divelab/Sys2Bench huggingface dataset:
Question: If a man lost 4% by selling oranges at the rate of 12 a rupee at how many a rupee must he sell them to gain 44%?
Options:
A)1
B)8
C)9
D)4
E)3
Rationale: 96% ---- 12
144% ---- ?
96/144 * 12 = 8
Answer: B
Answer: B
Question: A rectangular rug with side lengths of 2 feet and 7 feet is placed on a square floor that has an area of 64 square feet. If the surface of the rug does not extend beyond the area of the floor, what fraction of the area of the floor is not covered by the rug?
Options:
A)A.3/16
B)1/4
C)C.1/2
D)25/32
E)7/8
Rationale: Area of the rectangular rug = 2*7 = 14
Fraction not covered by the rug = (Total Area - Rug area) / Total Area
= (64 - 14)/64
= 25/32=D
Answer: D
Question: The sequence x1, x2, x3,..., is such that Xn = 1/n - (1/(n+1)). What is the sum of the first 20 terms of the sequence?
Options:
A)201/100
B)99/100
C)100/101
D)1/10000
E)20/21
Rationale: Easy task and accomplish
X1=1-1/2
x2=1/2-1/3
x3=1/3-1/4
.....
x20=1/20-1/21
sum=X1+X2+X3+....X20=1-1/2+1/2-1/3+.......1/20-1/21=1-1/21=20/21
E is the answer
Answer: E
Question: A car consumes 210 liters of petrol weekly. For how many days will 1470 liters of petrol be sufficient?
Options:
A)38
B)20
C)28
D)49
E)10
Rationale: Explanation:
No explanation is available for this question!
ANSWER:D
Answer: D
Question: A larger cube has 343 cubic inch as a volume and in the cube there are 343 smaller cubes such that their volume is 1 cubic inch. What is the difference between the surface areas’ sum of the 343 smaller cubes and the surface area of the larger cube, in square inch?
Options:
A)54
B)64
C)81
D)108
E)1764
Rationale: Volume of larger cube = 343 = 7^3
Side of larger cube = 7
Volume of smaller cube = 1 --> Side of smaller cube = 1
Surface area of larger cube = 6 * 7^2 = 294
Surface area of 27 smaller cubes = 343 * 6 * 1 = 2058
Difference = 2058 - 294 = 1764
Answer: E
Answer: E
Question: How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 3-percent solution?
Options:
A)35
B)33 1/3
C)27
D)16 2/3
E)19.5
Rationale: How many liters of water must be evaporated from 50 liters of a 3-percent sugar solution to get a 3-percent solution?
3% of a 50 liter solution is 1.5L. So you are trying to determine how many liters must a solution be for the 1.5L to represent 3% of the solution. Set up an inequality and solve for x:
1.5/x = 1/3
x = 4.5
Since you need a 15L solution, you must evaporate 19.5 of the original 50L solution to get a 3% solution.
Answer is E.
Answer: E
Question: If s and t are positive integers such that s/t = 84.15, which of the following could be the remainder when s is divided by t ?
Options:
A)2
B)4
C)8
D)20
E)9
Rationale: s/t= 84.15
s = 84.15t
s = (84 + 0.15)t
s = 84t + (15/100)t
s = 84t + (3/20)t
So remainder will be multiple of 3. The only multiple of 3 is 9.
Ans. E
Answer: E
Question: A train passes a station platform in 36 sec and a man standing on the platform in 20 sec. If the speed of the train is 54 km/hr. What is the length of the platform?
Options:
A)287
B)240
C)772
D)211
E)288
Rationale: Speed = 54 * 5/18 = 15 m/sec.
Length of the train = 15 * 20 = 300 m.
Let the length of the platform be x m . Then,
(x + 300)/36 = 15 => x = 240 m.
Answer: B
Answer: B
Question: Currently mangoes cost 60 cents/pound. Due to a disease affecting the mango trees it is expected that next month mangoes will cost 200% more than they do currently. How much are mangoes expected to cost next month?
Options:
A)160 cents /pound
B)170 cents /pound
C)150 cents /pound
D)190 cents /pound
E)180 cents /pound
Rationale: If a new cost is p percent greater than the old cost, then (new cost) = (old cost) + (p/100)(old cost).
