divelab/Sys2Bench huggingface dataset:
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 222 runs?
Options:
A)6
B)6.25
C)7.25
D)7.5
E)4.75
Rationale: Required run rate = 222 - (3.2 x 10) =	190 = 4.75
40	40
E
Answer: E
Question: Two trains 200 m and 150 m long are running on parallel rails at the rate of 40 kmph and 48 kmph respectively. In how much time will they cross each other, if they are running in the same direction?
Options:
A)72 sec
B)132 sec
C)157.5 sec
D)252 sec
E)None
Rationale: Solution
Relative Speed	= (48 - 40 ) Kmph
= 8 kmph
=(8 x 5 / 18)m/sec
= (40 / 18 ) m/sec
Time taken	= (350 x 18 / 40) sec
= 157.5 sec.
Answer C
Answer: C
Question: A shopkeeper sells 20% of his stock at 10% profit ans sells the remaining at a loss of 5%. He incurred an overall loss of Rs. 400. Find the total worth of the stock?
Options:
A)23277
B)20000
C)28778
D)28788
E)18881
Rationale: Let the total worth of the stock be Rs. x.
The SP of 20% of the stock = 1/5 * x * 1.1 = 11x/50
The SP of 80% of the stock = 4/5 * x * 0.95 = 19x/25 = 38x/50
Total SP = 11x/50 + 38x/50 = 49x/50
Overall loss = x - 49x/50 = x/50
x/50 = 400 => x = 20000
Answer: B
Answer: B
Question: If a real number x is chosen at random in the interval [0,5] and a real number y is chosen at random in the interval [0,7], what is the probability that x < y?
Options:
A)5/7
B)2/3
C)9/14
D)4/5
E)7/8
Rationale: Since x is in [0,5] and y is in [0,7] we can draw a rectangle in the coordinate plane with vertices (0, 0), (5, 0), (0, 7), and (5, 7).
The points above the line y=x satisfy x < y.
The part of the rectangle below y=x has an area of 12.5
The whole rectangle has an area of 35.
P(x < y) = (35-12.5)/35 = 22.5/35 = 45/70 = 9/14
The answer is C.
Answer: C
Question: Three bottles whose capacities are as 5 : 3 : 2 are completely filled with milk mixed with water. The ratio of milk to water in the mixture of bottles are as 3 : 2, 2 : 1 and 3 : 1 respectively. Find the percentage of water in the new mixture obtained when 1/3rd of first, 1/2 of second and 2/3rd of the third bottle is taken out and mixed together
Options:
A)66.66%
B)50%
C)16.66%
D)33.33%
E)36.33%
Rationale: Let the percentage of water be X
The quantity of new mixture = (5X/3) + (3X/2 )+ (4X/3) = 27X/6 = 9X/2.
Percentage of milk = (5X/3) x (3/5) + (3X/2) x (2/3) + (4X/3) x (3/4) = 3X
Percentage of water = (5X/3) x (2/5) + (3X/2) x (1/3) + (X/2) x (2/3) = 3X/2
Percentage of water = (3X/2)/(9X/2) x 100
= 100/3
= 33 (1/3)%
ANSWER:D
Answer: D
Question: The total of a company's assets in 1994 was 100% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of the company's assets in 1992 was N dollars, what were the company's assets in 1994?
Options:
A)5N
B)7N
C)10N
D)15N
E)20N
Rationale: In 1992, the company's assets were N.
In 1993, the company's assets were N + 4N = 5N.
In 1994, the company's assets were 5N + 5N = 10N.
The answer is C.
Answer: C
Question: If A and B get profits of Rs.5,000 and Rs.2,000 respectively at the end of year then ratio of their investments are
Options:
A)4:1
B)1:4
C)5:2
D)2:3
E)2:5
Rationale: Ratio = 5000/2000 = 5 : 2
Answer : C
Answer: C
Question: If the cost price of 44 chocolates is equal to the selling price of 24 chocolates, the gain percent is :
Options:
A)83.55%
B)83.33%
C)80%
D)83.39%
E)84.33%
Rationale: Explanation :
Solution: Let C.P. of each chocolate be Re. 1. then, C.P. of 24 chocolates = Rs. 24;
S.P. of 24 chocolates =Rs. 44.
.'. Gain% = 20*100/24 =83.33%
Answer : B
Answer: B
Question: If x and y are positive integers, and 1 is the greatest common divisor of x and y, what is the greatest common divisor A of 2x and 3y?
Options:
A)A=1
B)A=Cannot be determined
C)2
D)5
E)6
Rationale: My explanation: from question stem we know that nothing is common between X and Y , X and Y are two prime numbers eg: X=2, Y=3 and their GCD(2,3) =1 and so 2X and 3Y will have a GCD(2X,3Y) = 1 . what if either X or Y was 1, eg: X=1,Y=4 then GCD(1,4) =1 , but GCD(2,12) = 2.
and hence answer B
Answer: B
Question: The original price of a certain TV set is discounted by d percent, and the reduced price is then discounted by 2d percent. If P is the original price of the TV Set, which of the following represents the price of the television set after the two successive discounts?
