer is: B | B |
mathematics | In a shower, 6 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is: | [
"75 cu. m",
"900 cu. m",
"750 cu. m",
"9000 cu. m",
"7.50 cu. m"
] | 1 hectare = 10000 sq mtr
The volume of water that falls on 1.5 hectares of ground = 0.06*1.5*10000 = 900 cub mtr .
ANSWER:B
The answer is: B | B |
mathematics | A train running at the speed of 60 km/hr crosses a pole in 9 seconds. What is the length of the train? | [
"126",
"217",
"150",
"277",
"212"
] | Speed=(60 * 5/18) m/sec = (50/3) m/sec Length of the train = (Speed x Time) = (50/3 * 9) m = 150 m. Answer:D
The answer is: D | D |
mathematics | A dishonest shopkeeper professes to sell pulses at the cost price, but he uses a false weight of 970gm. for a kg.His gain is …%. | [
"3.09%",
"5.36%",
"4.26%",
"6.26%",
"7.26%"
] | His percentage gain is 100*30/970 as he is gaining 30 units for his purchase of 970 units.
so 3.09%.
ANSWER:A
The answer is: A | A |
mathematics | The sum of a number and the number preceding it is 33. By how much is two less than six times the
number? | [
"196",
"94",
"90",
"100",
"120"
] | two numbers must be 16 and 17
16+17=33
required number is 17
six times of this number= 6*17=102
two less than 102= 102-2= 100
ANSWER:D
The answer is: D | D |
mathematics | (7 + 7 + 7 ÷ 7) / (5 + 5 + 5 ÷ 5) = ? | [
"1",
"1 / 5",
"15 / 11",
"3 / 11",
"None"
] | Answer
Given expression = (7 + 7 + 7 ÷ 7) / (5 + 5 + 5 ÷ 5)
= (14 + 1) / (10 + 1)
=15 / 11
Option: C
The answer is: C | C |
mathematics | How many diagonals does a 63-sided convex polygon have? | [
"1890",
"1953",
"3780",
"3843",
"3906"
] | A 63-sided convex polygon has 63 vertices.
If we examine a single vertex, we can see that we can connect it with 60 other vertices to create a diagonal. NOTE: there are 60 options because we can't connect the vertex to ITSELF, and we can't connect it to its ADJACENT vertices, since this would not create a diagonal.
If ... | A |
mathematics | There are three foam generators in the factory, each of the first two can generate 14 liters of foam in one hour and the third can generate 20 liters in an hour. The three generators start working together at the same time and after one hour and a half one of the first generators stops working and two hours after that ... | [
"120.",
"132.",
"146.",
"161.",
"166."
] | Let the foam generators capacity be -
A = 14 lit/hr
B = 14 lit/hr
C = 20 lit/hr
Total foam generation in 1 hour will be 48 lit ( 14 + 14 + 20 ) ; since in 1 and 1/2 hr they will generate 48 + 24 => 72 litres...
Now one of the first generators stops working ( Say A stops working ) , so we have -
B = 14 lit/hr
C = 20 lit... | D |
mathematics | If the price of gold increases by 40%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before? | [
"331/8%",
"26.67%",
"28.5%",
"332/3%",
"131/3%"
] | 100
140
------
140-------40
100-------? => 28.5%
Answer:C
The answer is: C | C |
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 F 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 F=5 x 3 x 28 x 3 = 1'260. Hence, solution B is correct.
The answer ... | B |
mathematics | Anand and Deepak started a business investing Rs. 6,000 and Rs. 8,000 respectively. Out of a total profit of Rs.4,600. Deepak's share is? | [
"s. 2600.31",
"s. 2628.57",
"s. 2450.32",
"s. 3400.41",
"s. 2400.32"
] | Ratio of their shares = 6000 : 8000 = 3 : 4
Deepak's share = Rs. (4600 * 4/7) = Rs. 2628.57 ANSWER "B
The answer is: B | B |
mathematics | Carina has 115 ounces of coffee divided into 5- and 10-ounce packages. If she has 2 more 5-ounce packages than 10-ounce packages, how many 10-ounce packages does she have? | [
"5",
"7",
"6",
"4",
"3"
] | Lets say 5 and 10 ounce packages be x and y respectively.
Given that, 5x+10y=115 and x=y+2. What is the value of y.
Substituting the x in first equation, 5y+10+10y=85 ->y=105/15.=7
B
The answer is: B | B |
mathematics | If two dice are thrown together, the probability of getting a doublet on the dice is | [
"1/6",
"1/5",
"1/4",
"1/3",
"1/2"
] | The number of exhaustive outcomes is 36.
Let E be the event of getting doublet on the dies is 6/36 = 1/6
P(E) = 1/6.
A)
The answer is: A | A |
mathematics | Which of the following is closer to (22!+21!)/(22!-21!)? | [
"49",
"36",
"1",
"16",
"25"
] | Notice that 22! = (22)(21!), so we can factor out 21! from top and bottom.
(22!+21!)/(22!-21!)=[21!(22+1)]/[21!(22-1)]
= (22+1)/(21-1)
= 23/21
≈ 1
Answer: C
The answer is: C | C |
mathematics | A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? | [
"90",
"94",
"96",
"97",
"99"
] | Let number of notes of each denomination be x.