In this case, (new cost) = 60 cents/pound + (200/100)(60 cents/pound)
= 60 cents/pound + 120 cents/pound
= 180 cents /pound
Answer : E
Answer: E
Question: A and B started business in partnership investing Rs. 20,000 and Rs. 15,000 respectively. After six months, C joined them with Rs. 20,000. What will be B's share in the total profit of Rs. 25,000 earned at the end of 2 years from the starting of the business?
Options:
A)7500
B)7502
C)2883
D)2790
E)2711
Rationale: A:B:C = (20000 * 24) : (15000 * 24) : (20000 * 18) = 4:3:3
B's share = 25000 * 3/10 = Rs. 7500.Answer: A
Answer: A
Question: One night 18 percent of the female officers on a police force were on duty. If 180 officers were on duty that night and half of these were female officers, how many female officers were on the police force?
Options:
A)90
B)180
C)270
D)500
E)1,000
Rationale: Let total number of female officers in the police force = F
Total number of officers on duty on that night = 180
Number of female officers on duty on that night = 180/2 = 90
(18/100)*F = 90
=>F = 500
Answer D
Answer: D
Question: By investing a 6% stock at 96 an income of Rs. 100 is obtained by making and investment of ?
Options:
A)Rs. 1600
B)Rs. 1504
C)Rs. 1666
D)Rs. 2000
E)Rs. 5760
Rationale: For an income of Rs. 6, investment = Rs. 96.
For an income of Rs. 100, investment = Rs. (96 / 6) x 100 = Rs. 1600
Answer : A
Answer: A
Question: I bought two books; for Rs.540. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
Options:
A)197
B)280
C)189
D)278
E)315
Rationale: x*(85/100)
= (540 - x)119/100
x = 315
Answer: E
Answer: E
Question: A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
Options:
A)176 m
B)786 m
C)500 m
D)865 m
E)796 m
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (800 + x)/60 = 65/3
x = 500 m.
Answer:C
Answer: C
Question: If a, b, and c are consecutive integers such that a < b < c and a is an even prime number, which of the following is true?
I. a + b + c > a^3
II. a × b × c < a^3
III. 5b > bc
Options:
A)I only
B)II only
C)III only
D)II and III
E)I, II, and III
Rationale: Only 'A' is possible solution. If a is even prime number i.e 2, b is 3 and c is 4
Putting the values in the answers only 'A' seems valid.
Answer: A
Question: The average age of 8 men increases by 2 years when two women are included in place of two men of ages 20 and 10 years. Find the average age of the women?
Options:
A)87
B)98
C)30
D)28
E)23
Rationale: 20 + 10 + 8 * 2
= 46/2
= 23
Answer:E
Answer: E
Question: An investor purchased 100 shares of stock X at 8 1/8 dollars per share and sold them all a year later at 24 dollars per share. If the investor paid a 2 percent brokerage fee on both the total purchase price and the total selling price, which of the following is closest to the investor's percent gain on this investment?
Options:
A)92%
B)240%
C)190%
D)300%
E)380%
Rationale: If the purchase price was 8$ per share then the investor would have made a profit of 200%.
Since the purchase price is slightly more than 8$ the profit would be slightly less than 200%.
Also a 2% brokerage is negligible and it brings down the profit percentage only by a small value. Approximation is very useful to solve these kind of problems as the answer choices are far apart.
Answer: C
Answer: C
Question: For the positive numbers, n, n + 1, n + 2, n + 3, and n + 4, the mean is how much greater than the median?
Options:
A)0
B)1
C)n+l
D)n+2
E)n+3
Rationale: Let’s first calculate the mean (arithmetic average).
mean = sum/quantity
mean = (n + n + 1 + n + 2 + n + 3 + n + 4)/5
mean = (5n + 10)/5
mean = n + 2
Next, we determine the median. The median is the middle value when the terms are ordered from least to greatest. The terms ordered from least to greatest are as follows:
n, n + 1, n + 2, n + 3, n + 4
The median is n + 2.
Finally we are asked how much greater the mean is than the median. To determine the difference we can subtract the smaller value (the median) from the larger value (the mean) and we get:
n + 2 – (n + 2) = n + 2 – n – 2 = 0
The answer is A
Answer: A
Question: A football coach must choose 5freshers from a team of 12players. How many different ways can the coach choose the freshers?
Options:
A)657
B)689
C)729
D)776
E)790
Rationale: Choose 5 starters from a team of 12 players. Order is not important.
\inline {\color{Black} 12C_{5}}= 729
C
Answer: C
Question: Difference between the length &breadth of a rectangle is 10 m. If its perimeter is 206 m, then its area is?
