divelab/Sys2Bench huggingface dataset:
Question: A boy rides his bicycle 10 km at an average speed of 12 km/hr and again travels 12 km at an average speed of 10 km/hr. His average speed for the entire trip is approximately?
Options:
A)10.8 km/hr
B)12.8 km/hr
C)11.8 km/hr
D)16.8 km/hr
E)17.8 km/hr
Rationale: A
10.8 km/hr
Total distance traveled = 10 + 12 = 22 km /hr.
Total time taken = 10/12 + 12/10 = 61/30 hrs.
Average speed = 22 * 30/61 = 10.8 km/hr.
Answer: A
Question: If one root of the equation 2x^2 + 3x – k = 0 is 5, what is the value of k?
Options:
A)65
B)79
C)68
D)87
E)90
Rationale: We just enter this root into the equation in order to recieve an equation to find the answer!
2*5^2+3*5-k=0
k=50+15=65
The answer is A
Answer: A
Question: For 600 km journey it will take 8hrs, if 120 km is done by bus and the rest by car. It takes 20 minutes more, if 200 km is done by busand the rest by car. The ratio of the speed of the train to that of the cars is?
Options:
A)1 : 3
B)3 : 4
C)1 : 6
D)2 : 7
E)3 : 8
Rationale: Let the speed of the train be x km/hr and that of the car be y km/hr.
Then, 120 + 480 = 8 1 + 4 = 1 ....(i)
x y x y 15
And, 200 + 400 = 25 1 + 2 = 1 ....(ii)
x y 3 x y 24
Solving (i) and (ii), we get: x = 60 and y = 80.
Ratio of speeds = 60 : 80 = 3 : 4
B
Answer: B
Question: Three walls have wallpaper covering a combined area of 300 square meters. By overlapping the wallpaper to cover a wall with an area of 180 square meters, the area that is covered by exactly two layers of wallpaper is 34 square meters. What is the area that is covered with three layers of wallpaper?
Options:
A)43 Square Meters
B)36 Square Meters
C)42 Square Meters
D)83.3 Square Meters
E)120 Square Meters
Rationale: 300 - 180 = 120 sq m of the wallpaper overlaps (in either two layers or three layers)
If 36 sq m has two layers, 120 - 34 = 86 sq m of the wallpaper overlaps in three layers. 86 sq m makes two extra layers hence the area over which it makes two extra layers is 43 sq m.
Answer (A).
Answer: A
Question: One hour after Sid started walking the 60 miles from X to Y, James started walking from X to Y as well. Sid walks 3 miles per hour and James walks 1 mile per hour faster than Sid . How far from X will James be when he catches up to Sid ?
Options:
A)8 miles
B)9 miles
C)12 miles
D)11 miles
E)13 miles
Rationale: First, determine how far Sid has walked in the one hour. he has walked three miles which means he is three miles ahead of James when he sets off. James walks at four miles/hour which means that every hour, james will get one mile closer to Sid . If he gets one mile closer every hour, it will take him three hours to catch up to him which means he travels 3hours * 4 miles/hour = 12 miles and he travels 4 hours * 3 miles/hour = 12 miles. He will be 12 miles from X when he catches up to her.
A slightly different way to solve...
We don't know how long they will walk before they catch up to one another but we do know that A walks for one hour more than J. J = T and A = T+1. We are looking for the distance at which they meet up which means the distance will be the same. D=r*t so,
r*t (james) = r*t (Sid )
r*(t) = r*(t+1)
4t = 3t+3
t=3
d=r*t
d=4*3
d=12
C) 12 miles
Answer: C
Question: The price of 2 sarees and 4 shirts is $1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?
Options:
A)3800
B)3300
C)2400
D)4200
E)1400
Rationale: C
$2400
Let the price of a saree and a shirt be $x and $y respectively.
Then, 2x + 4y = 1600 .... (i)
and x + 6y = 1600 .... (ii)
Divide equation (i) by 2, we get the below equation.
=> x + 2y = 800. --- (iii)
Now subtract (iii) from (ii)
x + 6y = 1600 (-)
x + 2y = 800
----------------
4y = 800
----------------
Therefore, y = 200.
Now apply value of y in (iii)
=> x + 2 x 200 = 800
=> x + 400 = 800
Therefore x = 400
Solving (i) and (ii) we get x = 400, y = 200.
Cost of 12 shirts = $(12 x 200) = $2400.
