divelab/Sys2Bench huggingface dataset:
Question: In a company of 10 employees, 5 employees earn $30,000, 3 employees earn $40,000, and the 2 highest-paid employees earn the same amount. If the average annual salary for the 10 employees is $65,000, what is the annual salary for each of the highest-paid employees?
Options:
A)$190,000
B)$170,000
C)$150,000
D)$130,000
E)$110,000
Rationale: 5*30,000+3*40,000+2x=10*65,000
2x=650,000-150,000-120,000
2x=380,000
x=190,000
The answer is A.
Answer: A
Question: How many pieces of 75 cm can be cut from a rope 45 meters long?
Options:
A)30
B)40
C)60
D)None
E)Cannot be determined
Rationale: Explanation :
Total pieces of 75 cm that can be cut from a rope of 45 meters long is
= (45 meters)/(75 cm)
= (45 meters)/(0.75 meters)
= 60
Answer : C
Answer: C
Question: If grapes are 90% water and raisins are 15% water, then how many kilograms did a quantity of raisins, which currently weighs 12 kilograms, weigh when all the raisins were grapes? (Assume that the only difference between their raisin-weight and their grape-weight is water that evaporated during their transformation.)
Options:
A)96
B)98
C)100
D)102
E)104
Rationale: Let x be the original weight of the grapes.
The weight of the grape pulp was 0.1x.
Since the grape pulp is 85% of the raisins, 0.1x = 0.85(12 kg).
Then x = 8.5*12 = 102 kg.
The answer is D.
Answer: D
Question: The number 106 can be written as the sum of squares of 3 integers. Which of the following could be the difference between the largest and smallest integers of the 3?
Options:
A)6
B)5
C)7
D)8
E)9
Rationale: Notice that the question asks which of the followingcouldbe the difference between the largest and smallest integers, not must be. The 3 integers could be: +/-4, +/-3 and +/-9, so the difference could be 6, or 12. Since only one of them is among the choices, then it must be the correct answer.
Answer:A
Answer: A
Question: On a certain transatlantic crossing, 25 percent of a ship's passengers held round-trip tickets and also took their cars abroad the ship. If 60 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship's passengers held round-trip tickets?
Options:
A)33.3%
B)40%
C)50%
D)60%
E)62.5%
Rationale: 0.25P = RT + C
0.6(RT) = no C
=> 0.40(RT) had C
0.25P = 0.40(RT)
RT/P = 62.5%
Answer - E
Answer: E
Question: A is twice as good as workman as B and together they finish a piece of work in 18 days. In how many days will B alone finish the work.
Options:
A)27 days
B)54 days
C)56 days
D)68 days
E)65 days
Rationale: Explanation:
As per question, A do twice the work as done by B.
So A:B = 2:1
Also (A+B) one day work = 1/18
To get days in which B will finish the work, lets calculate work done by B in 1 day =1/18*1/3=1/54
[Please note we multiplied by 1/3 as per B share and total of ratio is 1/3]
So B will finish the work in 54 days
ANSWER IS B
Answer: B
Question: Juan and his five friends will sit on six fixed seats around a circular table. If Juan must sit on the seat closest to the window and Jamal must sit next to Juan, in how many can Juan and his five friends sit?
Options:
A)20
B)24
C)48
D)72
E)120
Rationale: J = Juan, F = Jamal
Since J is always fixed, set J, set F relative to J, then see how many options there are:
J F 4 3 2 1 = 24 or
F J 4 3 2 1 = 24
24+24=48 … C
ANSWER:C
Answer: C
Question: If I walk at 5 km/h, I miss the bus by 12 minutes. If I walk at 6 km/h, I reach 15 minutes before the arrival of the bus. How far I walk to reach the bus stand ?
Options:
A)11.0 km
B)13.8 km
C)11.5 km
D)12.5 km
E)13.5 km
Rationale: d = product of speed difference of time /difference of speed
d = 5x6/60[12âˆ’(âˆ’15)/6-5]
[Here, â€“ve sign indicates before the schedule time]
â‡’ d = 13.5 km
Answer E
Answer: E
Question: When a positive integer A is divided by 11 and 3, the remainders obtained are 1 and 2, respectively. When the positive integer B is divided by 11 and 3, the remainders obtained are 1 and 2, respectively. Which of the following is a factor of (A - B)?
