subject stringclasses 1
value | question stringlengths 3 1.14k | options listlengths 5 5 | solution stringlengths 18 3.7k | answer stringclasses 5
values |
|---|---|---|---|---|
mathematics | Tough and Tricky questions: Coordinate Geometry.
Line L contains the points (2,3) and (e,q). If q = 2, which of the following could be the equation of line m, which is perpendicular to line L? | [
"2x + y = ex + 7",
"2x + y = –ex",
"x + 2y = ex + 7",
"y – 7 = x ÷ (e – 2)",
"2x + y = 7 – ex"
] | we need m=e-2, so we should gety=mx+bform in answer choices
(A) 2x+y=ex+7 => y=ex-2x+7 => y=x(e-2)+7. It is what we need
(B) 2x + y = –ex => y=-ex-2x => y=x(-e-2). Wrong
(C) x + 2y = ex + 7 => y=x(e-1/2)+7/2. Wrong
(D) y – 7 = x ÷ (e – 2) => y=(1/e-2)x+7. Wrong
(E) 2x + y = 7 – ex => y=-ex-2x+7 => y=x(-e-2)+7. Wrong
A
... | A |
mathematics | If I walk at 3 kmph, I miss the train by 2 min, if however, I walk at 4 kmph. I reach the station 2 min before the arrival of the train. How far do I walk to reach the station? | [
"4/5",
"4/9",
"4/6",
"4/2",
"4/1"
] | x/3 – x/4 = 4/60
x = 4/5 km
Answer: A
The answer is: A | A |
mathematics | A and B entered into a partnership with capitals in the ratio 4 : 5. After 3 months, A withdrew 1/4 of his capital and B withdrew 1/5 of his capital. At the end of 10 months, the gain was Rs.760. What is A's share in the profit? | [
"310",
"320",
"330",
"340",
"350"
] | Ratio of the initial capital of A and B = 4 : 5
Hence we can take the initial capitals of A and B as 4x and 5x respectively
Ratio in which profit will be divided
=((4x)3)+(3/4)×(4x)7 :((5x)3)+4/5×(5x)7
=(12+21):(15+28)
=33:43
A's share =760×33/76=330
Answer is C.
The answer is: C | C |
mathematics | In 10 years, P will be as old as Q is now. Ten years ago, Q was twice as old as P was then. How old is P now? | [
"15",
"20",
"25",
"30",
"35"
] | Q = P+10
Q-10 = 2(P-10)
P = 2P-20
P = 20
The answer is B.
The answer is: B | B |
mathematics | At a restaurant, glasses are stored in two different-sized boxes. One box contains 12 glasses, and the other contains 16 glasses. If the average number of glasses per box is 15, and there are 16 more of the larger boxes, what is the total number of glasses R at the restaurant? (Assume that all boxes are filled to capac... | [
"96",
"240",
"R=256",
"R=384",
"R=480"
] | Most Test Takers would recognize thesystemof equations in this prompt and just do algebra to get to the solution (and that's fine). The wording of the prompt and the 'spread' of the answer choices actually provide an interesting 'brute force' shortcut that you can take advantage of to eliminate the 4 wrong answers....
... | E |
mathematics | Six points lie on the circumference of a circle. What is the positive difference between the number of triangles and the number of quadrilaterals that can be created by connecting these points? | [
"4",
"5",
"6",
"15",
"20"
] | Let's start with the triangle: You have 6 points to choose from but only 3 points you will connect and 3 points you will not connect.
Hence number of possibilities for triangle: 6! / 3! * 3! = 20
Same goes for the quadrilateral: 6 points to choose from, 4 points which you will connect and 2 points which you won't conne... | B |
mathematics | A shopkeeper has 280 kg of apples. He sells 50% of these at 20% profit and remaining 60% at 30% profit. Find his % profit on total. | [
"24%",
"25%",
"26%",
"28%",
"35%"
] | If the total quantity was 100
Then 50X 20% + 60 X30%= 28
This profit will remain same for any total quantity unless the % of products remains the same. Hence 'D' is the answer
The answer is: D | D |
mathematics | A man travels from A to B at a speed of 30 kmph and returns with a speed of 60 kmph. What is the average speed of the man? | [
"87",
"29",
"40",
"77",
"101"
] | Explanation:
The average speed ‘v’, when a man travels two same distance with different speeds ‘v1’ and ‘v2’ is:
v = (2*v1*v2) / (v1 + v2)
In the above problem, v1 = 30 and v2 = 60
Therefore, v = (2*30*60)/(30 + 60) = 3600/90
v = 40
ANSWER:C
The answer is: C | C |
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 1225 sq.units. What is the area (in sq.units) of the rectangle if the rectangle if the breadth is 10 units? | [
"140 sq.units",
"786sq.units",
"167sq.units",
"178sq.units",
"176sq.units"
] | Given that the area of the square = 1225 sq.units
=> Side of square = √1225 = 35 units
The radius of the circle = side of the square = 35 units Length of the rectangle = 2/5 * 35 = 14 units
Given that breadth = 10 units
Area of the rectangle = lb = 14 * 10 = 140 sq.units
Answer:A
The answer is: A | A |
mathematics | The positive integers p and r have exactly three prime factors in common: two 2's and one 3. If p has exactly one additional prime factor x and r has exactly one additional prime factor y such that x ≠ y , which of the following represents the least common multiple of p and r? | [
"12xy",
"6xy",
"xy",
"12",
"6"
] | P and R have exactly 3 factors i.e. 2 , 2 and 3 which comes out to be 12 ;
so p and r will have 12 for sure as a factor ; ok .
now considering that both p -> x as a prime factor and r-> y as prime factor and x is not equal to y ;
LCM will be 12 * x * y
eg: -
let p and r be 12 and 12 each ; then 7 added to p and 11 adde... | A |
mathematics | Find the length of the wire required to go 14 times round a square field containing 5625 m2. | [
"15840",
"3388",
"4200",
"8766",
"66711"
] | a2 = 5625 => a = 75
4a = 300
300 * 14 = 4200
Answer: C
The answer is: C | C |
mathematics | In how many different ways can 3 identical gold shirts and 3 identical sliver shirts be distributed among 6 children such that each child receives a shirt? | [
"100",
"400",
"20",
"96416",
"62"
] | Approach 1:
1st Child: 6 has options
2nd Child: 5 has options…
Therefore, for all kids: 6 x 5 x 4 x 3 x 2 = 720 arrangements.