Options:
A)2400 m^2
B)1500 m^2
C)2520 m^2
D)1200 m^2
E)2580 m^2
Rationale: Solving the two equations, we get: l = 30 and b = 40.
Area = (l x b) = (30 x 40) m2 = 1200 m^2
D
Answer: D
Question: Find the product of the local value and absolute value of 4 in 564823
Options:
A)1600
B)8000
C)16000
D)12000
E)18000
Rationale: Explanation:
Place value = Local value
Face value = Absolute value
The place value of 4 in 564823 is 4 x 1000 = 4000
The face value of 4 in 564823 is nothing but 4.
=> 4000 x 4 = 16000
Answer: Option C
Answer: C
Question: A is twice as good a work man as B and together they finish the work in 14 days. In how many days A alone can finish the work?
Options:
A)5 days
B)21 days
C)15 days
D)25 days
E)30 days
Rationale: Explanation:
WC = 2:1
2x + x = 1/14 => x = 1/42
2x = 1/21
A can do the work in 21 days.
Answer: B
Answer: B
Question: A train 240 m in length crosses a telegraph post in 16 seconds. The speed of the train is?
Options:
A)40
B)88
C)77
D)6
E)23
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 360 + 140 = 500 m
Required time = 500 * 2/25 = 40 sec.Answer: A
Answer: A
Question: Two brothers took the GMAT exam, the higher score is P and the lower one is Q. If the difference between the two scores is equal to their average, what is the value of Q/P ?
Options:
A)3
B)2
C)1/2
D)1/3
E)There isn't enough data to answer the question.
Rationale: Answer is D : 1/3
P - Q = (P + Q)/2
Solving for Q/P = 1/3
D
Answer: D
Question: How many three digit number can be formed with the numbers 1,2,3,4,5.
Options:
A)125 ways
B)150 ways
C)175 ways
D)180 ways
E)115 ways
Rationale: Since the repetition of number allowed, the first place can be filled in 5 ways. The second place can be filled in 5ways.(repetition of numbers allowed). Third place can be arranged in 5ways. The required number of digit number =5x5x5=125 ways. Answer :A
Answer: A
Question: 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 W of ways this can be done is:
Options:
A)122
B)210
C)216
D)217
E)225
Rationale: 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 form our 5 digit number would be 15-0={1, 2, 3, 4, 5} and 15-3={0, 1, 2, 4, 5}. Meaning that no other 5 from given six will total the number divisible by 3.
Second step:
We have two set of numbers:
1, 2, 3, 4, 5 and 0, 1, 2, 4, 5. How many 5 digit numbers can be formed using these two sets:
1, 2, 3, 4, 5 --> 5! as any combination of these digits would give us 5 digit number divisible by 3. 5!=120.
0, 1, 2, 4, 5 --> here we can not use 0 as the first digit, otherwise number won't be any more 5 digit and become 4 digit. So, desired # would be total combinations 5!, minus combinations with 0 as the first digit (combination of 4) 4! --> 5!-4!=4!(5-1)=4!*4=96
120+96=216=W
Answer: C.
Answer: C
Question: If f(x) = x^4 - 4x^3 - 2x^2 + 5x , then f(-1) =
Options:
A)-4
B)-2
C)-1
D)1
E)2
Rationale: f(-1) = (-1)^4 - 4(-1)^3 - 2(-1)^2 + 5(-1) = 1+4-2-5 = -2
The answer is B.
Answer: B
Question: There are 5 Rock songs, 6 Pop songs, and 3 Jazz. How many different albums can be formed using the above repertoire if the albums should contain at least one Rock song and one Pop song?
Options:
A)15,624
B)16,384
C)6,144
D)384
E)240
Rationale: If there are 5 rock songs then there are 2^5 ways to make a combination. But there should be atleast 1 Rock song, so the total Rock combination will be 2^5 -1
Similar explanation for Pop
But the album can be formed without any Jazz so 2^3
((2^5)-1) * ((2^6)-1) * 2^3
Ans: 15624
Answer: A
Question: Find the value of y from (12)^3 x 6^3 ÷ 432 = y?
Options:
A)2134
B)2234
C)2540
D)2560
E)864
Rationale: 5184
E
Answer: E
Question: The table below shows how many coaches work with each of the major sports teams at Kristensen School. Although no single coach works with all three teams, 6 coaches work with both the Track and Tennis teams, 2 coaches work with both the Track and Baseball teams, and 1 coach works with both the Tennis and Baseball teams. How many different coaches work with these three teams?