Then x + 5x + 10x = 480
16x = 480
x = 30.
Hence, total number of notes = 3x = 90.
A
The answer is: A | A |
mathematics | Tom drives from town T to town B, driving at a constant speed of 60 miles per hour. From town B Tom immediately continues to town C. The distance between T and B is twice the distance between B and C. If the average speed of the whole journey was 36 mph, then what is Tom's speed driving from B to C in miles per hour? | [
"12",
"20",
"24",
"30",
"36"
] | Let's assume that it takes 4 hours to go from point T to B. Then the distance between them becomes 240 which makes distance between B and C 120. (240+120)/(4+x) gives us the average speed which is 36. You find x=6. So the question simplifies itself to 120/6=20
Hence the answer is B.
The answer is: B | B |
mathematics | A town's oldest inhabitant is x years older than the sum of the ages of the Lee triplets. If the oldest inhabitants is now J years old, how old will one of the triplets W be in 20 years?
J-X-40/3 is my answers.
J = X + L + L + L is the initial situation
After 20 years
J + 20 = X + L + L + L + 60 ...20 years for each tr... | [
"(J - 50)/3",
"3(J + 20)/x",
"(J + x - 50)/3",
"(J - x + 60)/3",
"(J + x - 20)/3"
] | here it goes:
Oldest inhabitant = sum of age of triplets + X
J = 3L + X so L = (J - X)/3
After 20 years = L + 20
= (J - X)/3 + 20
W= (J - X + 60)/3=D
The answer is: D | D |
mathematics | In a stack of cards, 9 cards are blue and the rest are red. If 2 cards are to be chosen at random from the stack without replacement, the probability that the cards chosen will both be blue is 9/11. What is the number of cards in the stack? | [
"10",
"11",
"12",
"15",
"18"
] | This question can be solved by TESTing THE ANSWERS.
We're told that we have 9 blue cards and an unknown number of red cards. We're also told that if 2 cards are to be chosen at random from the stack WITHOUT replacement, then the probability that the cards chosen will BOTH be BLUE is 9/11. We're asked for the TOTAL numb... | A |
mathematics | At a conference, the only events scheduled for the day are seminars and breaks. All seminars are the same length and are 10 times as long as each break. A break must be between two consecutive seminars. If the first seminar begins at 9:00 a.m. and the third one ends at 11:20 a.m., how long will the conference last if t... | [
"hours and 15 minutes",
"hours and 20 minutes",
"hours and 25 minutes",
"hours and 30 minutes",
"hours and 35 minutes"
] | Well its like this S B S B S B S B S B S
the interval between 9 am to 11:40 am is 160 min having 3 seminars and 2 breaks .If 1 break is of 5 min than time for 3 seminars = 160 - 2*5=150
Time of 1 seminar =150 /3=50 min .
So calculating for 6 seminars and 5 breaks ,total time comes out to be 5 hrs and 20 min .
Answer is... | B |
mathematics | How many words, with or without meaning, can be formed using all letters of the word EQUATION using each letter exactly once? | [
"38,320",
"39,320",
"40,320",
"38,400",
"39,400"
] | The Word EQUATION has exactly 8 letters which are all different.
Therefore the number of words that can be formed = Number of permutations of 8 letters taken all at a time.
= P (8, 8) = 8!
= 8 × 7 x 6 × 5 x 4 x 3 x 2 × 1
= 40,320
ANSWER:C
The answer is: C | C |
mathematics | A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 3 a rupee. Find his net profit or loss percent? | [
"33 1/8 %",
"33 8/3 %",
"33 1/3 %",
"93 1/3 %",
"43 1/3 %"
] | The total number of mangoes bought by the shopkeeper be 12.
If he buys 4 a rupee, his CP = 3
He selling at 3 a rupee, his SP = 4
Profit = SP - CP = 4 - 3 = 1
Profit Percent = 1/3 * 100 = 33 1/3 %
Answer:C
The answer is: C | C |
mathematics | If A and B are two prime numbers bigger than 2, which of the following can be true?
(1) A + B is an even number.
(2) A x B is also a prime number.
(3) A^B is also a prime number. | [
"1 only.",
"2 only.",
"3 only.",
"2 and 3 only.",
"1, 2 and 3."