Since the golds are identical, we divide by 3!; Since the silvers are identical, we divide by another 3!
So: in all, 720/[ 3! X 3! ] = 20 ways.
(e.g. Answer: C)
The answer is: C | C |
mathematics | There are 35 students in a hostel. If the no. of students increases by 7, 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? | [
"Rs. 34",
"Rs. 39",
"Rs. 42",
"Rs. 48",
"Rs. 49"
] | Suppose the average join the mess , total expenditure = 35x + 42
Now, the average expenditure = (35x + 42)/ (35 + 7) = x – 1
or, 35x + 42 = 42x – 42
or, x = 12
Thus the original expenditure of the mess = 35 x 12 = Rs. 42
C
The answer is: C | C |
mathematics | An office supply store stocks three sizes of notebooks, each in five colors: blue, green, yellow, red, or pink. The store packs the notebooks in packages that contain either 4 notebooks of the same size and the same color or 4 notebooks of the same size and of 4 different colors. If the order in which the colors are pa... | [
"18",
"24",
"30",
"45",
"60"
] | First let's consider the small notebooks.
There are 5 ways to choose notebooks of the same color.
The number of ways to choose four notebooks with different colors is 5C4=5.
There are 10 different packages we can make with the small notebooks.
We can use the same process to find 10 different packages with medium and la... | C |
mathematics | The two lines y = x and x = -3 intersect on the coordinate plane. If z represents the area of the figure formed by the intersecting lines and the x-axis, what is the side length of a cube whose surface area is equal to 6z? | [
"16",
"3/√2",
"8",
"2√2",
"(√2)/3"
] | 800score Official Solution:
The first step to solving this problem is to actually graph the two lines. The lines intersect at the point (-3, -3) and form a right triangle whose base length and height are both equal to 4. As you know, the area of a triangle is equal to one half the product of its base length and height:... | B |
mathematics | A five-digit number divisible by 3 is to be formed using numerical 0, 1, 2, 3, 4 and 5 without repetition. The total number of ways this can be done is: | [
"122",
"210",
"216",
"217",
"225"
] | First step:
We should determine which 5 digits from given 6, would form the 5 digit number divisible by 3.
We have six digits: 0, 1, 2, 3, 4, 5. Their sum=15.
For a number to be divisible by 3 the sum of the digits must be divisible by 3. As the sum of the six given numbers is 15 (divisible by 3) only 5 digits good to ... | C |
mathematics | A sum of Rs. 2795 is lent into two parts so that the interest on the first part for 8 years at 3% per annum may be equal to the interest on the second part for 3 years at 5% per annum. Find the second sum? | [
"1642",
"1640",
"1720",
"2795",
"6386"
] | (x*8*3)/100 = ((2795 - x)*3*5)/100
24x/100 = 41925/100 - 15x/100
39x = 41925 => x = 1075
Second sum = 2795 – 1075
=1720
Answer:C
The answer is: C | C |
mathematics | The difference of two numbers is 1385. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ? | [
"274",
"270",
"295",
"360",
"252"
] | Let the smaller number be x. Then larger number = (x + 1385).
x + 1385 = 6x + 15
5x = 1370
x = 274
Smaller number = 274.
ANSWER A
The answer is: A | A |
mathematics | In a simultaneous throw of pair of dice .find the probability of getting the total more than 7 | [
"7/9",
"5/7",
"11/7",
"8/9",
"5/12"
] | Here n(S)=(6*6)=36
let E=event of getting a total more than 7
={(2,6),(3,5),(3,6),(4,4),(4,5),(4,6),(5,3),(5,4),(5,5),(5,6),(6,2),(6,3),(6,4),(6,5),(6,6)}
P(E)=n(E)/n(S)=15/36=5/12
Ans: E
The answer is: E | E |
mathematics | how many 6 digit no. can be formed using digits 0 to 5,without repetition such that number is divisible by digit at its unit place? | [
"420",
"426",
"432",
"456",
"485"
] | when unit place is 1 then numbers which are divisible by 1 = 96 (4*4*3*2*1*1 ways)
when unit place is 2 then numbers which are divisible by 2 = 96 (4*4*3*2*1*1 ways)
when unit place is 3 then numbers which are divisible by 3 = 96 (4*4*3*2*1*1 ways)
when unit place is 3 then numbers which are divisible by 4 = 42 (3*3*2*... | B |
mathematics | Susan can type 10 pages in 5 minutes. Mary can type 5 pages in 10 minutes. Working together, how many pages can
they type in 30 minutes? | [
"15",
"20",
"25",
"65",
"75"
] | susan can type 2 pages in 1 min
mary can type 0.5pages in 1 min
so, both of them work together they type 2.5 pages in 1 min
so,in 30 min they type (30*2.5)= 75 pages
ANSWER:E
The answer is: E | E |
mathematics | Excluding stoppages, the speed of a bus is 90 km/hr and including stoppages, it is 84 km/hr. For how many minutes does the bus stop per hour? | [
"18 min",
"4 min",
"8 min",
"6 min",
"5 min"
] | Due to stoppages, it covers 6 km less.
Time taken to cover 6 km = 6/90 * 60
= 4 min.
Answer:B
The answer is: B | B |
mathematics | Two sets of 3 consecutive positive odd integers have exactly one integer in common. The sum of the integers in the set with greater numbers is how much greater than the sum of the integers in the other set? | [
"4",
"7",
"8",
"12",
"it cannot be determined from the information given."
] | A=(1,3,5), sum of this=9
B=(5,7,9), sum of this=21,
The differenct between 21-9=12
Hence,12 is the answer i.e.D
The answer is: D | D |
mathematics | The integer K is positive, but less than 400. If 21K is a multiple of 180, how many unique prime factors does K have? | [
"1",
"2",
"3",
"4",
"5"
] | Also note here the relevance of 'K must be less than 400'.