Options:
A)14
B)28
C)33
D)42
E)49
Rationale: A = 11k+1 = 3j+2
B = 11m+1 = 3n+2
A-B = 11(k-m) = 3(j-n)
A-B is a multiple of both 11 and 3, so it is a multiple of 33.
The answer is C.
Answer: C
Question: In a group of ducks and cows, the total number of legs are 36 more than twice the number of heads. Find the total number of cows.
Options:
A)12
B)14
C)16
D)18
E)20
Rationale: Let the number of ducks be d
and number of cows be c
Then, total number of legs = 2d + 4c = 2(d + 2c)
total number of heads = c + d
Given that total number of legs are 36 more than twice the number of heads
=> 2(d + 2c) = 36 + 2(c + d)
=> d + 2c = 18 + c + d
=> 2c = 18 + c
=> c = 18
i.e., total number of cows = 18
Answer is D.
Answer: D
Question: 1100 boys and 700 girls are examined in a test; 31% of the boys and 23% of the girls pass. The percentage of the total who failed is ?
Options:
A)A)63.3%
B)B)52.4%
C)C)81.2%
D)D)75.4%
E)E)72.11%
Rationale: Total number of students = 1100+700 = 1800
Number of students passed = (31% of 1100+23% of 700) = 341+161 = 502
number of failures = 1298*100/1800= 72.11%
Answer is E
Answer: E
Question: The banker's gain on a sum due 3 years hence at 12% per year is Rs. 270. The banker's discount is:
Options:
A)960
B)840
C)1020
D)760
E)920
Rationale: T.D. =(B.G. x 100/R x T)
= Rs.(270 x 100/12 x 3)= Rs. 750.
Therefore, B.D. = Rs.(750 + 270) = Rs. 1020.
Answer is C
Answer: C
Question: There are 4 books on fairy tales,5 novels and 3 plays.In how many ways can you arrange these so that books on fairy tales are together,novels are together and plays are together and in the order,books on fairy tales,novels and plays.
Options:
A)22000
B)19261
C)17280
D)18168
E)21671
Rationale: There are 4 books arranged in 4!ways
Similarly,5 novels arranged in 5!ways.
And 3 plays arranged in 3!ways.
Counting principle all of them together can be arranged=4!*5!*3!
=[(4*3*2*1)*(5*4*3*2*1)*(3*2*1)]
=17280 ways
Option C
Answer: C
Question: M is the set of all consecutive odd integers between A and B. If B>A>1, and both A and B are even integers, what is the average (arithmetic mean) of M?
Options:
A)(A−B)/2
B)(A−B)/2 + 1
C)(A+B−1)/2
D)(A+B)/2
E)(A+B+1)/2
Rationale: Let A be 2 and B be 6...as per condition..A and B have to be even...
2,3,4,5 and 6...then M is avg of odd integers...in our case 3+5/2 = 4..
We need to check which option is going to yield 4 and only option D does..
6+2/2 = 4...
Answer option D.
Answer: D
Question: If x represents the sum of the interior angles of a square and y represents the sum of the interior angles of a regular pentagon, then the difference between x and y is equal to the sum of the interior angles of what geometric shape?
Options:
A)Triangle
B)Square
C)Rhombus
D)Trapezoid
E)Pentagon
Rationale: Sum of angles of square = 180*(4-2) = 360 => using formula sum of angles of polygon = 180*(n-2) where n is the number of sides in a polygon
Sum of angles in Pentagon = 180*(5-2) =540
Difference = 540 - 360 = 180 => Triangle
hence (A).
Answer: A
Question: Bradley owns b video game cartridges. If Bradley’s total is one-third the total owned by Andrew and five times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?
Options:
A)(16/3)b
B)(17/4)b
C)(13/4)b
D)(21/5)b
E)(7/12)b
Rationale: Step 1: Categorize the problem
This problem is testing basic algebra and equations, with an extra layer of complexity by having variables in the answer choices.
Step 2: Think like the test maker
What is the key detail or key details in the problem? The key detail to immediately recognize is that the problem gives you Andrew and Charlie’s totals in relation to Bradley’s total rather than giving you Bradley’s total in relation to the other two; and then the problem asks you to solve the problem in terms of b. This means that you have to relate Andrew and Charlie’s values in relation to Bradley’s total. The test maker is attempting to force you to structure the problem in the opposite way that most people are used to structuring information. By gaining this insight, it makes it easier to solve the problem.