] | Answer is D : 2 and 3 only
(1) A + B is an even number. : All primes beyond 2 are odd, so odd+odd = even, so true
(2) A x B is also a prime number. : Beats the property of primes, so false
(3) A^B is also a prime number. : Beats the property of primes, so false
Ans :A
The answer is: A | A |
mathematics | Elvin's monthly telephone bill is the sum of the charge for the calls he made during the month and a fixed monthly charge for Internet service. Elvin's total telephone bill for January was $46 and Elvin's total telephone bill for February was 76$. If Elvin's charge for the calls he made in February was twice the charge... | [
"$5",
"$10",
"$14",
"$16",
"$28"
] | Bill = Fixed Charge + Charge of Calls made
in Jan, Bill = Fixed Charge(Let, y) + Charge of calls made in Jan (Let, x) = $46
in Feb, Bill = Fixed Charge (Let, y) + Charge of calls made in Feb (Then, 2x) = $76
i.e. x+y = 46
and 2x+y = 76
Take the difference if two equations
i.e. (2x+y) - (x+y) = 76 - 46
i.e. x = 30
i.e. ... | D |
mathematics | For positive integers k and n, the k-power remainder of n is defined as r in the following equation:
n = k^w + r, where w is the largest integer such that r is not negative. For instance, the 3-power remainder of 13 is 4, since 13 = 3^2 + 4. In terms of k and w, what is the largest possible value of r that satisfies th... | [
"(k – 1)k^w – 1",
"k^w – 1",
"(k + 1)k^w – 1",
"k^(w+1) – 1",
"(k + 1)k^(w+1) – 1"
] | n = k^w + r, where w is the largest integer such that r is not negative
This means k^w <= n, and k^(w+1) > n
So n lies between k^w and k^(w+1)
Now, r = n - k^w, which means r is the distance between n and k^w
This distance is maximised at the highest possible value of n, which can be just below k^(w+1)
So n = k^(w+1) -... | A |
mathematics | The H.C.F of two numbers is 8. Which one of the following can never be their L.C.M? | [
"8",
"12",
"60",
"72",
"None"
] | Solution
H.C.F of two numbers divides their L.C.M exactly.
Clearly, 8 is not a factor of 60.
Answer C
The answer is: C | C |
mathematics | Sum of the squares of three numbers is 522 and the sum of their products taken two at a time is 131. Find the sum? | [
"20",
"22",
"25",
"27",
"28"
] | (a + b + c)2 = a2 + b2 + c2 + 2(ab +bc + ca) = 522 + 2* 131
a + b + c = √784 = 28
E
The answer is: E | E |
mathematics | The value of a 10.5% stock, in which an income of Rs.756 is derived by investing Rs.9000, brokerage being% is : | [
"110.43",
"120.65",
"124.75",
"134.56",
"165.9"
] | For an income of Rs.756, investment = Rs.9000
For an income of Rs., investment = = Rs.125
For a Rs.100 stock, investment = Rs.125.
Market value of Rs. 100 stock = = Rs. 124.75
C
The answer is: C | C |
mathematics | George does 3/5th of a piece of work in 9 days. He then calls in Paul , and they finish the work in 4 days. How long would Paul take to do the work by himself? | [
"30",
"40",
"50",
"60",
"70"
] | 100% work will be done by George in 15 days
(1/15)9+(1/15+1/x)4=1
solving this eqn.
we get x=30
hence Paul take to do the work in 30 days
ANSWER:A
The answer is: A | A |
mathematics | The greatest possible length which can be used to measure exactly the length 6m, 4m 20cm, 4m is | [
"20",
"27",
"35",
"87",
"98"
] | Explanation:
Required Length = H.C.F of 600 cm, 420 cm and 400 c
= 20 cm.
Answer: A) 20 cm
The answer is: A | A |
mathematics | Mixture A is 10 percent alcohol, and mixture B is 40 percent alcohol. If the two are poured together to create a 4-gallon mixture that contains 20 percent alcohol, approximately how many gallons of mixture A are in the mixture? | [
"1.6",
"1.7",
"1.8",
"1.9",
"2.0"
] | (40-20)/(20-15) = Qa/Qb
20/10 = Qa/Qb
2/1 = Qa/Qb
Qa = (2/5) * 4 = 8/5 = 1.6 approx
Answer : A
The answer is: A | A |
mathematics | A certain company has budgeted $1380 for entertainment expenses for the year, divided into 12 equal monthly allocations. If by the end of the third month, the total amount spent on entertainment was $400, how much was the company under budget or over budget? | [
"$55 under budget",
"$30 under budget",
"$30 over budget",
"$55 over budget",
"$90 over budget"
] | The budget for 3 months is (3/12)*$1380 = $345
The company is $55 over budget.
The answer is D.
The answer is: D | D |
mathematics | Two trains, each 100 m long, moving in opposite directions, cross other in 5 sec. If one is moving twice as fast the other, then the speed of the faster train is? | [
"22",
"96",
"60",
"88",
"12"
] | Let the speed of the slower train be x m/sec.
Then, speed of the train = 2x m/sec.
Relative speed = ( x + 2x) = 3x m/sec.
(100 + 100)/5 = 3x => x = 40/3.
So, speed of the faster train = 80/3 = 80/3 * 18/5 = 96 km/hr.
Answer:B
The answer is: B | B |
mathematics | A rectangular carpet has an area of 60 sq.m. If its diagonal and longer side together equal 5 times the shorter side, the length of the carpet is: | [
"5m",
"12m",
"13m",
"14.5m",
"15.5m"
] | Let, length= x meters and breadth= y meters
Then xy=60 and (x2+y2) + x= 5
Therefore, x=60 and (x2+y2)= (5y-x)2
Or xy=60 and 24y2-10xy=0.
Therefore, 24y2-10*60=0 or y2= 25 or =5.
