divelab/Sys2Bench huggingface dataset:
Question: If a1 = 1 and an+1= 2an + 5, n = 1, 2 .. , then a50 is equal to ?
Options:
A)a. 5*2^99-6
B)b. 5*2^99+6
C)c. 6*2^99+5
D)d. 6*2^99-5
E)e. 6*2^99-6
Rationale: Here is my solution:
an+1=2an+5............(1)
lets ADD 5 to both sides....
so (an+1) + 5= 2 (an+5)....................taking 2 as common factor
now a1=1. so for n=1, an+5=6.......
putting n=1. we get both sides as,
a2 + 5= 2 * 6 ..............as ( an+5=6 .......(for n=1)..)
a2= 2 *6 - 5
a2= 2 * 2 *3 - 5
a2= 2^2 *3 - 5................. so with same progression
a50= 2^50 * 3 - 5
a50=2 * 2^49 * 3 - 5
a50= 6*2^49 - 5
E
Answer: E
Question: A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km.
Options:
A)24 kmph
B)22 kmph
C)21 kmph
D)28 kmph
E)29 kmph
Rationale: A
24 kmph
Total time taken = x/40 + 2x/20 hours
= 5x/40 = x/8 hours
Average speed = 3x/(x/8) = 24 kmph
Answer: A
Question: A theater charges $12 for seats in the orchestra and $8 for seats in the balcony. On a certain night, a total of 360 tickets were sold for a total cost of $3,320. How many more tickets were sold that night for seats in the balcony than for seats in the orchestra?
Options:
A) 90
B) 110
C) 120
D) 140
E) 220
Rationale: Orchestra Seats - a
Balcony Seats - b
a+b = 360
and 12a + 8b = 3320
Solving equations simultaneously (Multiply Equation 1 with 8 and subtract from second equation)
4a = 3320 - 8*360 = 3320 - 2880 = 440
i.e. a = 110
and b = 360-110 = 250
More seats in balcony than orchestra = b-a = 250 - 110 = 140
Answer: option D
Answer: D
Question: When 732 is subtracted form the square of a number, the answer that is obtained is 5280. What is the number?
Options:
A)97
B)103
C)99
D)101
E)None of these
Rationale: Let the number be x
x2 - 732 = 5280
x2 = 5280 + (70+3)2 = 5280 + 4900 + 420 + 9 = 10609
= 10000 + 2(100)(3) + 32 = (100 + 3)2
x = 100 + 3 = 103.
ANSWER:B
Answer: B
Question: Of the 20,210 employees of the anvil factory, 2/7 are journeymen. If half of the journeymen were laid off, what percentage of the total remaining employees would be journeymen?
Options:
A) 14.3%
B) 16.67%
C) 33%
D) 28.6%
E) 49.67%
Rationale: The exam gives us a number that is easily divisible by 7 to pique our curiosity and tempt us into calculating actual numbers (also because otherwise the ratio would be incorrect). Since the question is about percentages, the actual numbers will be meaningless, as only the ratio of that number versus others will be meaningful. Nonetheless, for those who are curious, each 1/7 portion represents (14210/7) 2,030 employees. This in turn means that 4,060 employees are journeymen and the remaining 10,150 are full time workers.
If half the journeymen were laid off, that would mean 1/7 of the total current workforce would be removed. This statistic is what leads many students to think that since half the journeymen are left, the remaining journeymen would represent half of what they used to be, which means 1/7 of the total workforce. If 1/7 of the workforce is journeymen, and 1/7 is roughly 14.3%, then answer choice A should be the right answer. In this case, though, it is merely the tempting trap answer choice.
What changed between the initial statement and the final tally? Well, you let go of 1/7 of the workforce, so the total number of workers went down. The remaining workers are still 1/7 of the initial workers, but the group has changed. The new workforce is smaller than the original group, specifically 6/7 of it because 1/7 was eliminated. The remaining workers now account for 1/7 out of 6/7 of the force, which if we multiply by 7 gives us 1 out of 6. This number as a percentage is answer choice B, 49.67%.
Using the absolute numbers we calculated before, there were 4,060 journeymen employees out of 14,210 total. If 2,030 of them are laid off, then there are 2,030 journeyman employees left, but now out of a total of (14,210-2,030) 12,180 employees. 2,030/12,180 is exactly 1/6, or 16.67%. The answer will work with either percentages or absolute numbers, but the percentage calculation will be significantly faster and applicable to any similar situation.