Step 3: Solve the problem
b = Bradley’s total
3b = Andrew’s total
(1/5)b = Charlie’s total
Add each total
b + 3b+ (1/5)b = 4b + (1/5)b = (16/4)b + (1/5)b = (21/5)b
Therefore,choose D.
Answer: D
Question: If the volume of two cubes are in the ratio 27:1, the ratio of their edges is:
Options:
A)3:1
B)3:5
C)3:8
D)3:29
E)3:11
Rationale: Let the edges be a and b of two cubes, then
a3b3=271=>(ab)3=(31)3ab=31=>a:b=3:1
Answer: A
Answer: A
Question: The value of (34.31*0.473*1.567)/(0.0673*23.25*7.57) is close to
Options:
A)2
B)1.15
C)2.05
D)2.15
E)2.35
Rationale: (34.31*0.473*1.567)/(0.0673*23.25*7.57) = 25.4303/11.845
= 2.15
ANSWER:D
Answer: D
Question: Cricket match is conducted in US. The run rate of a cricket game was only 3.2 in first 10 over. What should be the run rate in the remaining 40 overs to reach the target of 252 runs?
Options:
A)6
B)6.25
C)7.25
D)5.5
E)8
Rationale: Required run rate = 252 - (3.2 x 10) =	220 = 5.5
40	40
D
Answer: D
Question: Raj is working on a set of Data Sufficiency problems for his December GMAT: a geometry problem, an algebra problem, and a data interpretation problem. He has determined that statement 1 of the geometry problem is insufficient on its own, that both statement 1 and 2 of the algebra problem are insufficient on their own, and that statement 2 of the data interpretation problem is insufficient on its own. If the probabilities are expressed as percents W, approximately how much greater is the probability that all three answers are “C” after Raj figures out that statement 1 of the data interpretation problem is also insufficient on its own?
Options:
A)W=2.3%
B)W=2.8%
C)W=3.3%
D)5.6%
E)8.3%
Rationale: Step 1: Figure out what we need to know.We have two probabilities that we need to figure out: the one before Raj figures out that statement 1 of the data interpretation problem is also insufficient, and the one after. The answer is the difference between them, in the form of a percent.
Step 2: The first probability.
If statement 1 of the geometry problem is insufficient, then the only valid answer choices are B, C, and E; the probability that it is C is 1/3.
If both statements of the algebra problem are insufficient on their own, then the only remaining valid answers are C and E; the probability that it is C is 1/2
If statement 2 of the data interpretation problem is insufficient, then the remaining answers are A, C, and E, and the probability that C is correct is 1/3.
The probability of all three occurring is the product of the probability fractions: (1/3)*(1/2)*(1/3) = 1/18.
Step 3: The second probability.
Only the third problem has changed; if Raj now knows that statement 1 is also insufficient, the valid answer choices are only C and E, leaving a 1/2 probability that the answer is C.
The probability of all three occurring is still the product of those fractions, but this time they are (1/3)*(1/2)*(1/2) = 1/12.
Step 4: The answer.Note that here, as will sometimes happen on the GMAT, values that you compute “along the way” appear as wrong answer choices. This problem calls for the difference between our two numbers,W (1/12)-(1/18) = 1/36, which is a 2.77777% chance, rounded to 2.8% —the correct answer is Choice B.
Answer: B
Question: At Company X, senior sales representatives visit the home office once every 15 days, and junior sales representatives visit the home office once every 10 days. The number of visits that a junior sales representative makes in a 2-year period is approximately what percent greater than the number of visits that a senior representative makes in the same period?
Options:
A)10%
B)25%
C)33%
D)50%
E)67%
Rationale: Each 30-day period, senior representatives visit the home office 2 times while junior representatives visit 3 times, thus 50% more.
The answer is D.
Answer: D
Question: A survey of n people in the town of Eros found that 50% of them preferred Brand A. Another survey of 130 people in the town of Angie found that 60% preferred Brand A. In total, 55% of all the people surveyed together preferred Brand A. What is the total number of people surveyed?
Options:
A)50
B)100
C)150
D)260
E)250
Rationale: It is simply a weighted average question. Since the given average of 50% and 60% is 55% (right in the middle), it means the number of people surveyed in Eros (n) is same as the number of people surveyed in Angie.