21K is 180n (a multiple of 180).
180n = 2^2 * 3^2 * 5 * n = 3*7*K
n must have a 7 at least.
K must have two 2s, a 3 and a 5 at least. This means it must be at least 2*2*3*5 = 60.
So K has the following prime factors: 2, 3 and 5. Can it have any other prime fact... | C |
mathematics | A pupil's marks were wrongly entered as 83 instead of 63. Due to that the average marks for the class got increased by half. The number of pupils in the class is | [
"36",
"40",
"99",
"13",
"12"
] | Let there be x pupils in the class.
Total increase in marks = (x * 1/2) = x/2.
x/2 = (83 - 63) => x/2 = 20 => x = 40.
Answer: B
The answer is: B | B |
mathematics | A boat can travel with a speed of 12 km/hr in still water. If the speed of the stream is 4 km/hr, find the time taken by the boat to go 68 km downstream. | [
"4.25 hr",
"5.25 hr",
"8.25 hr",
"2.25 hr",
"2.50 hr"
] | speed of boat in still water = 12 km/hr
speed of the stream = 4 km/hr
Speed downstream = (12+4) = 16 km/hr
Time taken to travel 68 km downstream = 68⁄16 = 17⁄4 = 4.25 hours
Answer is A
The answer is: A | A |
mathematics | There is a clock which shows false timing ie it shows 10 minutes less for each 1 hour....if the clock shows 12 noon now how many minutes will be lost when it shows 3 pm ? | [
"16 minutes",
"26 minutes",
"36 minutes",
"46 minutes",
"56 minutes"
] | For 1 hour, 10minutes is slower, then for
06 miuntes - 1 minutes is slower
30 minutes - 5 minutes
Actual time false time
12 12
01 PM 12.50 PM (10 minutes slower)
02 PM 01.40 PM (12.50 + 60 min - 10 minutes slower)
03 PM 02.30 PM (01.40 + 60 min - 10 minutes slower)
03.36 PM 03.00 PM (02.30 + 36 min - 6 minutes slower )... | C |
mathematics | H.C.F of 136, 144 and a third number is 8 and their L.C.M is 2^4 * 3^2 * 17 * 7. The third number is: | [
"154",
"248",
"360",
"424",
"168"
] | 136 = 2^3 * 17;
144 = 2^4 * 3^2
H.C.F = 2^3 = 8
Since H.C.F is the product of lowest powers of common factors, so the third number must have (2^3 ) as its factor.
Since L.C.M is the product of highest powers of common prime factors, so the third number must have 3 and 7 as its factors.
Third number = 2^3 * 3 * 7
= 168
... | E |
mathematics | The following sets each have a mean of 5 and the standard deviations are given in variable form.
Set I = {5, 5, 5, 5, 5, 5}, standard deviation = H
Set II = {1, 1, 1, 9, 9, 9}, standard deviation = J
Set III = {2, 3, 4, 6, 7, 8}, standard deviation = K
Rank these three standard deviations from least to greatest. | [
"K, J, H",
"K, H, J",
"H, J, K",
"H, K, J",
"J, H, K"
] | The answer should be D as the mean is least deviated in Set I followed by Set III and then Set II.
The answer is: D | D |
mathematics | A man swims downstream 120 km and upstream 50 km taking 5 hours each time; what is the speed of the current? | [
"3 kmph",
"7 kmph",
"13 kmph",
"6.5 kmph",
"7:3kmph"
] | Explanation:
120 --- 5 DS = 24
? ---- 1
50 ---- 5 US = 10
? ---- 1 S = ?
S = (24 - 10)/2 = 7
Answer: Option B
The answer is: B | B |
mathematics | A factory has a fixed cost of $45,000 a month, and a cost of $2.5 for every item produced. If the selling price of a single item is $5.5, what is the number of items must be sold monthly for the factory to cover its cost exactly? | [
"9,000",
"15,000",
"18,000",
"22,500",
"27,000"
] | selling price - Cost price = 3 so per unit profit =3
cost to recover =45000
no of items required = 45000/3 = 15000
Ans B
The answer is: B | B |
mathematics | A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform? | [
"120 m",
"240 m",
"300 m",
"120 m",
"None of these"
] | Speed = 54 x 5/18 m/sec = 15 m/sec.
Length of the train = (15 x 20)m = 300 m.Let the length of the platform be x metres.
Then, 9x + 3000/36 = 15
x + 300 = 540
x = 240 m. Answer: Option B
The answer is: B | B |
mathematics | If x : y = 1 : 2, find the value of (2x + 3y) : (x + 4y) | [
"5 : 6",
"7 : 8",
"8 : 9",
"9 : 10",
"11 : 12"
] | x : y = 1 : 2 means x/y = 1/2
Now, (2x + 3y) : (x + 4y) = (2x + 3y)/(x + 4y) [Divide numerator and denominator by y.]
= [(2x + 3y)/y]/[(x + 4y)/2] = [2(x/y) + 3]/[(x/y) + 4], put x/y = 1/2
We get = [2 (1/2) + 3)/(1/2 + 4) = (1 + 3)/[(1 + 8)/2] = 4/(9/2) = 4/1 × 2/9 = 8/9
Therefore the value of (2x + 3y) : (x + 4y) = 8 ... | C |
mathematics | What is the approx. value of W, if W=(1.5)11, Given log2 = 0.301, log3 = 0.477 | [
"85",
"84",
"86",
"87",
"99"
] | Explanation :
W = (1.5)11
Take log both sides:
=> logW = 11 x log(1.5) =11 x log(3/2)
=> logW = 11 x (log3 - log2) = 11 x 0.176 = 1.936
=> W = 101.936
=> W = 86 (approx)
Answer : C
The answer is: C | C |
mathematics | The positive number a is q percent greater than the positive number b, which is y percent less than a itself. If a is increased by y percent, and the result is then decreased by q percent to produce a positive number c, which of the following could be true?