The underlying principle of percentages (and, on a related note, ratios) can be summed up in the brainteaser I like to ask my students: If you’re running a race and you overtake the 2nd place runner just before the end, what position do you end up in?
The correct answer is 2nd place.
Percentages, like ratios and other concepts of relative math, depend entirely on the context. Whether 100% more of something is better than 50% more of something else depends on the context much more than the percentages quoted. When it comes to percentages on the GMAT, the goal is to understand them enough to instinctively not fall into the traps laid out for you.E
Answer: E
Question: In packing for a trip, Sarah puts three pairs of socks - one red, one blue, and one green - into one compartment of her suitcase. If she then pulls four individual socks out of the suitcase, simultaneously and at random, what is the probability that she pulls out exactly two matching pairs?
Options:
A)1/5
B)1/4
C)1/3
D)2/3
E)4/5
Rationale: the successful events are when Sarah pulls 2 matching pair of socks out of 3 matching pairs of socks, which can be done in 3C2 ways as the order is not important
So,3C2 = 3 ways are:
RRBB
RRGG
BBGG
Now,the ways in which 4 socks can be pulled out of 6 socks (3 pairs) = 6C4 = 15
So, probability = 3/15 = 1/5
Ans: A
Answer: A
Question: Tom purchased 8kg of apples at the rate of 70 per kg and 9 kg of mangoes at the rate of 70 per kg. How much amount did he pay to the shopkeeper?
Options:
A)A)1040
B)B)1045
C)C)1055
D)D)1190
E)E)1075
Rationale: Cost of 8 kg apples= 70 × 8 = 560.
Cost of 9 kg of mangoes = 70 × 9 = 630.
Total cost he has to pay = 560 + 630 = 1190.
D)
Answer: D
Question: The ratio of income of Anand to that of Balu is 5 : 4 and the expenditure of Anand to that of Balu is 3: 2. If at the end of the year, each saves Rs, 800, the income of Anand is :
Options:
A)Rs 1600
B)Rs 1800
C)Rs 2000
D)Rs 2200
E)None of these
Rationale: Explanation :
Let the income of Anand and Balu be 5x and 4x and. the expenditures of Anand and Balu be 3y and 2y.
Then, 5x3y = 800 and 4x 2y= 800.
On solving we get : x = 400. As income = 5x = Rs. 2000.
Answer : C
Answer: C
Question: The average runs of a cricket player of 10 innings was 20. How many runs must he make in his next innings so as to increase his average of runs by 4?
Options:
A)22
B)77
C)64
D)19
E)17
Rationale: Explanation:
Average after 11 innings = 24
Required number of runs = (24 * 11) – (20 * 10)
= 264 – 200 = 64
ANSWER: C
Answer: C
Question: A shopkeeper buys two articles for Rs.1000 each and then sells them, making 10% profit on the first article and 10% loss on second article. Find the net profit or loss percent?
Options:
A)200
B)100
C)276
D)280
E)279
Rationale: Profit on first article = 10% of 1000 = 100.
This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.
Answer: B
Answer: B
Question: On my sister's birthday, she was 126 cm in height, having grown 5% since the year before. How tall was she the previous year?
Options:
A)124 cm
B)120 cm
C)116 cm
D)112 cm
E)110 cm
Rationale: Let the previous year's height be x.
1.05x = 126
x = 120
The answer is B.
Answer: B
Question: The average temperature of the town in the first four days of a month was 58 degrees. The average for the second, third, fourth and fifth days was 60 degrees. If the temperatures of the first and fifth days were in the ratio 7 : 8, then what is the temperature on the fifth day ?
Options:
A)22 degrees
B)64 degrees
C)77 degrees
D)26 degrees
E)18 degrees
Rationale: Sum of temperatures on 1st, 2nd, 3rd and 4th days = (58 * 4) = 232 degrees ... (1)
Sum of temperatures on 2nd, 3rd, 4th and 5th days - (60 * 4) = 240 degrees ....(2)
Subtracting (1) From (2), we get :
Temp, on 5th day - Temp on 1st day = 8 degrees.
Let the temperatures on 1st and 5th days be 7x and 8x degrees respectively.
Then, 8x - 7x = 8 or x = 8.
Temperature on the 5th day = 8x = 64 degrees.
Answer: B
Answer: B
Question: Mr. Kela purchased two steel factories, one in india and other one in Malaysia for total Rs. 72
crores. Later on he sold the india factory at 16% profit and malaysian factory at 24% profit.