Answer: C
Question: If doubling a number and adding 20 to the result gives the same answer as multiplying the number by 8 and taking away 4 from the product, the number is
Options:
A)2
B)3
C)4
D)6
E)7
Rationale: Solution
Let the number be x.	= Then, 2x+20 = 8x–4
= 6x = 24
‹=›x = 4.
Answer C
Answer: C
Question: The diameter of the wheel of a car is 120m. How many revolution/min must the wheel makein order to keep a speed of 60 km/hour approximately?
Options:
A)210
B)245
C)230
D)254
E)265
Rationale: Distance to be covered in 1 min. = (60 X 1000)/(60) m = 1000 m.
Circumference of the wheel = (2 x (22/7) x 0.60) m = 3.77 m.
Number of revolutions per min. =(1000/3.77) = 265
E
Answer: E
Question: Indu gave Bindu Rs.6500 on compound interest for 2 years at 4% per annum. How much loss would Indu has suffered had she given it to Bindu for 2 years at 4% per annum simple interest?
Options:
A)12.8
B)20
C)10.4
D)11.6
E)15
Rationale: 6500 = D(100/4)2
D = 10.4
Answer: C
Answer: C
Question: Anand and Deepak started a business investing Rs. 27,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is?
Options:
A)7728
B)2888
C)8400
D)2882
E)2781
Rationale: Ratio of their shares = 27500 : 35000 = 11:14
Deepak's share = 13800 * 14/25 = Rs. 7728.
Answer: A
Answer: A
Question: A math teacher has 27 cards, each of which is in the shape of a geometric figure. Half of the cards are rectangles, and a third of the cards are rhombuses. If 8 cards are squares, what is the maximum possible number of cards that re circles.
Options:
A)9
B)10
C)11
D)12
E)13
Rationale: a square is a special kind of rhombus (sides are perpendicular)
a square is a special kind of rectangles (sides with same length)
Among the 27 cards with have:
15 rectangles
10 rhombus
8 squares
Among the 15 rectangles, there could be 8 special ones (with sides of same length) that are squares. That lets at least 7 rectangles that are not square.
Among the 10 rectangles, there could be 8 special ones (with sides perpendicular) that are squares. That lets at least 2 rhombus that are not square.
We have 8 squares.
So the minimum different cards that represent a square, a rhombus or a rectangle is 2 + 7 + 8 = 17
Which means that the maximum number of circles that you could have is 27 - 17 = 10
Answer (B)
Answer: B
Question: Dexter was born between October 6th and 10th (6th and 10th excluding). His year of birth is also known. What is the probability of Dexter being born on a Saturday?
Options:
A)0 or 1/3
B)1/7 or 3/7
C)1/3 or 1/7
D)1/3 or 1/4
E)cannot be determined.
Rationale: Explanation :
Since the year of birth is known, the birthday being on Saturday can have a zero probability.
Also since between 6th and 10th, there are three days i.e. 7th,8th and 9th.
Therefore, probability of birthday falling on Saturday can be 1/3.
Answer : A
Answer: A
Question: 3 houses are available in a locality.3 persons apply for the houses.Each apply for one house without consulting others.the probablity that all 3 apply for the same house is:
Options:
A)2/9
B)1/9
C)8/9
D)7/9
E)1/4
Rationale: let there be three house a,b,c then there would be 27 ways in which 3 person x,y,z select house
there will be 1 case when x,y,z will buy house a
another when they buy house b
and another when they buy house c
so the prob that they buy same house is 3*1/27=1/9
ANSWER:B
Answer: B
Question: A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age?
Options:
A)177
B)199
C)800
D)171
E)128
Rationale: 25 = E/(1000 - E) * 100
1000 - E = 4E
1000 = 5E => E = 200
1000 - 200 = 800
Answer: C
Answer: C
Question: From a group of boys and girls, 15 girls leave. They are then left 2 boys for each girl. After this, 72 boys leave. There are then 5 girls for each boy. Find the number of girls in the beginning
Options:
A)20
B)10
C)30
D)55
E)40
Rationale: Assume the number of boys at present = x
Then, the number of girls at present = 5x
Before the boys left, the number of boys were (x+72) and number of girls were 5x
Hence, 2(5x) = x + 72
=> 10x = x + 72
=> x = 8
Number of girls in the beginning = (5x + 15) = (5×8 + 15) = 55
Answer is D.
Answer: D
Question: When positive integer N is divided by positive integer J, the remainder is 27. If N/J = 204.09, what is value of J?