Sports No of coaches
Track 8
Tennis 5
Baseball 4
Options:
A)8
B)9
C)11
D)12
E)17
Rationale: X = 8 + 5 + 4 - (6 + 2 + 1) = 8
Answer is A
Answer: A
Question: A cube is painted red on all faces. It is then cut into 27 equal smaller cubes. How many J cubes are painted on only 2 faces?
Options:
A)12
B)8
C)6
D)10
E)16
Rationale: 1) Draw a simple cube
2) Draw 9 squares on each face of the cube (so that it looks like a Rubik's Cube) - this is what the cube will look like when it's cut into 27 equal smaller cubes.
3) Remember that the OUTSIDE of the cube is the part that's painted....
The mini-cubes with 2 painted sides are ALL on the edge of the cube, in themiddleof the edge. There are 4 in front, 4 in back and 4 more on thestripthat runs around the left/top/right/bottom of the cube. J=4 + 4 + 4 = 12. Answer A
Answer: A
Question: A certain car can travel 20 minutes on a gallon of gasoline at 60 miles per hour. If the car had started with a full tank and had 8 gallons of gasoline left in its tank at the end, then what percent of the tank was used to travel 80 miles at 60 mph?
Options:
A)33%
B)20%
C)25%
D)30%
E)40%
Rationale: Total time for travelling 80 miles @ 60 mph = 80/60 = 4/3 hour = 80 minutes.
Given, the car uses 1 gallon for every 20 minutes of driving @ 60 mph. Thus in 80 minutes it will use = 4 gallons. Thus, full tank = 4+8 = 12 gallons ---> 4/12= 33% of the fuel used. A is the correct answer.
Answer: A
Question: Two pipes A and B can fill a tank in 10 minutes and 20 minutes respectively. If both the taps are opened simultaneously, and the tap A is closed after 5 minutes, then how much more time will it take to fill the tank by tap B?
Options:
A)5min
B)6min
C)10min
D)7min
E)12min
Rationale: Part filled in 5 min. = 5(1/10 + 1/20) = 5*3/20 = 3/4
Remaining part = 1 - 3/4 = 1/4
Part filled by B in 1min. = 1/20
1/20 : 1/4 :: 1:x
x = 1/4 *1 * 20 = 5min
Answer is A
Answer: A
Question: A, B and C enter into a partnership. They invest Rs. 40,000, Rs. 80,000 and Rs. 1,20,000 respectively. At the end of the first year, B withdraws Rs. 40,000, while at the end of the second year, C withdraws Rs. 80,000. In what ratio will the profit be shared at the end of 3 years ?
Options:
A)8:7:4
B)1:3:5
C)3:4:7
D)4:5:9
E)None of these
Rationale: Explanation:
A:B:CA:B:C =(40000Ã—36)=(40000Ã—36) :(80000Ã—12+40000Ã—24):(80000Ã—12+40000Ã—24) :(120000Ã—24+40000Ã—12):(120000Ã—24+40000Ã—12)
=144:192:336=144:192:336 =3:4:7=3:4:7.
ANSWER IS C
Answer: C
Question: 5358 x 51 = ?
Options:
A)273255
B)273257
C)273258
D)273260
E)273262
Rationale: 5358 x 51	= 5358 x (50 + 1)
= 5358 x 50 + 5358 x 1
= 267900 + 5358
= 273258.
C)
Answer: C
Question: Jacob brought a scooter for a certain sum of money. He spent 10% of the cost on repairs and sold the scooter for a profit of Rs. 1100. How much did he spend on repairs if he made a profit of 20%?
Options:
A)300
B)278
C)500
D)277
E)261
Rationale: Let the C.P. be Rs. x. Then, 20% of x = 1100
20/100 * x = 1100 => x = 5500
C.P. = Rs. 5500, expenditure on repairs = 10%
Actual price = Rs. (100 * 5500)/110 = Rs. 5000
Expenditures on repairs = (5500 - 5000) = Rs. 500.Answer: C
Answer: C
Question: The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8600. If his salary for the month of May is Rs.6500, find his salary for the month of January?