Thus he gained a total profit of 19%. The selling price of Indian factory is:
Options:
A)52.2 crores
B)56 crores
C)55.5 crores
D)59.3 crores
E)None of these
Rationale: Explanation :
If price(in crore) of Indian factory=x and Malaysian factory=72-x, then
=> x*(116/100) + (72-x)*(124/100) = 72*(119/100)
=> 1.16x+89.28-1.24x = 85.68
=> x = 45
So selling price of an Indian factory = 45*(116/100) = 52.2
Hence (A) is correct answer.
Answer : A
Answer: A
Question: There were 35 students in a hostel. Due to the admission of 7 new students the expenses of the mess were increased by Rs.42 per day while the average expenditure per head diminished by Re 1. What was the original expenditure of the mess?
Options:
A)Rs. 450
B)Rs. 320
C)Rs. 550
D)Rs. 420
E)None
Rationale: Solution:
Let the original average expenditure be Rs.x then, 42(x - 1) - 35x = 42.
=> 7x = 84
=> x = 12
Therefore original expenditure,
= Rs.(35 × 12)=Rs.420.
Answer: Option D
Answer: D
Question: A container has a capacity of 20 gallons and is full of spirit. 4 gallons of spirit is drawn out and the container is again filled with water. This process is repeated 3 times. Find how much spirit is left in the resulting mixture finally?
Options:
A)6(257/525) gallons
B)6(346/625) gallons
C)6.5 gallons
D)6.25 gallons
E)None of these
Rationale: There is a direct formula to calculate such repetition:
Left QTY / Orig QTY = ( (Orig QTY - Rep QTY) / Orig QTY )^n
where n is number of times mixing done:
Left QTY / 20 = (20 -4)^3 / 20^3
Left QTY = 20 (16/20)^3
Left QTY = 20 ( 4/5 )^3
Left QTY = 10.24
Answer is E
Answer: E
Question: If a, b, c are consecutive positive integers and a<b<c, which of the following must be true?
I. c+a=b+a+1
II. abc is an even integer
III. (a+b+c)/3 is an integer
Options:
A)I
B)II
C)I and II
D)II and III
E)all are true
Rationale: 1. c+a=b+a+1 --> a, b, c are consequitive positive integers and a<b<c then c+a=b+a+1. So this statement is always true;
2. abc is an even integer --> out of any 3 consecutive integers at least one must be even thus abc=even. So this statement is also always true;
3. (a+b+c)/3 is an integer --> the sum of odd number of consecutive integers is ALWAYS divisible by that odd number. So this statement is also always true. Or: (a+b+c)/3=(a+a+1+a+2)/3=(3a+3)/3=a+1=integer.
Answer: E.
Answer: E
Question: From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?
Options:
A)756
B)730
C)250
D)600
E)350
Rationale: We may have (3 men and 2 women) or (4 men and 1 woman) or (5 men only).
Required number of ways	= 7C3*6C2 + 7C4*6C1 + 7C5=>756
ANSWER A
Answer: A
Question: Two trains 150 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
Options:
A)10.16 sec
B)18.8 sec
C)14.8 sec
D)10.8 sec
E)11.16 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 150 + 160 = 310 m.
Required time = 310 * 9/250 = 279/25 = 11.16 sec.
Answer: E
Answer: E
Question: At Deluxe paint store, Fuchsia paint is made by mixing 5 parts of red paint with 3 parts of blue paint. Mauve paint is made by mixing 4 parts of red paint with 5 parts blue paint. How many liters of blue paint must be added to 32 liters of Fuchsia to change it to Mauve paint?
Options:
A)9
B)13
C)15
D)16
E)18
Rationale: in 32 liters, Red = 5/8 * 32 = 20 and Blue = 12
so, 20/(12+x) = 4/5
or, x = 13 (Answer B)
Answer: B
Question: (1000)7÷(10)18=?
Options:
A)10
B)100
C)1000
D)10000
E)None of these
Rationale: Explanation:
=(103)7/(10)18
=(10)21/(10)18=10(3)=1000
Option C
Answer: C
Question: What is the principal sum?
I. The sum amounts to Rs. 690 at S.I.
II. Total year is 8 years.
III. The rate of interest is 5% p.a.
Options:
A)I and III only
B)II and III only
C)I and II only
D)Any two of the three
E)All I, II and III
Rationale: Explanation:
Clearly, all the three statements are needed to solve this question
Answer: E
Answer: E
Question: If 'a' and 'b' are non-zero numbers such that their sum is seven times the product, what is the value of 1/a + 1/b?