Options:
A)300
B)320
C)360
D)410
E)420
Rationale: When a number is divided by another number, we can represent it as : Dividend = Quotient * Divisor + Remainder
So, Dividend/Divisor = Quotient + Remainder/Divisor
Given that N/J = 204.09
Here 204 is the quotient.
Given that Remainder = 27
So, 204.09= 204 + 27/J
So, J = 300
Answer: A
Answer: A
Question: The length of a train and that of a platform are equal. If with a speed of 180 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
Options:
A)1500
B)266
C)299
D)750
E)261
Rationale: Speed = [180 * 5/18] m/sec = 50 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 50 => x = 50 * 60 / 2 = 1500
Answer: A
Answer: A
Question: If you drew a dot on the edge of a wheel and traced the path of the dot as the wheel rolled one complete revolution along a line, then the path formed would be called a cycloid, combining both forward and circular motion. What is the length of the path formed by one complete revolution? Assume the wheel has a radius of r.
Options:
A)8r
B)4r
C)9r
D)7r
E)10r
Rationale: Hint: (1-cos(t))0.5 = 20.5×sin(t/2)
The answer is 8r.
Imagine the circle resting on coordinate (0,0) and moving east.
Also magine the point on the circle to start at (0,0).
Let t be the angle between the point on the circle and the center of the circle.
The position of the point on the circle, relative to t, is:
x = rt - r×sin(t)
y = r - r×cos(t)
Taking the derivatives:
dx/dt = r - r×cos(t)
dy/dt = r×sin(t)
The change in arc length can be defined as ( (dx/dt)2 + (dy/dt)2 ) 1/2.
So the total arc length is the integral from 0 to 2pi of ( (dx/dt)2 + (dy/dt)2 ) 1/2.
After a few steps this integral becomes:
r×21/2 × (1-cos(t))1/2.
Using the hint:
r×21/2 × 21/2 × integral of sin(t/2) dt from 0 to 2×pi
= 2×r × (-2×cos(t/w) from 2×pi to 0)
= 8r
correct answer A
Answer: A
Question: Seven 6 faced dice are thrown together. The probability that all the three show the same number on them is?
Options:
A)1/32
B)1/46656
C)1/33
D)1/38
E)1/34
Rationale: The three dice can fall in 6 * 6 * 6 * 6 * 6 * 6 * 6 = 279936 ways.
Hence the probability is 6/279936
= 1/46656
Answer: B
Answer: B
Question: In a hostel there were 100 students. 20 students left the hostel,the average budget is increased by rupees 10. But total expenditure increased by Rs.400. Find the total expenditure of the hostel now?
Options:
A)2200
B)1660
C)5400
D)2400
E)1800
Rationale: Let average is x
100x + 400 = 80(x+10)
x = 20
100 * 20 + 400 = 2400
Answer:D
Answer: D
Question: man can row upstream at 30 kmph and downstream at 40 kmph, and then find the speed of the man in still water?
Options:
A)30
B)35
C)40
D)70
E)45
Rationale: US = 30
DS = 40
M = (30 + 40)/2
= 35
Answer:B
Answer: B
Question: Find the odd man out
6, 13, 29, 61, 125, 253, 509
Options:
A)6
B)13
C)29
D)125
E)509
Rationale: 1*2+3 = 5
5*2+3 = 13
13*2+3 = 29
29*2+3 = 61
61*2+3 = 125
125*2+3 = 253
253*2+3= 509
ANSWER:A
Answer: A
Question: The equation of line a is y = 4/3*x - 100. What is the smallest possible distance in the xy-plane from the point with coordinates (0, 0) to any point on line a?
Options:
A)48
B)50
C)60
D)75
E)100
Rationale: This can be solve in two steps and without any complex calculation.
Given : equation of line a as y=(4/3)x -100. So the line intercept the axes at (0,-100) and (75,0).
This can be considered a right angle triangle with right angle at (0,0) . So Base=100 , Height=75 and Hypotenuse =125 (By Pythagoras triplet)
So a perpendicular from the (0,0) to hypotenuse will be the answer.
Area of triangle= 0.5*100*75=0.5*125* x
=> x=60;
SO answer is 60=C
Answer: C
Question: A telephone company needs to create a set of 3-digit area codes. The company is entitled to use only digits 2, 4 and 6, which can be repeated. If the product of the digits in the area code must be even, how many different codes can be created?
Options:
A)27
B)22
C)24
D)26
E)30
Rationale: Total # of codes possible is 3*3*3 = 27. Oit of those 27 codes
Answer: A
Answer: A
Question: Insert the missing number.