I. c > a
II. c = a
III. c < a | [
"I only",
"II only",
"III only",
"I and II only",
"II and III only"
] | Let q = 10% then y = 100/11 %
let b = 100 then a = 110
after increasing a by y and decreasing b yq we get c= 108
therefore c<a
C it is answer
The answer is: C | C |
mathematics | Claire has a total of 90 pets consisting of gerbils and hamsters only. One-quarter of the gerbils are male, and one-third of the hamsters are male. If there are 25 males altogether, how many gerbils does Claire have? | [
"39",
"50",
"66",
"57",
"60"
] | G+H =90 ...1 ; G/4 +H/3 =25 ....2 OR 3G +4H =25*12 =300
G =90-H OR 3(90-H) +4H =300 H = 300-270 =30 THEN G= 96-30 =66
C
The answer is: C | C |
mathematics | how much time does Suresh take to cover a distance of 280 m, if he runs at a speed of 7 km/hr ? | [
"2 min. 24 sec.",
"3 min. 10 sec.",
"1 min. 56 sec.",
"4 min. 32 sec.",
"None of these"
] | Explanation :
Solution: s= 7 km/hr = (7*5/18) m/sec = 35/18 m/sec.
Required time = (280*18/35)sec = 144 sec.
= 1min. 24 sec.
Answer : A
The answer is: A | A |
mathematics | Tough and Tricky questions: Combinations.
Seven contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded? | [
"6",
"7",
"12",
"16",
"21"
] | Number of ways First-place medal can be awarded to four contestants = 7
Number of ways Second-place medal can be awarded to contestants after awarding First-place medal =3
Therefore number of possibilities = 7*3 =21
Answer:E
The answer is: E | E |
mathematics | Find the value of y from (12)^3 x 6^3 ÷ 432 = y? | [
"2134",
"2234",
"2540",
"2560",
"864"
] | 5184
E
The answer is: E | E |
mathematics | A block of wood has dimensions 10cm x 10cm x 50cm. The block is painted red and then cut evenly at the 25 cm mark, parallel to the sides, to form two rectangular solids of equal volume. What percentage of the surface area of each of the new solids is not painted red? | [
"5.5%",
"8.3%",
"11.6%",
"14.2%",
"17.5%"
] | The area of each half is 100+4(250)+100 = 1200
The area that is not painted is 100.
The fraction that is not painted is 100/1200 = 1/12 = 8.3%
The answer is B.
The answer is: B | B |
mathematics | A garrison of 400 men had a provision for 31 days. After 26 days 275 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient? | [
"16 days",
"45 days",
"10 days",
"17 days",
"18 days"
] | 400 --- 31
400 --- 5
125 --- ?
400*5 = 125*x => x =16 days.
Answer: A
The answer is: A | A |
mathematics | If x and y are integers and x + y = 5, which of the following must be true? | [
"x and y are consecutive integers.",
"If x < 0, then y > 0.",
"If x > 0, then y < 0.",
"Both x and y are even.",
"Both x and y are less than 5."
] | Notice that the question asks which of the following MUST be true, not COULD be true.
Given: x + y = 5
A. x and y are consecutive integers: not necessarily true, for example x=1 and y=4;
B. If x < 0, then y > 0: if x is negative then y must be positive in order x+y to be positive, so this statement must be true;
C. If ... | B |
mathematics | A and B starts a business with Rs.8000 each, and after 9 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months? | [
"4:3",
"18:5",
"14:10",
"18:14",
"14:11"
] | A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 9 months and then withdraws Rs.4000. So, the investment of B for remaining 9 months is Rs.4000 only.
A : B
8000*18 : (8000*9) + (4000*9)
14400 : 108000
A:B = 4:3
Answer: A
The answer is: A | A |
mathematics | If 2 cards are selected at random from the deck of 52 cards then What is the probability of one of the selected cards will be King and other will be 10?
A deck of cards has a total of 52 cards, consisting of 4 suits; (spades(Black), hearts(Red), diamond(Red)s, and clubs(Black)); and 13 cards including 1 king, 1 queen a... | [
"8/2652",
"18/2652",
"1/2652",
"12/2652",
"16/2652"
] | 2 possible cases:
King - 10 or 10 -King (4 kings and 4 10).
Either way,
the total probability = 2( King -10) = 2 (4/52 * 4/51) = 18/2652. B is the correct answer.
The answer is: B | B |
mathematics | Special codes are designated by either a 7-letter or an 8-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different codes that can be designated with this system? | [
"2 (26)^8",
"26(26)^7",
"27(26)^7",
"26(26)^8",
"27(26)^8"
] | 26^7+26^8 = 26^7(1+26)=27*26^7
The answer is C.
The answer is: C | C |
mathematics | Ram's age and Shyam's age are in the ratio 3:4. Seven years ago the ratio of their ages was 2:3. Find the ratio of their ages five years hence? | [
"26/73",
"26/39",
"26/93",
"26/33",
"26/13"
] | Let ages of Ramu and Shyam be x and y respectively.
x/y = 3/4 => x = 3/4 y
(x- 7)/(y - 7) = 2/3
=> 3x - 21 = 2y - 14 => 3x = 2y + 7
But x = 3/4 y
3 * 3/4 y = 2y + 7
9y = 8y + 28 => y = 28years
=> x = 21 years
Ratio of their ages five years hence, (21 + 5)/(28 + 5) = 26/33.
Answer: D
The answer is: D | D |
mathematics | What least number must be added to 3000 to obtain a number exactly divisible by 19 ? | [
"1",
"2",
"3",
"4",
"5"
] | Sol. On dividing 3000 by 19, we get 17 as remainder.
Number to be added = (19 - 17) = 2.