Therefore, x= (60/5)m= 12m. So, length of the carpet = 12m
ANSWER:B
The answer is: B | B |
mathematics | The tax on a commodity is diminished by 20% and its consumption increased by 15%. The effect on revenue is? | [
"7% decrease",
"8% decrease",
"9% decrease",
"6% decrease",
"4% decrease"
] | 100 * 100 = 10000
80 * 115 = 9200
-----------
10000-----------800
100-----------? => 8% decrease
Answer: B
The answer is: B | B |
mathematics | In Plutarch Enterprises, 70% of the employees are marketers, 10% are engineers, and the rest are managers. Marketers make an average salary of $50,000 a year, and engineers make an average of $80,000. What is the average salary for managers if the average for all employees is also $80,000? | [
"$80,000",
"$130,000",
"$240,000",
"$370,000",
"$320,000"
] | For sake of ease, let's say there are 10 employees: 7 marketers, 1 engineers, and 2 manager.
Average company salary * Number of employees = Total company salary
>>> $80,000 * 10 = $800,000
Subtract the combined salaries for the marketers (7 * $50,000) and the engineers ( $80,000)
>>> $800,000 - $350,000 - $80,000 = $37... | D |
mathematics | Six computers, each working at the same constant rate, together can process a certain amount of data in 6 days. How many additional computers, each working at the same constant rate, will be needed to process the same amount of data in 4 days? | [
"3",
"5",
"6",
"9",
"12"
] | Explanation: If six computers require 6 days to process the data, thats
a total of 36 computer-days the product of 6 and 6. If you change the number
of computers or the number of days, 36 will have to remain the product, whether
that means 36 days of one computer or one day with 36 computers.
In 4 days, the number of c... | A |
mathematics | The length of a rectangle is three - fifths of the radius of a circle. The radius of the circle is equal to the side of the square, whose area is 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units? | [
"240 sq.units",
"140 sq.units",
"120 sq.units",
"130 sq.units",
"150 sq.units"
] | Given that the area of the square = 1600 sq.units
=> Side of square = √1600 = 40 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 3/5 * 40 = 24units
Given that breadth = 10 units
Area of the rectangle = lb = 24* 10 = 240 sq.units
Answer:A
The answer is: A | A |
mathematics | A man has Rs. 480 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ? | [
"45",
"60",
"75",
"90",
"80"
] | By verifying options ,we can solve this problem.
Given that no. of denominations are equal i.e.,3(like one rupee,5 rupee and 10 rupee notes)
45/3=15 i.e 15*1+15*5+15*10 =240
...
..
90/3=30 i.e.,30*1+30*5+30*10 =480
answer is 90.
ANSWER:D
The answer is: D | D |
mathematics | Compound X contains elements A and B at an approximate ratio, by weight, of 2:10. Approximately how many grams of element B are there in 300 grams of compound X? | [
"54",
"162",
"250",
"270",
"322"
] | total number of fractions =2+10=12
element B constitutes =10 out of 12 parts of X
So in 300 gms of X have 300*10/12=250 gms of B
and 300-250=50 gms of A.
cross check:- A/B = 50/250 =2/10 (as given)
Ans C
The answer is: C | C |
mathematics | Choose any 4 desserts from a menu of 10? | [
"120",
"140",
"180",
"210",
"240"
] | 10c4 = 210
Answer is D
The answer is: D | D |
mathematics | A man buys Rs. 20 shares paying 9% dividend. The man wants to have an interest of 12% on his money. The market value of each share is: | [
"12",
"13",
"14",
"15",
"18"
] | Dividend on Rs 20 = 9/100*20 = 9/5
is 12 income 100
9/5 is an income on Rs (100/12*9/5) = Rs 15
ANSWER D
The answer is: D | D |
mathematics | A garrison of 2000 men has provisions for 54 days. At the end of 15 days, a reinforcement arrives, and it is now found that the provisions will last only for 20 days more. What is the reinforcement? | [
"1898",
"9801",
"1987",
"1900",
"8373"
] | 2000 ---- 54
2000 ---- 39
x ----- 20
x*20 = 2000*39
x = 3900
2000
-------
1900
Answer:D
The answer is: D | D |
mathematics | The cross-section of a cannel is a trapezium in shape. If the cannel is 16 m wide at the top and 4 m wide at the bottom and the area of cross-section is 700 sq m, the depth of cannel is? | [
"76",
"28",
"27",
"80",
"70"
] | 1/2 * d (16 + 4) = 700
d = 70
Answer: E
The answer is: E | E |
mathematics | A paint crew gets a rush order to paint 80 houses in a new development. They paint the first y houses at a rate of x houses per week. Realizing that they'll be late at this rate, they bring in some more painters and paint the rest of the houses at the rate of 1.25x houses per week. The total time E it takes them to pai... | [
"0.8(80 – y)",
"0.8 + 0.0025y",
"80/y – 1.25",
"80/1.25y",
"80 – 0.25y"
] | This may be a case of bad numberpicking but it worked for me.
80 houses. Let's say that y=40 houses are painted at the rate x=10 houses per week <=> 1/10 week per house. 40*1/10 = 4 houses per week will be painted at this rate.
80-y = 80-40 = 40 houses are to be painted at the faster rate. X*1,25=12,5 houses per week <... | B |
mathematics | A basketball team scored x points per game in its first n games of the season, and in all the following games it scored an average (arithmetic mean) of y points per game. What was the average number of points per game in its first n + 7 games? | [
"x + 3y/(n + 3)",
"x + y/(n + 3)",
"(x + 3y)/(n + 3)",
"(nx + 3y)/(n + 7)",
"(3x + ny)/(n + 3)"
] | Total points in first n games = nx
Total marks in next 3 games is 3y
So, Average marks in n + 7 games = (nx+3y)/(n+7)
Hence, correct answer will be (D)
The answer is: D | D |
mathematics | A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B? | [
"76 years",
"88 years",
"55 years",
"10 years",
"15 years"
] | Let C's age be x years.