So n = 130
Total = 130 + 130 = 260
Answer (D)
Answer: D
Question: A train starts full of passengers at the first station it drops 1/3 of the passengers and takes 280more at the second station it drops one half the new total and takes twelve more .on arriving at the third station it is found to have 248 passengers. Find the no of passengers in the beginning?
Options:
A)288
B)321
C)651
D)246
E)248
Rationale: Let no of passengers in the beginning be x
After first station no passengers=(x-x/3)+280=2x/3 +280
After second station no passengers =1/2(2x/3+280)+12
½(2x/3+280)+12=248
2x/3+280=2*236
2x/3=192
x=288
Option A is answer
Answer: A
Question: The ratio of the number of boys and girls in a college is 7:8. If the percentage increase in the number of boys and girls be 20% and 10% respectively. What will be the new ratio?
Options:
A)21:24
B)21:24
C)21:22
D)21:45
E)21:97
Rationale: Originally, let the number of boys and girls in the college be 7x and 8x respectively.
Their increased number is (120% of 7x) and (110% of 8x).
i.e., (120/100 * 7x) and (110/100 * 8x)
i.e., 42x/5 and 44x/5
Required ratio = 42x/5 : 44x/5 = 21:22
Answer: C
Answer: C
Question: The ratio between the sale price and the cost price of an article is 6:2. What is the ratio between the profit and the cost price of that article?
Options:
A)23
B)1:2
C)2:5
D)3:5
E)2:1
Rationale: C.P. = Rs. 2x and S.P. = Rs. 6x.
Then, Gain = Rs. 4x
Required ratio = 4x : 2x = 2:1
E
Answer: E
Question: A train is 360 meter long is running at a speed of 45 km/hour. In what time will it pass a bridge of 240 meter length?
Options:
A)65 seconds
B)46 seconds
C)40 seconds
D)97 seconds
E)48 seconds
Rationale: Speed = 45 Km/hr = 45*(5/18) m/sec = 25/2 m/sec
Total distance = 360+240 = 600 meter
Time = Distance/speed
= 600 * (2/25)
= 48 seconds
Answer:E
Answer: E
Question: A line has a slope of 3/4 and intersects the point W (-12, -39). At which point does this line intersect the x-axis?
Options:
A)(40,0)
B)(30,0)
C)(0,40)
D)(40,30)
E)(0,30)
Rationale: Assume that the equation of the line is y=mx+c, where m and c are the slope and y-intercept.
You are also given that the line crosses the point (-12,-39), this means that this point will also lie on the line above.
Thus you get -39=m*(-12)+c , with m=3/4 as the slope is given to be 3/4.
After substituting the above values, you get c = -30.
Thus the equation of the line is y=0.75*x-30 and the point where it will intersect the x-axis will be with y coordinate = 0.
Put y=0 in the above equation of the line and you will get, x=40.
Thus, the point W of intersection is (40,0).
A is the correct answer.
Answer: A
Question: 5 persons working eight hours daily can complete a wall in 10 days. When they have Worked for 4 days, 5 more persons are brought to work. The wall can now be completed in?
Options:
A)one more day
B)two more days
C)three more days
D)four more days
E)five more days
Rationale: Let D be the number of required days
Using the chain rule,
M1 x T1 = M2 x T2 + M3 x T3
5 x 8 x 10 = (4 x 5 x 8) + (10 x 8 x D)
D = 3.
Hence, the wall will be completed in 3 more days.
ANSWER:C
Answer: C
Question: At a certain committee meeting only associate professors and assistant professors are present. Each associate professor has brought 2 pencils and 1 chart to the meeting, while each assistant professor has brought 1 pencil and 2 charts. If a total of 11 pencils and 16 charts have been brought to the meeting, how many people are present?
Options:
A)6
B)7
C)8
D)9
E)10
Rationale: Say there are 'A' associate professors. So we have 2A pencils and A charts.
Say there are 'B' assistant professors. So we have B pencils and 2B charts.
Total pencils are 10 so 2A + B = 11
Total charts are 11 so A + 2B = 16
Add both: 3A + 3B = 27 so A + B = 9
Total number of people = 9
D
Answer: D
Question: A man can row with a speed of 20 kmph in still water. If the stream flows at 12 kmph, then the speed in downstream is?