Option B
The answer is: B | B |
mathematics | If A lends Rs.3500 to B at 10% per annum and B lends the same sum to C at 11.5% per annum then the gain of B in a period of 3 years is? | [
"157.55",
"157.76",
"157.5",
"157.57",
"157.87"
] | (3500*1.5*3)/100
=> 157.50
Answer: C
The answer is: C | C |
mathematics | Ram professes to sell his goods at the cost price but he made use of 900 grms instead of a kg, what is the gain percent? | [
"11 1/8%",
"31 1/9%",
"11 1/9%",
"11 8/9%",
"13 1/9%"
] | 900 --- 100
100 --- ? => 11 1/9%
Answer:C
The answer is: C | C |
mathematics | If r = 2^3 * 5^2 * 7 and s = 2^3 * 3^2 * 5^3, which of the following is equal to the greatest common divisor of r and s? | [
"2 * 5",
"2^2 * 5",
"2^3 * 5^2",
"2*3*5*7",
"2^3 * 3^2 *5^2 * 7"
] | GCD = product of prime factors raised to the least power = 2^3 * 5^2
The answer is C.
The answer is: C | C |
mathematics | Tickets to a certain concert sell for $20 each. The first 10 people to show up at the ticket booth received a 40% discount, and the next 20 received a 15% discount. If 52 people bought tickets to the concert, what was the total revenue from ticket sales? | [
"$600",
"$740",
"$850",
"$900",
"$1,140"
] | Price of 1 ticket = 20$
Revenue generated from sales of first 10 tickets = 10 * (60/100 * 20 )
= 10 * 12 = 120
Revenue generated from sales of next 20 tickets = 20 *(85/100 * 20 )
=20*17 = 340
Revenue generated from sales of last 22 tickets = 20 * 22
= 440
Revenue generated from sales of 52 tickets = 120 + 340 + 440
= ... | D |
mathematics | During a Pizza buffet where A eats more times 5 than B, and B eats 7 times less than C.find the least number of times all the three has to eat | [
"35",
"45",
"25",
"28",
"42"
] | A eats more than B if B eats 1 times than the ratio of A and B is A:B is 5:1 and as B eat 7 times less the C the the ratio of B : C is 1:7 the the least number of times all three has eat is the LCM of A,B,C that is 35 ..
ANSWER:A
The answer is: A | A |
mathematics | In a market, a dozen eggs cost as much as a pound of rice, and a half-liter of kerosene costs as much as 4 eggs. If the cost of each pound of rice is $0.33, then how many cents does a liter of kerosene cost? [One dollar has 100 cents.] | [
"0.22",
"0.44",
"0.55",
"22",
"55"
] | A dozen eggs cost as much as a pound of rice --> 12 eggs = 1 pound of rice = 33 cents;
A half-liter of kerosene costs as much as 8 eggs --> 4 eggs = 1/2 liters of kerosene.
How many cents does a liter of kerosene cost --> 1 liter of kerosene = 8 eggs = 8/12*33 = 22 cents.
Answer: D.
The answer is: D | D |
mathematics | A dog has 15 bones, then he finds 8 more bones. Now how many bones does he have. | [
"A) 7",
"B) 27",
"C) 23",
"D) 19",
"E) 21"
] | 15 + 8 = 23. Answer is C.
The answer is: C | C |
mathematics | By selling an article at Rs.600, a profit of 25% is made. Find its cost price? | [
"228",
"267",
"287",
"480",
"811"
] | SP = 600
CP = (SP)*[100/(100+P)]
= 600 * [100/(100+25)]
= 600 * [100/125] = Rs.480
Answer: D
The answer is: D | D |
mathematics | Julie put half of her savings in a savings account that pays an annual simple interest and half in a savings account that pays an annual compound interest. After two years she earned $120 and $122 from the simple interest account and the compound interest account respectively. If the interest rates for both accounts we... | [
"600",
"720",
"1080",
"2200",
"3600"
] | $120 for 2 years = $60 per year.
Extra $2 yearned with the compound interest is the percent yearned on percent. So, $2 is yearned on $60, which means that the interest = 30%.
This on the other hand means that half of the savings = 60*30 = $1800. Twice of that = $3,600.
Answer: E.
The answer is: E | E |
mathematics | At a particular graduation party with 220 guests, 70% of the guests brought gifts, and 40% of the female guests brought gifts. If 12 males did not bring gifts to the party, how many females did bring gifts? | [
"18",
"36",
"42",
"68",
"70"
] | the correct method
total = 220..
70% of 220= 154 got gifts..
66 did not get gift, out of which 12 are males, so remaining 60-12=54 are females..
But 40% females brought gift, so 60% did not get it..
so 60% = 54, 100%= 54*100/60= 90..
ans 40% of 90 =36
B
The answer is: B | B |
mathematics | The average of seven numbers is 18. The average of first three numbers is 14 and the average of last three numbers is 19. What is the middle number? | [
"19",
"22",
"27",
"29",
"31"
] | The total of seven numbers = 7X18 = 126
The total of first 3 and last 3 numbers is = 3 X 14+3 X 19 = 99
So, the middle number is (126 - 99 ) = 27
C)
The answer is: C | C |
mathematics | If n is an integer, then the least possible value of |31 - 4n| is? | [
"0",
"1",
"2",
"3",
"4"
] | |31 - 4n| represents the distance between 31 and 4n on the number line. Now, the distance will be minimized when 4n, which is multiple of 4, is closest to 31. Multiple of 4 which is closest to 31 is 32 (for n = 8),
so the least distance is 1: |31 - 32| = 1.
Answer: B.
The answer is: B | B |
mathematics | X and Y invest Rs.21000 and Rs.17500 respectively in a business. At the end of the year, they make a profit of Rs.26400. What is the share of X in the profit? | [
"14400",
"26400",
"12000",
"12500",
"14500"
] | Explanation:
Ratio of the investment
=21000:17500=210:175
=42:35=6:5
Share of X in the profit
=2400 x 6/11
=2400×6=14400
Answer: Option A
The answer is: A | A |
mathematics | A was born when B was 1 year and 3 months old. C was born when A was 2 years 1 month old. What is the age of B when C is 4 years and 6 months old? | [
"4 yr 10 month",
"6 yr 10 month",
"7 yr 11 month",
"7 yr 10 month",
"8 yr 10 month"
] | When C is 4yr 6 month i.e. 54 months old
A is 79 month old..