Options:
A)6
B)7
C)8
D)14
E)21
Rationale: a+b = 7ab
1/a + 1/b = (b + a)/(ab) = 7.
The answer is B.
Answer: B
Question: The product of two natural numbers is 17. Then, the sum of the reciprocals of their squares is:
Options:
A)1/289
B)289/290
C)290/289
D)289
E)300
Rationale: Explanation:
Let the numbers be a and b. Then,
ab = 17, a = 1 and b = 17
So, 1/a2 + 1/b2 = (a2 + b2)/a2 b2
= (12 + 172)/(1 * 17)2 = 290/289
ANSWER IS C
Answer: C
Question: The average of five consecutive even numbers A, B, C, D and E is 20. What percent of E is D?
Options:
A)90.1
B)91.7
C)97.1
D)101.1
E)107.1
Rationale: Explanation :
In such a case the middle number (C) is the average
∴ C = 20 and D = 22 and E = 24
Required percentage = 22/24 x 100 = 91.7
Answer : Option B
Answer: B
Question: Mixture A, which is 20% oil, contains 20 gallons of water and mixture B is 80% oil. If the combination of mixture A and B has a 4.5 : 3 ratio of oil to water, how many gallons of water does mixture B have?
Options:
A)5
B)10
C)30
D)40
E)50
Rationale: Combined mixture has oil: water = 4.5:3 ie. Oil = (4.5/7.5)*100% = 60%
Now by Alligation Rule:
A . ......... B
20% . . . 80%
. . 60% . .
(80-60) . (60-20)
=20 : =40
Qty A: Qty B = 1:2 ( A & B are mixed in 1: 2 ration)
So if A contains 20 gallons water ie total Qty of A= 25 gallons (Since water is 80%)
So as per above ration Qty B mixed will be 50 gallons.
Qty of water in mixture B = 20% of 50 = 10 gallons.
ANSWER:B
Answer: B
Question: A jogger running at 9 kmph along side a railway track is 230 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?
Options:
A)3.6 sec
B)18 sec
C)35 sec
D)72 sec
E)None of these
Rationale: Speed of train relative to jogger
= (45 – 9) km/h = 36 km/h
= (36 × 5⁄18) m/sec = 10 m/sec
Distance to be covered = (230 + 120) m = 350 m.
∴ Time taken = (350⁄10) sec = 35 sec.
Answer C
Answer: C
Question: The simple interest on Rs. 8 for 12 months at the rate of 5 paise per rupeeper month is
Options:
A)1.2
B)4.8
C)4.4
D)3.21
E)None
Rationale: Sol.
S.I. = Rs. [8 * 5/100 * 12] = Rs. 4.8
Answer B
Answer: B
Question: Two commodities have cost per kg is 4.75Rs & 3.20Rswere mixed in a certain
ratio so as to make cost price of mixture as 17.75 Rs. Find the ratio
Options:
A)14.55:13
B)15.55:13
C)16.55:13
D)17.55:13
E)18.55:13
Rationale: mixture17.75-3.20=14.55
mixture 17.75-4.75=13
14.55:13
ANSWER:A
Answer: A
Question: Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 1800. What is their H.C.F.?
Options:
A)10
B)20
C)30
D)40
E)50
Rationale: Let the numbers be 3x, 4x and 5x.
Then, their L.C.M. = 60x
60x = 1800
x = 30
The numbers are (3 x 30), (4 x 30) and (5 x 30).
The H.C.F. is 30.
The answer is C.
Answer: C
Question: There is a rectangular prism made of 1 in cubes that has been covered in tin foil. There are exactly 128 cubes that are not touching any tin foil on any of their sides. If the width of the figure created by these 128 cubes is twice the length and twice the height, what is the measure q in inches of the width of the foil covered prism?
Options:
A)4
B)6
C)8
D)9
E)10
Rationale: If the width is w, then length and height would be w/2.
So, w*w/2*w/2 = 128 => w^3 = (2^3)*64 = (2^3) * (4^3)
=> w = 2*4 = 8 in.
Along the width of the cuboid, 8 cubes don't touch the tin foil. So the actual width will be non-touching cubes + touching cubes
= 8 +2 =q=10
Ans E.
Answer: E
Question: Two cars start at the same time from opposite ends of a highway that is 175 miles long. One car is riding at 25 mph and the second car is riding at 45 mph. How long after they begin will they meet?
Options:
A)2
B)2.5
C)3
D)3.5
E)4
Rationale: As cars are moving in opposite directions their speeds will be added. So their relative speeds: 45+25 = 70 mph
Total distance to be covered = 175 miles.