8, 7, 11, 12, 14, 17, (....)
Options:
A)27
B)20
C)22
D)17
E)26
Rationale: There are two series (8, 11, 14, 17) and (7, 12, 17) increasing by 3 and 5 respectively.
answer : D
Answer: D
Question: From a group of boys and girls, 15 girls leave. They are then left 2 boys for each girl. After this, 63 boys leave. There are then 5 girls for each boy. Find the number of girls in the beginning
Options:
A)20
B)10
C)30
D)50
E)40
Rationale: Assume the number of boys at present = x
Then, the number of girls at present = 5x
Before the boys left, the number of boys were (x+63) and number of girls were 5x
Hence, 2(5x) = x + 63
=> 10x = x + 63
=> x = 7
Number of girls in the beginning = (5x + 15) = (5×7 + 15) = 50
Answer is D.
Answer: D
Question: Six students are equally divided into 3 groups, then, the three groups were assigned to three different topics. How many different arrangements R are possible?
Options:
A) 30
B) 60
C) 90
D) 180
E) 540
Rationale: 90 is the number of ways you can assign 3 teams formed out of 12 people to 3 different tasks.
But now you can order the 3 tasks in 3! ways. T1 T2 T3 or T2 T1 T3.... etc etc.
I was confused between 90 and 540 but since question used the wordarrangementsdecided to go with complete arrangements R INCLUDING the order of tasks.
could you explain the highlighted step... i'm getting 90 = 15 * 3!
suppose the students are numbered 1,2,3,4,5,6 and tasks are X,Y and Z
one of the 15 possible ways of forming teams is 12, 34, 56. these teams can be assigned to 3 tasks in 3! = 6 ways
X--	Y--	Z
12--	34--	56
12--	56--	34
34--	12--	56
34--	56--	12
56--	12--	34
56--	34--	12
so the answer should be 15*6 = 90
But now you can fruther decide which task you want to perform first X Y or Z..C
Answer: C
Question: How many no.'s with 3 different digits, 2, 3, 5, 6, 7 and 9, which are divisible by 5?
Options:
A)10
B)20
C)40
D)35
E)45
Rationale: Since each desired number is divisible by 5, so we must have 5 at the unit place. So, there is 1 way of doing it.
The tens place can now be filled by any of the remaining 5 digits (2, 3, 6, 7, 9). So, there are 5 ways of filling the tens place.
The hundreds place can now be filled by any of the remaining 4 digits. So, there are 4 ways of filling it.
Required number of numbers = (1 x 5 x 4) = 20
B
Answer: B
Question: Divide Rs. 1500 among A, B and C so that A receives 1/3 as much as B and C together and B receives 2/3 as A and C together. A's share is?
Options:
A)375
B)400
C)450
D)350
E)250
Rationale: A+B+C = 1500
A = 1/3(B+C); B = 2/3(A+C)
A/(B+C) = 1/3
A = 1/4 * 1500 => 375
ANSWER A
Answer: A
Question: If a man can cover 12 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
Options:
A)288
B)162
C)878
D)168
E)122
Rationale: 12 m/s = 12 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 12 * 18/5 * 15/4 km = 162 km.
Answer: B
Answer: B
Question: If 10 crates have 96 apples each and how many apples more is required in order to make 100 apples in each crate?
Options:
A)5
B)10
C)40
D)20
E)0
Rationale: Each crate requires 4 apples and totally there are 10 crates so required apples = 10 * 4 = 40
Answer: C
Answer: C
Question: 85% of a number is added to 24, the result is the same number. Find the number?
Options:
A)277
B)267
C)222
D)160
E)123
Rationale: (85/100) * X + 24 = X
3X = 480
X = 160
Answer:D
Answer: D
Question: If the sides of a rectangle are increased by 35%, what is the percentage increase in the area?
Options:
A)38.25%
B)40.25%
C)82.25%
D)50%
E)65%
Rationale: If sides are a and b, after increase sides would be 1.35a and 1.35 b.
Percentage increase in area = (1.35a*1.35b - ab) *100/ab = 82.25
Answer : C
Answer: C
Question: The average weight of 10 person's increases by 3.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
Options:
A)100 kg
B)102.5 kg
C)85 kg
D)Data inadequate
E)None of these
Rationale: Explanation:
Total weight increased = (10 x 3.5) kg = 35 kg.
Weight of new person = (65 + 35) kg = 100 kg.