B is 15 month older than A
When A is 79 months old then,
B is 94 months old i.e. 7yr 10 month
ANSWER:D
The answer is: D | D |
mathematics | Tap 'A' can fill the tank completely in 6 hrs while tap 'B' can empty it by 12 hrs. By mistake, the person forgot to close the tap 'B', As a result, both the taps, remained open. After 4 hrs, the person realized the mistake and immediately closed the tap 'B'. In how much time now onwards, would the tank be full? | [
"2 hours",
"4 hours",
"5 hours",
"1 hour",
"None of these"
] | Explanation :
Tap A can fill the tank completely in 6 hours
=> In 1 hour, Tap A can fill 1⁄6 of the tank
Tap B can empty the tank completely in 12 hours
=> In 1 hour, Tap B can empty 1⁄12 of the tank
i.e., In one hour, Tank A and B together can effectively fill 1⁄6 - 1⁄12 = 1⁄12 of the tank
=> In 4 hours, Tank A and B ... | B |
mathematics | If there are ten positive real numbers n1 < n2 < n3 … < n10, how many triplets of these numbers (n1, n2, n3), (n2, n3, n4) … can be generated such that in each triplet the first number is always less than the second number, and the second number is always less than the third number? | [
"45",
"90",
"120",
"180",
"150"
] | Three numbers can be selected and arranged out of ten numbers in 10P3 ways=10!/7!=10*9*8. Now this arrangement is restricted to a given condition that first number is always less than the second number, and the second number is always less than the third number. Hence three numbers can be arranged among themselves in 3... | C |
mathematics | The perimeter of a semi circle is 180 cm then the radius is? | [
"22",
"28",
"35",
"37",
"13"
] | 36/7 r = 180
=> r
= 35
Answer: C
The answer is: C | C |
mathematics | Let y = 2g + x^2 and g = 5x + 1.
If g^2 = 121, then which of the following can be a value of 2y + 3g? | [
"81",
"130",
"141",
"142",
"160"
] | 800score Official Solution:
First note that g can either be 11 or -11. We are going to have to use both to find all solutions before we can choose a final answer. We begin by substituting g = 11 and then g = -11. If g = 11, then x = 2. If g = -11, then x = -12/5. Since all of our solutions are whole numbers, we can dis... | A |
mathematics | Find the compound interest on $1200 for 6 years at 20% p.a. if CI is component yearly? | [
"$120",
"$150",
"$2383",
"$250",
"$300"
] | A = P(1 + R/100)^T
= 1200(1 + 20/100)^6
=$3583
CI = $2383
Answer is C
The answer is: C | C |
mathematics | The sum of two numbers is 216 and their H.C.F. is 27. The number are: | [
"27, 189",
"81,189,",
"108, 108",
"154, 162",
"none of these"
] | Let the required numbers be 27a and 27b.Then, 27a+27b=216
a+b=8
Now, co-primes with sum 8 are(1, 7)and(3,5).
required numbers are (27*1*, 27*7) and (27*3,27*5)
i.e., (27, 189)and (81,135)
out of these, the given one in the answer is the pair(27,189).
correct Option:A
The answer is: A | A |
mathematics | What is the smallest integer q greater than 1 that leaves a remainder of 1 when divided by any of the integers 6, 8, and 10? | [
"q=21",
"q=41",
"q=121",
"q=241",
"q=481"
] | Or u can just use the answer choices here. Since the answers are already arranged in ascending order, the first number which gives remainder q as 1 for all three is the correct answer. In the given question, the first number which gives a remainder of 1 for 6,8 and 10 is 121.C
The answer is: C | C |
mathematics | Fill in the blank with the correct number in this number series: 3, 9, 8, 7, __, 5, 18, ? | [
"6",
"7",
"9",
"10",
"13"
] | This is a simple alternating subtraction and addition series; The first series begins with 3 and adds 5; the second begins with 9 and subtracts 2, and so on.
Answer: E
The answer is: E | E |
mathematics | If 4 people are selected from a group of 6 married couples, what is the probability that none of them would be married to each other? | [
"1/33",
"2/33",
"1/3",
"16/33 probability",
"11/12"
] | Each couple can send only one "representative" to the committee. We can choose 4 couples (as there should be 4 members) to send only one "representatives" to the committee in C46C64 # of ways.
But these 4 chosen couples can send two persons (either husband or wife): 2∗2∗2∗2=242∗2∗2∗2=24.
So # of ways to choose 4 people... | D |
mathematics | If the average marks of three batches of 55, 60 and 45 students respectively is 40, 55, 60, then the average marks of all the students is: | [
"51.25",
"54.68",
"55",
"56",
"None of these"
] | Explanation:
Required average = (55 × 40 + 60 × 55 + 45 × 60/55 + 60 + 45)
= (2200 + 3300 + 2700/160)
= 8200/160
= 51.25
Answer: A
The answer is: A | A |
mathematics | A box contains Six bulbs out of which five are defective. If five bulbs are chosen at random, find the probability that all the four bulbs are defective? | [
"1/127",
"1/129",
"1/12",
"1/8",
"1/6"
] | Out of six, one are good and five are defective. Required probability
= 5C5/6C5
= 1/6
Answer: E
The answer is: E | E |
mathematics | which of the following statement is not correct? | [
"log10 10 = 1",
"log(2+3)= log(2*3)",
"log10 1= 0",
"log(1+2+3)= log1 + log2 + log3",
"none"
] | a) loga a=1, so log10 10 = 1
b) log(2+3) = log 5 and log(2*3) = log 6 = log 2 + log 3
therefore log(2+3) # log (2*3)
c) since loga 1=0, so log10 1 = 0
d) log(1+2+3) = log 6= log(1*2*3)= log 1+log 2+log 3
e)none
Correct Answer (B)
The answer is: B | B |
mathematics | If the price has fallen by 16% what percent of its consumption be: increased so that the expenditure may be the same as before? | [
"11 1/8%",
"11 1/5%",
"11 1/9%",
"19 1/21%",
"21 1/9%"
] | 100 – 16 = 84
84------16
100------? => 19 1/21%
Answer: D
The answer is: D | D |
mathematics | A certain number X when divided by 243 leaves a remainder of 95. Which of the following can be subtracted from X to make X divisible by 79? | [
"17",
"22",
"37",
"47",
"57"
] | Least possible value of the number is 243 + 95 = 338
Further it is given the number must be divisible by 79 .