Time taken would be: 175 miles/70 mph = 2.5 hours
B is the answer.
Answer: B
Question: Find the highest value of 'a' so that 365a16 is divisible by 8.
Options:
A)9
B)8
C)0
D)2
E)1
Rationale: Explanation:
Given, number is divisible by 8 only if 'a16' is divisible by 8.
.: highest value of a is '8'.
Answer: Option B
Answer: B
Question: A certain machine produces 780 units of product P per hour. Working continuously at this constant rate, this machine will produce how many units of product P in 4 days?
Options:
A)7,000
B)24,000
C)74,880
D)100,000
E)168,000
Rationale: Since 7 days consist of 24*4 hours the total is 96 hours.
Since every hour the machine produces 780 units of product P the total product during 96 hours is 96*780=74,880.
Correct Option : D
Answer: D
Question: At a certain hospital, 75% of the interns receive fewer than 6 hours of sleep and report feeling tired during their shifts. At the same time, 70% of the interns who receive 6 or more hours of sleep report no feelings of tiredness. If 80% of the interns receive fewer than 6 hours of sleep, what percent Q of the interns report no feelings of tiredness during their shifts?
Options:
A)6
B)14
C)19
D)20
E)81
Rationale: < 6 hours sleep>= 6 hours sleepTOTAL
Tired75--
Not Tired-0.7*X?
TOTAL80X100
Interns who receive< than 6 hours sleepandNot Tired= 80 - 75 = 5;
TOTAL interns who receive >= 6 hours sleep= 100 - 80 = 20, so interns who receive>= 6 hours sleepand areNot Tired= 0.7 * 20 =14;
Interns who areNot Tired Q= 5 + 14 = 19.
Answer: C.
Answer: C
Question: ABCD is a square where AB =âˆš4008. Let X be a point on AB and Y be a point on CD such that AX = CY . Compute the area of trapezoid AXYD.
Options:
A)3008
B)2004
C)1008
D)2016
E)3000
Rationale: Note that trapezoids AXY D and BXY C are congruent, so the area of AXY D is
always
4008/2= 2004 .
correct answer B
Answer: B
Question: If x, y, and z are positive integers such that x^2 + y^2 + z^2 = , which of the following could be the values of x, y, and z?
I)x=10 y=20 z=30
II)x=5 y=30 z=13
III)x=20 y=-30 z=10
Options:
A)I only
B)II only
C)III only
D)I​ and II
E)I and III
Rationale: The x,y and z are easiest number,so it is easy to find the squares of the values.
Here III) option gives y=-30..(30^2) and(-30^2) are equal.
Answer is option E
Answer: E
Question: A technician makes a round-trip to and from a certain service center by the same route. If the technician completes the drive to the center and then completes 40 percent of the drive from the center, what percent of the round-trip has the technician completed?
Options:
A)30
B)40
C)70
D)80
E)60
Rationale: round trip means 2 trips i.e.to and fro. He has completed one i.e 50% completed. then he traveled another 40% of 50% i.e 20%. so he completed 50 +20 =70 % of total trip
C
Answer: C
Question: A man can row 30 km downstream and 20 km upstream in 4 hours. He can row 45 km downstream and 40 km upstream in 7 hours. Find the speed of man in still water?
Options:
A)12.7
B)16.5
C)12.3
D)12.5
E)12.1
Rationale: Let the speed of the man in still water be a kmph and let the speed of the stream be b kmph.
Now 30/(a + b) + 20/(a - b) = 4 and 45/(a + b) + 40/(a - b) = 7
Solving the equation, the speed of man in still water is 12.5 kmph.
Answer: D
Answer: D
Question: 70, 75, 80, 85, 90, 105, 105, 130, 130, 130
The list shown consists of the times, in seconds, that it took each of 10 schoolchildren to run a distance of 400 on of meters. If the standard devastation of the 10 running times is 26.4 seconds, rounded to the nearest tenth of a second, how many of the 10 running times are more than 1 standard deviation below the mean of the 10 running times?
Options:
A)one
B)two
C)three
D)four
E)five
Rationale: The most time consuming part in this question is to define the mean. Under exam pressure and time pressure it is very easy to make mistake.
it is easier to group numbers: 130*3=390; 105*2=210; 75+85=160; 70+80=150; 90;
Next stage combine results, again using more convenient ways to calculate: 390+210=600; 160+150=310; 90. 600+310+90=1000. Since there are 10 numbers the mean is 100. Questions asks to find the quantity of numbers one SD BELOW the mean, which is 100-26,4=73,6. There are only two numbers below 73,6. The answer is B
Answer: B
Question: What is the remainder when (55)(57) is divided by 8?