Then, B's age = 2x years.
A's age = (2x + 2) years.
(2x + 2) + 2x + x = 27
5x = 25 => x = 5
Hence, B's age = 2x = 10 years.Answer:D
The answer is: D | D |
mathematics | Alice and Bob race around a running track. Alice runs at a constant rate of one lap every 5 minutes and Bob runs at a constant rate of one lap every 6 minutes. If they both start at the same time, how many minutes will it take for Alice to get exactly one lap ahead of Bob? | [
"30",
"32",
"35",
"36",
"40"
] | Let x be the number of minutes it takes for Alice to get one lap ahead.
Then Alice ran x/5 laps and Bob ran x/6 laps.
x/5 = 1+x/6
6x=30+5x
x=30
The answer is A.
The answer is: A | A |
mathematics | Three cars A,B and C started at same point and time. After A reach 50 km, B and C are backward by 10km and 20 km. When B reach 200km, find the position of A and C? | [
"240 and 160km",
"170 and 230 km",
"180 and 240 km",
"235 and 165 km",
"250 and 150 km"
] | Explanation:
A:B = 50 : 40 = 5 : 4
A:C = 50 : 30 = 5 : 3
=>B:C = 4:3
When B covers 40 km , C Covers 30 km
When B covers 200 km , C Covers
=> 150 km
When B covers 40 km , A Covers 50 km
When B covers 200 km , A Covers
=> 250 km
Answer: E
The answer is: E | E |
mathematics | A bag contains 5 white balls, 4 black balls, and 3 red balls. One by one, three balls are drawn out without replacement. What is the probability that the third ball is red? | [
"1/2",
"1/4",
"3/8",
"5/16",
"2/5"
] | The probability for each ball to be drawn third is equal.
Then the probability a red ball is drawn third is 3/12 = 1/4.
The answer is B.
The answer is: B | B |
mathematics | The forth proportional to 5,10,20 is? | [
"20",
"40",
"45",
"80",
"35"
] | Let the fourth proportional to 5,10,20 be x
then 5:10::20:x
5x = 10*20
x = 40
Answer is B
The answer is: B | B |
mathematics | If the cp of 12 rubbers is equal to the sp of 8 rubbers, the gain %is ? | [
"25%",
"30%",
"50%",
"70%",
"80%"
] | (Explanation:Friends, we know we will need gain amount to get gain percent, right.
So lets get gain first.
Let the cost price of 1 pen is Re 1 Cost of 8 pens = Rs 8 Selling price of 8 pens = 12
Gain = 12 - 8 = 4 Gain%=(GainCost*100)%=(48*100)%=50%
C
The answer is: C | C |
mathematics | Sripad has scored average of 68 marks in three objects. In no subjects has he secured less than 58 marks. He has secured more marks in Maths than other two subjects. What could be his maximum score in Maths ? | [
"79",
"28",
"38",
"27",
"88"
] | Assuming Sripad has scored the least marks in subject other than science,
Then the marks he could secure in other two are 58 each.
Since the average mark of all the 3 subject is 68.
i.e (58+58+x)/3 = 68
116 + x = 204
x = 88 marks.
Therefore, the maximum marks he can score in maths is 88.
Answer: E
The answer is: E | E |
mathematics | If x is to be chosen at random from the set {1,2,3,4} and y is to be chosen at random from the set {3,4,5}, what`s the probability that xy will be even? | [
"1/6",
"2/3",
"1/2",
"1/3",
"5/6"
] | The product to be even either one or both must be even, so:
P(x=even OR y=even)=P(x=even)+P(y=even)-P(x=even AND y=even)=2/4+1/3-2/4*1/3=2/3;
Or: P(xy=even)=1-P(xy=odd)=1-2/4*2/3=2/3, so basically we find the probability of the product to be odd (which happens when both x and y are odd) and subtract it from 1.
Answer: ... | B |
mathematics | 1=5,2=25,3=253,4=150,5=225 then 150=? | [
"1",
"255",
"4",
"445",
"235"
] | 1=5,2=25,3=253,4=150,5=225 then 150=?
150=4
check the fourth eqn.
ANSWER:C
The answer is: C | C |
mathematics | Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. In how much time will the trains cross each other? | [
"80/9",
"80/7",
"80/2",
"80/1",
"80/3"
] | Relative speed = (54 + 72)* 5/18 = 7 * 5 = 35 mps.
The time required = d/s = (100 + 100 + 200)/35
= 400/35 = 80/7 sec.
Answer: B
The answer is: B | B |
mathematics | For the past 3 weeks, Rikki has gone to the gym an average of 2 times per week. After 1 more week, the average number of times Rikki goes to the gym increases to 3 times per week. How many times did Rikki visit the gym during the most recent week? | [
"7",
"3",
"6",
"2",
"4"
] | Total times per week over 3 weeks = 3*2 = 6
Total times per week over 4 weeks = 4*3 = 12
Number of visits in most recent week = 12-6 = 6 visits
Answer is C
The answer is: C | C |
mathematics | A and B are two stations 390 km apart. A train starts from A at 10 a.m. and travels towards B at 65 kmph. Another train starts from B at 11 a.m. and travels towards A at 35 kmph. At what time do they meet? | [
"2.15 pm",
"2.15 am",
"3.15 pm",
"3.15 am",
"None of them"
] | Suppose they meet x hours after 10 a.m. Then,
(Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs]=390.