338/79 = Gives remainder as 22
So, 22 must be subtracted from the number , answer is (B)
The answer is: B | B |
mathematics | Jake, Lena, and Inna need to drive home from a corporate reception in an SUV that can seat 5 people. If only Inna or Jake can drive, how many seat allocations are possible? | [
"24",
"42",
"120",
"360",
"720"
] | 3 people ,5 seats, only 2 can drive
if inna is in one seat remaining, 2 people can be arranged in 2p2 i.e 2! =2 ways
since any one can drive total ways = 2 *2= 4 ways
4 seats can be chosen out of remaining 5 seats in 5c4 ways = 5!/(3!*2!)= 6 ways
4*6=24
A
The answer is: A | A |
mathematics | If a number is formed by writing integers 1 to 150 one after another, like 12345...150. How many T digits does this integer consists of? | [
"150",
"339",
"342",
"359",
"362"
] | Number of single digit integers = 9
Number of 2 digit integers = 99 - 10 + 1 = 90
Number of 3 digit integers = 150 - 100 + 1 = 51
Number of digits in the integer T= 1*9 + 2*90 + 3*51 = 9 + 180 + 153 = 342
Answer: C
The answer is: C | C |
mathematics | The cost of 3 kg of sugar is $ 60. What will the cost of 8 kg of sugar be? | [
"20",
"40",
"80",
"160",
"180"
] | This is a situation of direct variation, now we solve using unitary method.
Cost of 3 kg of sugar = $ 60
Cost of 1 kg of sugar = $ 60/3 = $ 20
Cost of 8 kg of sugar = $ 20 × 8
Therefore, cost of 8 kg of sugar = $ 160
ANSWER -D
The answer is: D | D |
mathematics | In how many ways, a committee of 8 members can be selected from 10 men and 8 ladies, consisting of 5 men and 3 ladies? | [
"15000",
"14567",
"14112",
"13445",
"14431"
] | (5 men out 10) and (3 ladies out of 8) are to be chosen
Required number of ways = 10C5*8C3 = 14112
Answer is C
The answer is: C | C |
mathematics | For integers x and y if x^2+x/y is always an odd integer then which of the following must be true? | [
"x is even ; y is odd",
"x is even ; y is even",
"x is odd ; y is odd",
"x is odd ; y is even",
"cannot be determined"
] | Given x and y are integers...NOTE : While taking values, x/y must be properly divisible and the result has to integer itself..
x^2+x/y = odd always...
lets take x even (2) and y even (2)
4 + 2/2 = odd...
lets take x odd(3) and y odd(3)
9+3/3 = even...
So only x even and y even satisfies the equation..
If we take one ev... | B |
mathematics | In one hour, a boat goes 14 km/hr along the stream and 8 km/hr against the stream. The speed of the boat in still water (in km/hr) is: | [
"12 km/hr",
"11 km/hr",
"18 km/hr",
"10 km/hr",
"13 km/hr"
] | Speed in still water =1/2(14+8) kmph = 11 kmph.
Answer : Option B
The answer is: B | B |
mathematics | Lorna invests $7000, with some at 6% annual interest and some at 11% annual interest. If she receives a total of $580 from these investments at the end of a year, how much was invested at the 6% interest rate? | [
"$160",
"$1,600",
"$2,200",
"$1,400",
"$5,840"
] | We have that 'x' invested at 6%
We also have that '6000-x' invested at 11%
Now then 580/7000 is approx 10%
Therefore, -4x+7000-x=0
5x=7000
x=1400 approximately. Probably higher
Only D matches
The answer is: D | D |
mathematics | A sells his goods 50% cheaper than B but 50% dearer than C. The cheapest is? | [
"33.8",
"33.7",
"33.3",
"33.2",
"33.1"
] | Let B = 100
A = 50
C * (150/100) = 50
3C = 100
C = 33.3 then 'C' Cheapest
Answer:C
The answer is: C | C |
mathematics | A train covers a distance in 50 min, if it runs at a speed of 48kmph on an average. The speed at which the train must run to reduce the time of journey to 40min will be | [
"45 min",
"60 min",
"55 min",
"70 min",
"75 min"
] | Time = 50/60 hr = 5/6hr
Speed = 48mph
distance = S*T = 48 * 5/6 = 40km
time = 40/60hr = 2/3hr
New speed = 40* 3/2 kmph = 60kmph
Answer : B
The answer is: B | B |
mathematics | The salaries of A and B together amount to $2000. A spends 95% of his salary and B, 85% of his. If now, their savings are the same, what is A's salary? | [
"$1000",
"$1250",
"$2500",
"$1500",
"$1200"
] | Let A's salary is x
B's salary = 2000-x
(100-95)% of x = (100-85)% of (2000-x)
x = $1500
Answer is D
The answer is: D | D |
mathematics | The distance from City A to City B is 30 miles. While driving from City A to City B, Bob drives at a constant speed of 40 miles per hour. Alice leaves City A 30 minutes after Bob. What is the minimum constant speed in miles per hour that Alice must exceed in order to arrive in City B before Bob? | [
"45",
"88",
"120",
"152",
"154"
] | The time it takes Bob to drive to City B is 30 / 40 =0.75 hours.
Alice needs to take less than 0.25 hours for the trip.
Alice needs to exceed a constant speed of 30 /0.25 = 120 miles per hour.
The answer is C.