Options:
A)1
B)2
C)4
D)5
E)7
Rationale: (55)(57) = (56-1)(56+1) = 56^2 - 1 which is 1 less than a multiple of 8.
Then the remainder will be 7.
The answer is E.
Answer: E
Question: If 40 sheep eat 40 bags of grass in 40 days. In how many days one sheep will eat one bag of grass?
Options:
A)1
B)20
C)40
D)80
E)70
Rationale: Explanation :
Let the required number of days be x.
Less sheep, More days (Indirect Proportion)
Less bags, Less days (Direct Proportion)
Sheep 1 : 40 :: 40 : x
Bags 40 : 1
1 x 40 x x = 40 x 1 x 40
x = 40.
Answer : C
Answer: C
Question: Avinash covers a distance of 8km in 50 minutes. If he covers 3km distance in 2/5th of time then, What speed should he maintain to cover the remaining distance in the remaining time?
Options:
A)10 Kmph
B)15 Kmph
C)25 Kmph
D)27 Kmph
E)30 Kmph
Rationale: Total distance = 8 Km
Total time = 50 Km
Time taken to cover the distence of 3 Km = 50*2/5 = 20 min = 1/3 hours
Remaining distance = 8 - 3 = 5 Km
Required speed = 5/1/3 = 15 Kmph
B
Answer: B
Question: A man sells a horse for Rs.800 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
Options:
A)850
B)860
C)890
D)900
E)950
Rationale: CP = SP + 1CP = SP - g
800 + x = 980 - 2x
3x = 180 => x = 60
CP = 800 + 60 = 860
Option B
Answer: B
Question: If (1/5)^m * (1/4)^4 = 1/(16*(10)^4), then m =
Options:
A)3
B)2
C)1
D)4
E)8
Rationale: (1/5)^m (1/4)^4 = 1/{16(10)^4}
16(10)^4/4^4 = 5^m
[16(2^4)(5^4)]/[2^8] = 5^m
5^4 = 5^m
m=4
D
Answer: D
Question: A trained covered x km at 40 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 4x km.
Options:
A)25kmph
B)30kmph
C)32kmph
D)40kmph
E)42kmph
Rationale: Total time taken = x/40 + 2x/20 hours
= 5x/40 = x/8 hours
Average speed = 4x/(x/8)
= 32 kmph
Answer:C
Answer: C
Question: Suzy has a lot of skeins of yarn, she has blue, yellow, and red yarn. She has twice as much blue yarn as yellow yarn, and she has twice as much yellow yarn as she has red yarn. If she has X skeins of yarn, how many of the skeins are red, in terms of X?
Options:
A)X/8
B)X/7
C)X/6
D)X/5
E)X/4
Rationale: Since the total number of skeins is X, then X = Blue + Yellow + Red
Because there are twice as many Blue as Yellow, then Blue = 2*Yellow
Thus X = 2*Yellow + Yellow + Red, which simplifies to X = 3*Yellow + Red
Because there are twice as many Yellow as Red, then Yellow = 2*Red
Thus X = 3*(2*Red) + Red, which simplifies to X = 7*Red
Therefore Red = X/7
Answer: B
Answer: B
Question: The speed of a boat in upstream is 50 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
Options:
A)15 kmph
B)11 kmph
C)16 kmph
D)18 kmph
E)19 kmph
Rationale: Speed of the boat in still water = (50+80)/2 = 65 kmph. Speed of the stream = (80-50)/2 = 15 kmph.Answer: A
Answer: A
Question: The ratio, by volume, of bleach(B) to detergent(D) to water in a certain solution is 2 : 40 : 100. The solution will be altered so that the ratio of bleach to detergent is tripled while the ratio of detergent to water is halved. If the altered solution will contain 300 liters of water, how many liters of detergent will it contain?
Options:
A)60
B)50
C)40
D)80
E)70
Rationale: B:D:W = 2:40:100
Bnew / Dnew = (1/3)*(2/40) = (1/60)
Dnew / Wnew = (1/2)*(40/100) = (1/5)
Wnew = 300
Dnew = Wnew/5 = 300/5 = 60
So, answer will be
A
Answer: A
Question: If m<0, which of the following represents a positive number?
Options:
A)-d|d|
B)d/ |d|
C)|d|d
D)|d|/d
E)d|d|
Rationale: Answer : A
Answer: A