Options:
A)s.4100
B)s.4270
C)s.4500
D)s.4550
E)s.2500
Rationale: Sum of the salaries of the person for the months of January, February, March and April
= 4 * 8000 = 32000 ----(1)
Sum of the salaries of the person for the months of February, March, April and May
= 4 * 8600
= 34400 ----(2)
(2)-(1) i.e. May - Jan = 2400
Salary of May is Rs.6500
Salary of January = Rs.4100
Answer:A
Answer: A
Question: How many integers between 100 and 600 are there such that their unit digit is odd?
Options:
A)100
B)250
C)200
D)50
E)150
Rationale: 500 numbers between - 100 and 600
Out of which half would be even, half odd.
Number of odd unit digit number =250.
correct option is B
Answer: B
Question: Right now, Al and Eliot have bank accounts, and Al has more money than Eliot. The difference between their two accounts is 1/10 of the sum of their two accounts. If Al’s account were to increase by 10% and Eliot’s account were to increase by 20%, then Al would have exactly $22 more than Eliot in his account. How much money does Eliot have in his account right now?
Options:
A)$110
B)$152.3
C)$180
D)$220
E)$260
Rationale: Lets assume Al have amount A in his bank account and Eliot's bank account got E amount. We can form an equation from the first condition.
A-E = 1/10*(A+E) ==> 9A = 11E ------------ (1)
Second condition gives two different amounts, Al's amount = 1.1A and Eliot's amount = 1.2E
1.1A = 22 + 1.2E ==> 11A =220 +12E -------(2)
Substituting (1) in (2):
11E/9*11 = 220+12E or (121/9-12) E = 220 or 13/9 E =220 E = 220*9/13 =152.3
B
Answer: B
Question: A shopkeeper sells 300 metres of cloth for Rs. 18000 at a loss of Rs.5 per metre. Find his cost price for one metre of cloth?
Options:
A)12
B)27
C)29
D)50
E)65
Rationale: SP per metre = 18000/300 = Rs. 60 Loss per metre = Rs. 5 CP per metre = 60 + 5 = Rs. 65.Answer: E
Answer: E
Question: Find the sum of prime numbers lying between 60 and 75?
Options:
A)198
B)201
C)252
D)272
E)None
Rationale: Solution
Required sum	= 61 + 67 + 71 + 73)
= 272.
Answer D
Answer: D
Question: The list price of an article is Rs.65. A customer pays Rs.57.33 for it. He was given two successive discounts, one of them being 10%. The other discount is?
Options:
A)8%
B)7%
C)10%
D)12%
E)2%
Rationale: Option E
Explanation:
65*(90/100)*((100-x)/100) = 57.33
x = 2%
Answer: E
Question: In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
Options:
A)209
B)210
C)211
D)213
E)215
Rationale: In a group of 6 boys and 4 girls, four children are to be selected such that at least one boy should be there.
Hence we have 4 options as given below
We can select 4 boys ...(option 1)
Number of ways to this = 6C4
We can select 3 boys and 1 girl ...(option 2)
Number of ways to this = 6C3 × 4C1
We can select 2 boys and 2 girls ...(option 3)
Number of ways to this = 6C2 × 4C2
We can select 1 boy and 3 girls ...(option 4)
Number of ways to this = 6C1 × 4C3
Total number of ways
= 6C4 + 6C3 × 4C1 + 6C2 × 4C2 + 6C1 × 4C3
= 6C2 + 6C3 × 4C1 + 6C2 × 4C2 + 6C1 × 4C1[∵ nCr = nC(n-r)]
=
6
×
5
2
×
1
+
6
×
5
×
4
3
×
2
×
1
×
4
=6×52×1+6×5×43×2×1×4
+
6
×
5
2
×
1
×
4
×
3
2
×
1
+
6
×
4
+6×52×1×4×32×1+6×4
=
15
+
80
+
90
+
24
=
209
Answer is A
Answer: A
Question: Set S contains points whose abscissa and ordinate are both natural numbers. Point P, an element in set S has the property that the sum of the distances from point P to the point (8, 0) and the point (0, 12) is the lowest among all elements in set S. How many such points P exist in set S?
Options:
A)1
B)5
C)11
D)8
E)3
Rationale: Explanatory Answer
The sum of the distances from point P to the other two points will be at its lowest only when point P lies on the line segment joining the points (8, 0) and (0, 12).
The equation of the line segment joining the points (8, 0) and (0, 12) is x/8 + y/12 = 1
Or the equation is 12x + 8y = 96 or 3x + 2y = 24.
The question states that the elements of set S contain points whose abscissa and ordinate are both natural numbers.