Answer: A
Answer: A
Question: Equal amount of water were poured into two empty jars of different capacities, which made one jar 1/6 full and other jar 1/5 full. If the water in the jar with lesser capacity is then poured into the jar with greater capacity, what fraction of the larger jar will be filled with water?
Options:
A)1/7
B)2/7
C)1/3
D)7/12
E)2/3
Rationale: Same amount of water made bigger jar 1/6 full, thenthe same amount of water(stored for a while in smaller jar) were added to bigger jar, so bigger jar is 1/6+1/6=2/6= 1/3 full.
Answer: C.
Answer: C
Question: The difference between the value of a number increased by 12.5% and the value of the original number decreased by 25% is 30. What is the original number?
Options:
A)60
B)80
C)40
D)120
E)160
Rationale: Explanatory Answer
Let the original number be x.
Let A be the value obtained when x is increased by 12.5%.
Therefore, A = x + 12.5% of x
Let B be the value obtained when x is decreased by 25%.
Therefore, B = x - 25% of x
The question states that A - B = 30
i.e., x + 12.5% of x - (x - 25% of x) = 30
x + 12.5% of x - x + 25% of x = 30
37.5% of x = 30
x = 30/37.5*100 = 80
The correct choice is (B)
Answer: B
Question: A person saved $10 in buying an item on sale. If he spent $100 for the item, approximately how much percent he saved in the transaction?
Options:
A)8%
B)10%
C)2%
D)5%
E)6%
Rationale: Actual price = 100+10 = $110
Saving = 10/110 * 100 = 100/11 =10% approximately
Answer is B
Answer: B
Question: If a tire rotates at 400 revolutions per minute when the car is traveling 72km/h, what is the circumference of the tire?
Options:
A)2 meters
B)6 meters
C)5 meters
D)3 meters
E)7 meters
Rationale: 400 rev / minute = 400 * 60 rev / 60 minutes
= 24,000 rev / hour
24,000 * C = 72,000 m : C is the circumference
C = 3 meters
correct answer D
Answer: D
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)159
B)194
C)205
D)209
E)None of these
Rationale: We may have 1 boy and 3 girls or 2 boys and 2 girls or 3 boys and 1 girl or 4 boys
Required number of ways = (6C1 x 4C3) + (6C2 x 4C2) + (6C3 x 4C1) + 6C4
= (6C1 x 4C1) + (6C2 x 4C2) + (6C3 x 4C1) + 6C2
= (6 x 4) +[(6x5)/(2x1) x (4x3)/(2x1)] + [(6x5x4)/(3x2x1)) x 4] +[(6x5)/(2x1)]
= 24 + 90 + 80 + 15 = 209
Answer D.
Answer: D
Question: 1/2-[(2/5*5/32)+1]+9/16=
Options:
A)29/16
B)19/16
C)15/16
D)9/13
E)0
Rationale: 1/2 - [(2/5*5/32) + 1] + 9/16 =
1/2 - [(1/16) + 1] + 9/16 =
1/2 - [17/16] + 9/16 =
8/16 - 17/16 + 9/16 = 0
The answer is E.
Answer: E
Question: A man sold two chairs at Rs. 1,200 each. On one he gained 20% and on the other he lost 20%. His gain or loss in the whole transaction is:
Options:
A)1% loss
B)2% loss
C)4% loss
D)15 gain
E)NOne
Rationale: Solution: In the case where loss and gain percentage is common on same selling price, always a loss incurs in total deal. And this can be calculated by a short-cut:
Loss on total deal,
= (Common loss or gain percentage /10)2 = (20/10)2
= 4%
Alternatively, It can be also calculated through Graphic Change Method: This can be given by,
100==20% gain ==>120==20% loss==>96.
Loss = 4% (As 100 became 96).
Answer: Option C
Answer: C
Question: If - 5 < x < 7 and y < - 9, then the lowest possible value for (-xy) is
Options:
A)between 60 and 70
B)between 0 and 60
C)0
D)between 0 and -70
E)none of these
Rationale: If - 5 < x < 7 and y < - 9,
Say y = -100 (y<-9)
x = 6
So -xy =600 which is more than 70.
Answer is E.
Answer: E
Question: A dishonest dealer professes to sell goods at the cost price but uses a false weight and gains 25%. Find his false weight age?
Options:
A)277
B)276
C)800
D)271
E)255
Rationale: 25 = E/(1000 - E) * 100
1000 - E = 4E
1000 = 5E => E = 200
1000 - 200 = 800
Answer: C
Answer: C
Question: C and D start a business with Rs.4000 and Rs.10000 respectively. Hoe should they share their profits at the end of one year?