65x + 35(x-1) = 390 => 100x = 425 => x = 17/4
So, they meet 4 hrs.15 min. after 10 a.m i.e., at 2.15 p.m.
Answer is A.
The answer is: A | A |
mathematics | A car traveled 281 miles in 4 hours 41 minutes. What was the average speed of the car in miles per hour? | [
"100 miles / hour",
"90 miles / hour",
"70 miles / hour",
"60 miles / hour",
"30 miles / hour"
] | We first convert the time of 4 hours 41 minutes in minutes
4 hours 41 minutes = 4 ? 60 + 41 = 281 minutes
Average speed S is given by distance / time. Hence
S = 281 miles / 281 minutes = 1 mile / minute
= 60 miles / hour
correct answer D
The answer is: D | D |
mathematics | Eight cubes, each with a volume of 512 cm^3, are joined to form one large cube. What is the surface area of the large cube? | [
"4096 sq cm",
"1536 sq cm",
"1024 sq cm",
"2048 sq cm",
"512 sq cm"
] | volume = a x a x a = a ^3
volume of cube = 8 x 512 = 4096 cm^3
4096 = a^3
a = 16
surface area of cube = 6 a^2 = 6 x 16^2 = 1536
Answer is B
The answer is: B | B |
mathematics | Two pipes A and B can fill a tank in 12 hours and 15 hours respectively. If both the pipes are opened simultaneously, how much time will be taken to fill the tank? | [
"20 hours",
"15 hours",
"10 hours",
"12 hours",
"7 4/9 hours"
] | Part filled by A in 1 hour = 1/12
Part filled by B in 1 hour = 1/15
Part filled by (A+B) in 1 hour = 1/12 + 1/15 = 9/60
Both the pipes together fill the tank in 60/9 = 7 4/9 hours
Answer is E
The answer is: E | E |
mathematics | If each side of a square is increased by 25%, find the percentage change in its area? | [
"65.25",
"56.25",
"65",
"56",
"25"
] | let each side of the square be a , then area = a x a
New side = 125a / 100 = 5a / 4
New area =(5a x 5a) / (4 x 4) = (25a²/16)
increased area== (25a²/16) - a²
Increase %= [(9a²/16 ) x (1/a² ) x 100]% = 56.25%
Answer: B
The answer is: B | B |
mathematics | The division of a whole number N by 10 gives a quotient of 15 and a remainder of 2. Find N. | [
"152",
"197",
"597",
"997",
"297"
] | According to the division process of whole numbers, N can be written, using multiplication, as follows
N = quotient *divisor + remainder = 15* 10 + 2 = 152 correc answer A
The answer is: A | A |
mathematics | At a loading dock, each worker on the night crew loaded 1/2 as many boxes as each worker on the day crew. If the night crew has 4/5 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load? | [
"1/2",
"2/5",
"3/5",
"4/5",
"5/7"
] | Method: X = No. of boxes loaded by day crew.
Boxes by night crew = 1/2 * 4/5 X = 2/5 X
% loaded by day crew = X/(X + 2/5X) = 5/7
Answer E
The answer is: E | E |
mathematics | What annual payment will discharge a debt of Rs. 1025 due in 2 years at the rate of 5% compound interest? | [
"551.28",
"551.25",
"551.2",
"551.23",
"551.21"
] | Let each installment be Rs. x. Then,
x/(1 + 5/100) + x/(1 + 5/100)2 = 1025
820x + 1025 * 441
x = 551.25
So, value of each installment = Rs. 551.25.Answer: B
The answer is: B | B |
mathematics | If an article is sold at 19% profit instead of 12% profit, then the profit would be Rs. 105 more. What is the cost price? | [
"1509",
"1528",
"1500",
"1598",
"1512"
] | Let the cost price of an article be Rs. x.
(19% of x) - (12% of x) = 105
19x/100 - 12x/100 = 105 => 7x = 105 * 100
=> x = 1500
Cost price = Rs. 1500.Answer:C
The answer is: C | C |
mathematics | A sequence of numbers a1a1, a2a2, a3a3,…. is defined as follows: a1=3a1=3, a_2 = 5, and every term in the sequence after a2a2 is the product of all terms in the sequence preceding it, e.g, a3=(a1)(a2)a3=(a1)(a2) and a4=(a1)(a2)(a3)a4=(a1)(a2)(a3). If an=tan=t and n>2n>2, what is the value of an+2an+2 in terms of t? | [
"4t",
"t^2",
"t^3",
"t^4",
"t^8"
] | An = (A1)(A2)......(An-1) = t
An+1 = t * An = t^2
An+2 = t * An * An+1 = t * t * t^2 = t^4
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? | [
"15 days",
"14 days",
"13 days",
"11 days",
"10 days"
] | Explanation:
x/24 + x/30 + x/40 = 1
x = 11 days
Answer: D
The answer is: D | D |
mathematics | 12 spheres of the same size are made from melting a solid cylinder of 8 cm diameter and 27 cm height. What is the diameter of each sphere? | [
"2 cm",
"4 cm",
"6 cm",
"8 cm",
"10 cm"
] | Volume of cylinder = pi*r^2*h
Volume of a sphere = 4*pi*R^3 / 3
12*4*pi*R^3 / 3 = pi*r^2*h
R^3 = r^2*h / 16 = 27 cm^3
R = 3 cm
D = 6 cm
The answer is C.