Options:
A)27
B)23
C)20
D)32
E)12
Rationale: M = 20
S = 12
DS = 20 + 12 = 32
Answer: D
Answer: D
Question: The length of the bridge, which a train 160 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
Options:
A)328
B)279
C)215
D)288
E)211
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (160 + X)/30 = 25/2 ==> 2(160 + X) = 750 ==> X = 215 m.Answer: C
Answer: C
Question: Two dice are thrown together .What is the probability that the sum of the number on the two faces is divided by 4 or 6
Options:
A)7/18
B)2/7
C)7/9
D)4/7
E)4/5
Rationale: Clearly n(S)=6*6=36
Let E be the event that the sum of the numbers on the two faces is divided by 4 or 6.Then
E={(1,3),(1,5),(2,2),(2,4),(2,6),(3,1),(3,3),(3,5),(4,2),(4,4),(5,1),(5,3),(6,2),
(6,6)}
n(E)=14.
Hence p(e)=n(e)/n(s)=14/36=7/18
Option A
Answer: A
Question: There are two numbers. If 30% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?
Options:
A)A)3/7
B)B)5/8
C)C)5/6
D)D)6/7
E)E)7
Rationale: Let the two numbers be x and y.
30/100 * x + y = 5/4y
=> 3/10 x = 1/4 y => x/y = 5/6
C)
Answer: C
Question: 10% people of a village in Sri Lanka died by bombardment, 20% of the remainder left the village on account of fear. If now the population is reduced to 4554, how much was it in the beginning?
Options:
A)7349
B)6300
C)6325
D)6939
E)2989
Rationale: X * (90/100) * (80/100) = 4554
X = 6325
Answer: C
Answer: C
Question: An Olympic diver received the following scores: 4, 3, 7, 6, and 5. The standard deviation of her scores is in which of the following ranges?
Options:
A)2.4 to 2.8
B)1.4 to 1.8
C)3.4 to 3.8
D)4.4 to 4.8
E)5.4 to 5.8
Rationale: 4+3+7+6+5/5 = 5
|4-5| = 1 1^2 = 0
|3-5| = 2 2^2 = 4
|7-5| = 2 2^2 = 4
|6-5| = 1 1^2 = 1
|5-5| = 0 0^2 = 0
SD = sqrt 10/5 =1.41
Answer : B
Answer: B
Question: In a division, a student took 63 as divisor instead of 36. his answer was 24 . The correct answer is-
Options:
A)42
B)32
C)48
D)28
E)38
Rationale: X/63 = 24.
X = 24 *63.
So correct answer would be,
(24 *63) /36 = 42.
ANSWER : A
Answer: A
Question: A shopkeeper purchased 150 identical pieces of calculators at the rate of 250 each. He spent an amount of 2500 on transport and packing. He fixed the labelled price of each calculator at 320. However, he decided to give a discount of 5% on the labelled price. What is the percentage profit earned by him ?
Options:
A)14 %
B)15 %
C)16 %
D)20 %
E)None of these
Rationale: C.P. of 150 calculators
= 150 × 250 + 2500 = 37500 + 2500 = 40000
Labelled price of 150 calculators
= 150 × 320 = 48000
Discount allowed = 5%
∴ S.P. of 150 calculators
= 48000 – 5% = 45600
∴ Profit % = 5600⁄40000 × 100 = 14
Answer A
Answer: A
Question: The largest six digit number which is a perfect cube, is:
Options:
A)970299
B)907289
C)992289
D)900279
E)999999
Rationale: Explanation:
99*99*99 = 970299
Answer: A
Answer: A
Question: if x = 4 + 4 - 4 + 4 - ......¥ find the value of x
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: x=4+4-x.
2x=8.
x=4
ANSWER:D
Answer: D
Question: A women walking at 5 Kmph reaches her office 8 minutes late. If she walks at 6 Kmph, she reaches there 8 minutes earlier. How far is the office from her house?
Options:
A)2 1/5 Km
B)3 1/5 Km
C)4 1/3 Km
D)8 Km
E)8 1/3 Km
Rationale: Formula = S1*S2/S2-S1 * T1+T2/60
= 5*6/1 * 16/60
= 30/1 * 16/60
= 30 * 4/15
= 8 Km
D
Answer: D
Question: In a company 10% of male staff are same in number as 1/4th of the female staff. What is the ratio of
male staff to female staff
Options:
A)3 : 2
B)5 : 2
C)2 : 1
D)4 : 3
E)3: 5
Rationale: Expl : 10% of MS = 1/4th of FS -> 10MS/100 = 1/4FS -> MS = 5/2 FS
:. MS/FS = 5/2 = MS : FS = 5 : 2
Answer: B
Answer: B
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58?