The answer is: C | C |
mathematics | Each digit in the two-digit number G is halved to form a new two-digit number H. Which of the following could be the sum of G and H | [
"153",
"150",
"137",
"132",
"89"
] | let the number be x, now x is halved => x/2..the question asks what is x?
x(number) + x/2 (half of that number) = something
=> 3x/2 = something
=> x = 2 (something) / 3
so the answer choice must be divisible by 3
eliminate C, E right away
check the rest
D satisfies
3x/ 2 = 132
=> x = 88
Verify. 88 + 44 = 132
Answer is ... | D |
mathematics | A big container is 30% full with water. If 27 liters of water is added, the container becomes 3/4 full. What is the capacity of the big container? | [
"36 liters",
"40 liters",
"45 liters",
"54 liters",
"60 liters"
] | A big container is 30% full with water and after 27 liters of water is added, the container becomes 75% full. Hence these 27 liters account for 45% of the container, which means that the capacity of it is 27/0.45=60 liters.
OR: if the capacity of the container is x liters then: 0.3x+27=0.75x --> x=60 liters.
Answer: E.... | E |
mathematics | Which of the following numbers must be added to 5678 to give a remainder of 35 when divided by 460? | [
"797",
"798",
"799",
"796",
"795"
] | 5678 - 35 + (one of the answer option) should be divisible by 460. Only option C satisfies.
Answer:A
The answer is: A | A |
mathematics | Five men and nine women can do a piece of work in 10 days. Six men and twelve women can do the same work in 8 days. In how many days can three men and three women do the work? | [
"80 days",
"70 days",
"20 days",
"10 days",
"30 days"
] | C
20 days
(5m + 9w)10 = (6m + 12w)8
=> 50m + 90w = 48w + 96 w => 2m = 6w => 1m = 3w 5m + 9w = 5m + 3m = 8m
8 men can do the work in 10 days.
3m +3w = 3m + 1w = 4m
So, 4 men can do the work in (10 * 8)/4 = 20 days.
The answer is: C | C |
mathematics | How much time will a train of length 250 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? | [
"55",
"99",
"88",
"76",
"12"
] | The distance to be covered = Sum of their lengths = 250 + 300 = 550 m.
Relative speed = 72 -36 = 36 kmph = 36 * 5/18 = 10 mps.
Time required = d/s = 550/10 = 55 sec.
Answer:A
The answer is: A | A |
mathematics | A can do a piece of work in 8 days and B alone can do it in 12 days. How much time will both take to finish the work ? | [
"A)4.8",
"B)6.333",
"C)7.333",
"D)8.5",
"E)9"
] | This question can be solved by different methods. We need to conserve time in exams so solving this problem using equations is the good idea.
Time taken to finish the job = XY / (X + Y)
= 8 x 12 / (8 + 12)
= 96 / 20
= 4.8 days
Answer: A
The answer is: A | A |
mathematics | Find the number of ways in which 10 different beads can be arranged to form a necklace. | [
"181440",
"245890",
"457890",
"124560",
"231560"
] | Since in forming a necklace clockwise and anticlockwise arrangements are not different, therefore,10 beads can be arranged to form a necklace in(10-1)! /2 ways
= 9!/2 = 181440ways
Answer is A
The answer is: A | A |
mathematics | What are the total number of divisors of 600(including 1 and 600)? | [
"4",
"24",
"40",
"16",
"20"
] | Write the prime factorization.
600 = (2^3)(3^1)(5^2)
The number of divisors (including 1 and the number itself) is the product of one plus the exponents.
(3+1)(1+1)(2+1) = 24
ANSWER:B
The answer is: B | B |
mathematics | What is the length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high ? | [
"13 m",
"14 m",
"15 m",
"16 m",
"17 m"
] | Explanation:
the length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high is=13mts.
ANSWER IS A
The answer is: A | A |
mathematics | The proportion of water to alcohol in Solution A is 5:4 and the proportion of water to alcohol in Solution B is 6:5. If an equal amount of each solution is mixed together, what is the concentration of alcohol in the new solution? | [
"40.9%",
"41.9%",
"42.9%",
"43.9%",
"44.9%"
] | Let V be the total volume of the new solution.
Then a volume of V/2 was added from each solution A and B.
The amount of alcohol added to the new solution was:
(4/9)(V/2)+(5/11)(V/2)=2V/9+5V/22=89V/198.
The concentration of alcohol is 89/198=44.9%
The answer is E.
The answer is: E | E |
mathematics | The average of 35 numbers is 25. If each number is multiplied by 5, find the new average? | [
"125",
"298",
"267",
"260",
"182"
] | Sum of the 35 numbers = 35 * 25
= 875
If each number is multiplied by 5, the sum also gets multiplied by 5 and the average also gets multiplied by 5.
Thus, the new average = 25 * 5
= 125.
Answer:A
The answer is: A | A |
mathematics | A small pool filled only with water will require an additional 600 gallons of water in order to be filled to 80% of its capacity. If pumping in these additional 600 gallons of water will increase the amount of water in the pool by 30%, what is the total capacity of the pool in gallons? | [
"1000",
"1250",
"1300",
"1600",
"2000"
] | Since pumping in additional 600 gallons of water will increase the amount of water in the pool by 30%, then initially the pool is filled with 1,000 gallons of water.
So, we have that 1,000 + 600 = 0.8*{total} --> {total} = 2,000.
Answer: E.
The answer is: E | E |
mathematics | A can do a piece of work in 15 days and B alone can do it in 10 days. B works at it for 5 days and then leaves. A alone can finish the remaining work in | [
"5days",
"6days",
"7.5days",
"8.5days",
"9days"
] | Explanation:
B's 5 days work =
1/10∗5=1/2
Remaining work =1−1/2=1/2
A can finish work =15∗1/2=7.5days
Option C
The answer is: C | C |
mathematics | How many words can be formed from the letters of the word ‘EXTRA’ so that the vowels are never together? | [
"48",
"120",
"72",
"110",
"116"
] | The given word contains 5 different letters.
Taking the vowels EA together, we treat them as one letter.
Then, the letters to be arranged are XTR (EA).
These letters can be arranged in 4! = 24 ways.
The vowels EA may be arranged among themselves in 2! = 2 ways.
Number of words, each having vowels together = (24x2) = 48... | C |
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