The answer is: C | C |
mathematics | In how many different ways can five people be seated on a five-seat bench if two of them must sit next to each other? | [
"24",
"48",
"120",
"240",
"480"
] | 5 people can sit in 5! ways.
If 2 of them must sit next to each other, they can sit in 4! ways.
Now, these 2 persons who sit next to each other , can sit in 2! ways.
Therefore, total different ways in which 5 people can sit are 2! x 4! = 48.
Correct answer is B.
The answer is: B | B |
mathematics | There are 200 cats in Cat-City. Out of the 200, 70 are street cats and the rest are domestic cats. 110 cats are gray, 20 out of the gray cats are NOT domestic ones. How many domestic cats are there which are not gray in Cat-City? | [
"90.",
"80.",
"50.",
"40.",
"25."
] | STREET-CAT DOMESTIC-Cat
70 130
(20gray+50other) 90gray+40other
Answer:D
The answer is: D | D |
mathematics | Is y is a positive number? Statement–1: 2x+y > 27; Statement–2: x–3y < 24 | [
"22",
"62",
"28",
"16",
"11"
] | Answer:B
The answer is: B | B |
mathematics | At a certain organisation, the number of male members went up by 12% in the year 2001 from year 2000, and the number of females members went down by 4% in the same time period. If the total membership at the organisation went up by 1.2% from the year 2000 to 2001, what was the ratio of male members to female members in... | [
"1:2",
"1:3",
"2:3",
"3:2",
"2:1"
] | men increase by 12% ==> 1.12M = males in 2001
women decrease by 4% ==> 0.96F = women in 2001
total employees increase by 1.2% ==> 1.012*(M + F) = total number of employees in 2001
Obviously
(males in 2001) + (females in 2001) = total number of employees in 2001
1.12M + 0.96F = 1.012*(M + F)
1.12M + 0.96F = 1.012M + 1.0... | A |
mathematics | There is 60 lit of milk and water in which milk forms 84%.Howmuch water must be added to this solution to make it solution in which milk forms 50% | [
"40.8",
"19.75",
"20.75",
"21.75",
"22.75"
] | 60*84/100=50.40 lit milk that is 9.60 lit water
let x lit water will be added then
(60+x)*50/100=50.40
so x=40.8
ANSWER:A
The answer is: A | A |
mathematics | If n is a positive integer, which one of these following numbers must have a remainder of 3 when
divided by any of the numbers 4, 5, and 6? | [
"125n + 3",
"240n + 3",
"380n + 3",
"590n + 3",
"700n + 3"
] | The numbers 4, 5, and 6 all divide 240 so they all divide 240n.
When we divide (240n + 3) by 4, 5, or 6, the remainder must be 3.
The answer is B.
The answer is: B | B |
mathematics | If a two-digit positive integer has its digits reversed, the resulting integer differs from the original by 63. By how much do the two digits differ? | [
"3",
"4",
"5",
"6",
"7"
] | Given that (10a + b) - (10b + a) = 63 --> 9a - 9b =63 --> a - b = 7.
Answer: E.
The answer is: E | E |
mathematics | The simple interest on a sum of money is 4/9 of the principal. Find the rate percentage and time, if both are numerically equal. | [
"6 1/3 % and 6 2/3 years",
"6 2/3 % and 6 1/3 years",
"6 2/3 % and 6 2/3 years",
"6 1/3 % and 6 1/3 years",
"6 % and 6 2/3 years"
] | Let sum = Rs. x. Then, S.l. = Rs. 4x/9
Let rate = R% and time = R years.
Then, (x*R*R)/100=4x/9 or R^2 =400/9 or R = 20/3 = 6 2/3.
Rate = 6 2/3 % and
Time = 6 2/3 years = 6 years 8 months
Answer is C
The answer is: C | C |
mathematics | A can finish a piece of work in 5 days. B can do it in 10 days. They work together for two days and then A goes away. In how many days will B finish the work? | [
"4",
"5",
"6",
"8",
"2"
] | 2/5 + (2 + x)/10 = 1 => x = 4 days
Answer: A
The answer is: A | A |
mathematics | A sum of money placed at C.I. interest doubles itself in 5 years. It will amount to eight times itself at the same rate of interest in? | [
"7 years",
"10 years",
"15 years",
"20 years",
"25 years"
] | P(1 + R/100)5 = 2P => (1 + R/100)5 = 2
Let P(1 + R/100)n = 8P
=> (1 + R/100)n = 8 = 23 = {(1 + R/100)5}3
=> (1 + R/100)n = (1 + R/100)15 => n = 15 Required time = 15 years.