Options:
A)3944
B)2877
C)267
D)2787
E)281
Rationale: Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 58 = Rs. 3944.
Answer:A
Answer: A
Question: In how many ways letters of the word RSCUPERATE be arranged?
Options:
A)154546
B)154632
C)164333
D)243456
E)302400
Rationale: RESUPERATE has 10 letters, out of which E repeated 3 times, R repeated 2 times. Hence total ways = 10! / (3!*2!) = 302400 ways
E
Answer: E
Question: A man can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit his target?
Options:
A)1
B)1/256
C)81/256
D)175/256
E)144/256
Rationale: "A man can hit a target once in 4 shots" means that the probability of hitting the target is 1/4, thus the probability of missing the target is 1-1/4=3/4.
The probability that he will hit a target while shooting 4 times is basically the probability that he will hit at least once, so 1-(the probability that he will miss all 4 times): P=1−(34)^4=175/256.
Answer: D.
Answer: D
Question: Of the 200 candidates who were interviewed for a position at a call center, 100 had a two-wheeler, 70 had a credit card and 140 had a mobile phone. 40 of them had both, a two-wheeler and a credit card, 30 had both, a credit card and a mobile phone and 60 had both, a two wheeler and mobile phone and 10 had all three. How many candidates had none of the three?
Options:
A)0
B)20
C)10
D)8
E)4
Rationale: Solution:
Number of candidates who had none of the three = Total number of candidates - number of candidates who had at least one of three devices.
Total number of candidates = 200.
Number of candidates who had at least one of the three = A U B U C, where A is the set of those who have a two wheeler, B the set of those who have a credit card and C the set of those who have a mobile phone.
We know that AUBUC = A + B + C - {A n B + B n C + C n A} + A n B n C
Therefore, AUBUC = 100 + 70 + 140 - {40 + 30 + 60} + 10
Or AUBUC = 190.
As 190 candidates who attended the interview had at least one of the three gadgets, 200 - 190 = 10 candidates had none of three.
Answer C
Answer: C
Question: Five years ago the average of the ages of A and B was 40 years and now the average of the ages of B and C is 46 years. What will be the age of the B ten years hence?
Options:
A)22
B)92
C)26
D)96
E)51
Rationale: Let the present ages of A, B and C be a, b and c respectively.
Given, [(a - 5) + (b - 5)] / 2 = 40 => a + b = 90 --- (1)
(b + c)/2 = 46 => b + c = 92 --- (2)
From (1) and (2), we cannot find b.
Answer: B
Answer: B
Question: By selling 22 pencils for a rupee a man loses 40%. How many for a rupee should he sell in order to gain 40%?
Options:
A)8.56
B)9.35
C)9.43
D)6.56
E)5.5
Rationale: 60% --- 22
140% --- ?
60/140 * 22 = 9.43
Answer: C
Answer: C
Question: In a bag there are coins of 50 paisa, 25 paisa and one rupee in the proportion 5:6:2. If there are in all Rs.42, the number of 25 paisa coins is?
Options:
A)31
B)42
C)102
D)52
E)62
Rationale: Answer: Option B
5x 6x 2x
50 25 100
250x + 150x + 200x = 4200
600x = 4200
x = 7 => 6x = 42
Answer: B
Question: A certain club has 20 members, including Harry. One of the 20 members is to be chosen at random to be the president, one of the remaining 19 members is to be chosen at random to be the secretary, and one of the remaining 18 members is to be chosen at random to be the treasurer. What is the probability that Harry will be either the member chosen to be the secretary or the member chosen to be the treasurer?
Options:
A) 1/720
B) 1/80
C) 1/10
D) 1/9
E)2/20
Rationale: This question is much easier than it appears.
Each member out of 10, including Harry, has equal chances to be selected for any of the positions (the sequence of the selection is given just to confuse us). The probability that Harry will be selected to be the secretary is 1/20 and the probability that Harry will be selected to be the treasurer is also 1/20. So, the probability that Harry will be selected to be either the secretary or the the treasurer is 1/20+1/20=2/20
Answer: E.
Answer: E