The equation of the line is 3x + 2y = 24 and hence, x will take even values while y will take values that are multiples of 3.
The values are x = 2, y = 9; x = 4, y = 6; x = 6, y = 3.
Hence, there are 3 such points that exist in set S.
The correct choice is (E)
Answer: E
Question: When n is divided by 15, the remainder is 8. What is the remainder when 5n is divided by 6?
Options:
A)2
B)6
C)3
D)4
E)1
Rationale: Let n=8 (leaves a remainder of 8 when divided by 48)
5n = 5(8) =40, which leaves a remainder of 4 when divided by 6.
Answer D
Answer: D
Question: In an express train, the passengers travelling in A.C. sleeper class, First class and Sleeper class are in the ratio 1 : 2 : 7, and rate for each class is in the ratio 5 : 4 : 2. If the total income from this train is 54,000 , find the income of Indian Railways from A.C. sleeper class.
Options:
A)12,000
B)20,000
C)22,000
D)10,000
E)None of these
Rationale: Let number of passengers = x, 2x, 7x
and Rate = 5y, 4y, 2y
Now, since income = Rate × Number of passengers
∴ Income = 5xy, 8xy, 14xy
∴ Income in ratio = 5 : 8 : 14
∴ Income from A.C. sleeper class = 5/5+8+14×54,000
= 10,000
Answer D
Answer: D
Question: 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?
Options:
A)1900
B)2776
C)8888
D)1666
E)1878
Rationale: 2000 ---- 54
2000 ---- 39
x ----- 20
x*20 = 2000*39
x = 3900
2000
-------
1900
Answer: A
Answer: A
Question: 1000 men have provisions for 20 days. If 650 more men join them, for how many days will the provisions last now?
Options:
A)12.9
B)12.5
C)12.6
D)12.2
E)12.1
Rationale: 1000*20 = 1650*x
x = 12.1
Answer: E
Answer: E
Question: Danny spends $360 buying his favorite dolls. If he buys only small LemonHead dolls, which are $1 cheaper than the large LemonHead dolls, he could buy 5 more dolls than if he were to buy only large LemonHead dolls. How much does a large LemonHead doll cost?
Options:
A)$5
B)$6
C)$7.2
D)$8
E)$9
Rationale: X: Price of small dolls; Y: Price of big dolls.
Y = X +1
360(1/x - 1/y) = 5
<=>x.y = 72
We can make trial: 9x8 = 72.
Choose (E) y = 9.
Answer: E
Question: For what range of values of 'x ' will the inequality 15x - 2/x > 1?
Options:
A)x > 0.4
B)x < 1/3
C)-1/3 < x
D)-1/3 < x and x< 0, x > 2/5
E)x < -1/3 and x > 2/5
Rationale: In Case 1 where x > 0, I agree. I calculated x > (-1/3) and x > 2/5, and because x > 0, it must be x > 2/5.
In Case 2 where x < 0, I don't understand why you say that the range must be x > -1/3 and x < 0, since the values that satisfy the inequality 15x^2 - x - 2 < 0show that x < -1/3 and x < 2/5.
I have the same doubt. Shouldn't the answer be D?
____________
The answer IS D.
Answer: D
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 320 resolutions?
Options:
A)724 m
B)704 m
C)287 m
D)450.6 m
E)927 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 320 resolutions.
= 320 * 2 * 22/7 * 22.4 = 45056 cm
= 450.6 m
Answer:D
Answer: D
Question: The distance between Delhi and Mathura is 110 kms. A starts from Delhi with a speed of 20 kmph at 7 a.m. for Mathura and B starts from Mathura with a speed of 25 kmph at 8 p.m. from Delhi. When will they meet?
Options:
A)12a.m
B)10a.m
C)19a.m
D)76a.m
E)37a.m
Rationale: D = 110 – 20 = 90
RS = 20 + 25 = 45
T = 90/45 = 2 hours
8 a.m. + 2 = 10 a.m.
Answer: B
Answer: B
Question: In a partnership between A, B and C. A's capital is Rs.2000. If his share of a profit of Rs.600 is Rs.200 and C's share is Rs.130, what is B's capital?
Options:
A)Rs.5500
B)Rs.5600
C)Rs.5700
D)Rs.5300
E)Rs.5400
Rationale: 200 + 130 = 330
600 - 330 = 270
200 ---- 2000
270 ---- ? => Rs.5400
ANSWER:E
Answer: E