ANSWER:C
The answer is: C | C |
mathematics | In the decimal notation of number (223)3(223)3, what is the third digit to the right of the decimal point? | [
"0",
"1",
"2",
"4",
"8"
] | Because (2/23)3<(2/20)3=(1/10)3=0.001, the third digit to the right of the decimal point in the decimal notation of (2/23)3 is 0.
Answer: A
The answer is: A | A |
mathematics | If a person walks at 15 km/hr instead of 10 km/hr, he would have walked 10km more. The actual distance traveled by him is? | [
"50 km",
"30 km",
"18 km",
"16 km",
"97 km"
] | Let the actual distance traveled be x km. Then,
x/10 = (x + 10)/15
5x - 150 =>x = 30 km.
Answer: B
The answer is: B | B |
mathematics | The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child? | [
"4 years",
"8years",
"10 years",
"12 years",
"None of these"
] | Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
5x = 20
x = 4.
Age of the youngest child = x = 4 years.
ANSWER:A
The answer is: A | A |
mathematics | 1100 male students and 700 female students are examined in a monthly test; 42% of the male students and 30% of the female students only pass in the examination. Find the percentage of the total failed? | [
"62*2/3",
"40*2/3",
"55*2/3",
"50*2/3",
"35*2/3"
] | Total number = 1100 + 700 = 1800.
tot students passed = (42% of 1100 + 30% of 700) - (462 + 210) = 672.
Number of failures = 1800-672 = 1128.
Percentage of failure = (1128/1800 * 100 )% = 62 * 2/3 %.
ANSWER A
The answer is: A | A |
mathematics | The price of 10 chairs is equal to that of 4 tables. The price of 15 chairs and 2 tables together is Rs. 4000. The total price of 12 chairs and 3 tables is: | [
"Rs. 3500",
"Rs. 3750",
"Rs. 3840",
"Rs. 3900",
"None"
] | EXPLANATION
Let the cost of a chair and that of a table be Rs. x and Rs. y respectively.
Then, 10x = 4y or y = 5b/2 x
15x + 2y = 4000
15x + 2 x 5/2 x= 4000
20x = 4000
x = 200.
So, y = 172 = 500.
Hence, the cost of 12 chairs and 3 tables = 12x + 3y
= Rs. (2400 + 1500)
= Rs. 3900.
Answer D
The answer is: D | D |
mathematics | A man can row upstream at 45km/hr and down stream at 36km/hr find mans rate of the current ? | [
"6.3km/hr",
"9.6km/hr",
"4.5km/hr",
"5.9km/hr",
"9.8km/hr"
] | given upstream(u) =45km/hr
down stream (v)= 36km/hr rate of the current =1/2(u-v) =1/2(45-36)=4.5km/hr
Answer is (C)
The answer is: C | C |
mathematics | The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides. | [
"0 sq m",
"3 sq m",
"2 sq m",
"6 sq m",
"9 sq m"
] | S = (1 + 2 + 3)/2 = 3
=> No triangle exists
ANSWER:A
The answer is: A | A |
mathematics | The probability that a computer company will get a computer hardware contract is 3/4 and the probability that it will not get a software contract is 5/9. If the probability of getting at least one contract is 4/5, what is the probability that it will get both the contracts? | [
"11/30",
"31/60",
"41/80",
"51/120",
"71/180"
] | Let, A ≡ event of getting hardware contract
B ≡ event of getting software contract
AB ≡ event of getting both hardware and software contract.
P(A) = 3/4, P(~B) =5/9
=> P(B) = 1- (5/9) = 4/9.
A and B are not mutually exclusive events but independent events. So,
P(at least one of A and B ) = P(A) + P(B) - P(AB).
=> 4/5 =... | E |
mathematics | If the price of gold increases by 50%, find by how much the quantity of ornaments must be reduced, so that the expenditure may remain the same as before? | [
"331/8%",
"331/3%",
"381/3%",
"351/3%",
"231/3%"
] | 100
150
------
150-------50
100-------? => 331/3%
Answer: B
The answer is: B | B |
mathematics | A company conducted a survey about its two brands, A and B. x percent of respondents liked product A, (x – 20) percent liked product B, 23 percent liked both products, and 23 percent liked neither product. What is the minimum number Q of people surveyed by the company? | [
"46",
"Q.80",
"Q.90",
"Q.100",
"200"
] | 100 = x + x - 20 + 23 - 23
x = 60,
So, Product A = 60%, Product B = 40%, Both = 23%, Neither = 23%
23% of the total no. of people should be an integer. So, A,BC are out.
60% of D and 40% of D are both integers. So, D satisfies all conditions.
So, answer is D.
The answer is: D | D |
mathematics | A certain candy store sold lollipops for $0.90 each and pieces of individually wrapped saltwater taffy for $0.20 each. If a customer purchased both lollipops and taffy from the store, and spent a total of $3.90, what total number of lollipops and saltwater taffy did the customer purchase? | [
"6",
"7",
"8",
"9",
"10"
] | we can take numbers, as price of lollipop 9, 2 for taffy and 39 total for ease.
Now we can determine quickly that total number should range between 39/9 <= N <=39/2, so ans should be between 4 and 20.
Now solving the expression 9A+2B =39
first possibility with 1 lollipop, 15 taffy we get $3.90 total amount, but 1+15=16... | D |
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