Options:
A)5:2
B)2:5
C)5:3
D)3:5
E)2:3
Rationale: They should share the profits in the ratio of their investments.
The ratio of the investments made by C and D =
4000 : 10000 => 2:5 .
Answer:B
Answer: B
Question: What is the area inscribed by the lines y = 10, x = 1, y = 3x+1 on an xy-coordinate plane?
Options:
A)a) 1
B)b) 2
C)c) 3
D)d) 6
E)e) 12
Rationale: First, let's graph the lines y = 10 and x = 1
At this point, we need to find the points where the line y = 3x+1 INTERSECTS the other two lines.
For the vertical line, we know that x = 1, so we'll PLUG x = 1 into the equation y = 3x+1 to get y = 3(1)+1 = 4
Perfect, when x = 1, y = 5, so one point of intersection is (1,4)
For the horizontal line, we know that y = 10, so we'll PLUG y = 10 into the equation y = 3x+1 to get 10 = 3x+1. Solve to get: x = 3
So, when y = 10, x = 3, so one point of intersection is (3,10)
Now add these points to our graph and sketch the line y = 3x+1
At this point, we can see that we have the following triangle.
The base has length 2 and the height is 6
Area = (1/2)(base)(height)
= (1/2)(2)(6)
= 6
Answer:
D
Answer: D
Question: The perimeters of two squares are 40 cm and 28 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares .
Options:
A)22 cm
B)28.4 cm
C)26 cm
D)28 cm
E)29 cm
Rationale: Explanation:
We know perimeter of square = 4(side)
So Side of first square = 40/4 = 10 cm
Side of second square = 28/4 = 7 cm
Area of third Square = 10*10 - 7*7
= 51 cm
So side of third square = 7.1 [because area of square = side*side]
Perimeter = 4*Side = 4*7.1 = 28.4 cm
Answer: Option B
Answer: B
Question: One used-car salesperson receives a commission of $ 200 plus 4 percent of $ 2,000 less than the car’s final sale price. Another car salesperson earns a straight commission of 6 percent of the car’s final sale price. What is the final sale price of a car if both salespeople would earn the same commission for selling it?
Options:
A)$ 5,000
B)$ 6,000
C)$ 8,000
D)$ 10,000
E)$ 12,000
Rationale: This question can be solved by TESTing THE ANSWERS.
We're given the pay rate of two different salespeople who sell cars:
1) A commission of $ 200 plus 4 percent of $ 1,000 less than the car’s final sale price.
2) A straight commission of 6 percent of the car’s final sale price.
We're asked for the final sale price of a car if both salespeople would earn the SAME commission for selling it?
Let's TEST Answer B: $6,000
1st salesperson = $200 + .04(6,000 - 1,000) = $200 + .04(5,000) = $200 + $200 = $400
2nd salesperson = .06(6,000) = $360
These totals are NOT the same, so we can eliminate B. Looking at the two pay 'formulas', we can see that the 2nd salesperson will make more money than the 1st when the price of the car increases to a significant level, so we need a price that is HIGHER than $6,000. Since the difference in pay is relatively small in Answer B, we're likely looking for a number that is fairly close to $6,000 though...
Let's TEST Answer C: $8,000
1st salesperson = $200 + .04(8,000 - 1,000) = $200 + .04(7,000) = $200 + $280 = $480
2nd salesperson = .06(8,000) = $480
These totals are the SAME, so this must be the answer.
Final Answer:
D
Answer: D
Question: Siddharth wants to borrow Rs.6000 at rate of interest 6% p.a. at S.I and lend the same amount at C.I at same rate of interest for two years. What would be his income in the above transaction?
Options:
A)21.6
B)21.69
C)21.66
D)21.64
E)21.61
Rationale: Amount of money Siddharth borrowed at S.I at 6% p.a. for two years = Rs.6,000
He lend the same amount for C.I at 6% p.a. for two years.
=> Siddharth's income = C.I - S.I
= p[1 + r/ 100]n - p - pnr/100
= p{ [1 + r/ 100]2 - 1 - nr/100
= 6,000{ [1 + 6/100]2 - 1 - 12/100}
= 6,000 {(1.06)2- 1 - 0.12} = 6,000(1.1236 - 1 - 0.12)
= 6,000 (0.0036) = 6 * 3.6 = Rs.21.60.Answer:A
Answer: A