Options:
A)P(1 - 0.03x + 0.02x^2)
B)P(1 - 0.03d + 0.0002d^2)
C)P(1 - 0.03x + 0.002x^2)
D)P(1 - 2x^2)
E)P(1 - 3x + 2x^2)
Rationale: Youcansolve this problem with number plugging.
Say the original price was $10 and d=50. Then after the first reduction the price would become $5 and after the second reduction of 2*50=100% the rprice would become $0.
Now, since P is not zero, then the expression in the brackets must be zero for d=50. Only answer choice B works.
Answer: B.
On this problem - number pluggin is not giving me the answer.. I initially used d = 10, then 2d = 20 and P = 100. Answer should after both consecutive discounts = 72. I plug in the respective values and I keep getting 68. Can you double check my math.
100 (1-0.03(10) + 0.0002 (10)^2)
100 (1-0.3 + 0.0002 (100))
100 (0.7 + 0.02)
100 (0.68) = 68????
double check my math. Am I missing something? I also plugged in your numbers and still did not get zero as final answer with choice B..
Answer: B
Question: Of 300 surveyed students, 20% of those who read book A also read book B and 50% of those who read book B also read book A. If each student read at least one of the books, what is the difference between the number of students who read only book A and the number of students who read only book B?
Options:
A)120
B)125
C)130
D)135
E)150
Rationale: Say the number of students who read book A is A and the number of students who read book B is B.
Given that 20% of those who read book A also read book B and 50% of those who read book B also read book A, so the number of students who read both books is 0.2A=0.5B --> A=2.5B.
Since each student read at least one of the books then {total}={A}+{B}-{Both} --> 300=2.5B+B-0.5B --> B=100, A=2.5B=250 and {Both}=0.5B=50.
The number of students who read only book A is {A}-{Both}=250-50=200;
The number of students who read only book B is {B}-{Both}=100-50=50;
The difference is 200-50=150.
Answer: E.
Answer: E
Question: John have a 630ml mixture of milk and water in the ratio 7:2. How much water must be added to make the ratio 7:3?
Options:
A)50 ml
B)60 ml
C)70 ml
D)80 ml
E)90 ml
Rationale: concentration of water in mixture1 =29 (since the ratio of milk and water = 7:2) ...(1)
concentration of water in pure water= 1 ...(2)
Now the above mentioned items are mixed to form mixture2 where milk and water ratio = 7 : 3
=> concentration of water in mixture2 =310
By rule of alligation,
concentration of water in mixture1 (29)
concentration of water in pure water (1)
Mean concentration
(310)
1−310=710
310−29=790
=> Quantity of mixture1 : Quantity of water
=710:790=110:190=1:19
Given that Quantity of mixture1 = 630 ml
=> 630 : Quantity of water =1:19
=> Quantity of water =630×19=70 ml
C
Answer: C
Question: By investing Rs. 1620 in 8% stock,Michael earns Rs. 135.The stock is then quoted at :
Options:
A)Rs. 80
B)Rs. 96
C)Rs. 106
D)Rs. 108
E)Rs. 109
Rationale: Solution
To earn Rs. 135, investment = Rs. 1620.
To earn Rs. 8, investment = Rs. (1620/135X8)= Rs. 96.
∴ Market value of Rs. 100 stock = Rs. 96.
Answer B
Answer: B
Question: The least number which must be subtracted from 509 to make it exactly divisible by 9 is:
Options:
A)A)2
B)B)3
C)C)5
D)D)5
E)E)6
Rationale: On dividing 509 by 9, we get remainder= 5
Therefore, required number to be subtracted= 5
Answer: C
Answer: C
Question: A watch was sold at a loss of 10%. If the watch was sold for $28 more, there would have been a gain of 4%. What is the cost price?
Options:
A)$180
B)$200
C)$220
D)$240
E)$260
Rationale: 0.9x + 20 = 1.04x
0.14x = 28
x = 200
The answer is B.
Answer: B
Question: In Net's hair salon 54% of the customers dye their hair blond, 36% dye their eyebrows blond and 35% straighten their hair. 20% of the customers have none of these three procedures, while 12% take all of these three procedures. What percent of the customers come for exactly 2 of these 3 procedures?
Options:
A)5%
B)9%
C)12%
D)15%
E)21%
Rationale: Let a total of 100 people visit the salon.
Total = 100
Dye hair blonde (A) = 54 % = 54
Dye Eyebrows blonde (B) = 36% = 36
Straighten Hair (C) = 35% = 35
Neither = 20% = 20
All Three = 12% =12
Total = A+B+C - (Sum of Exactly Two group overlaps) - 2*(All three) + Neither
100 = 54+36+35 - (Sum of Exactly Two group overlaps) - 2*12 + 20
(Sum of Exactly Two group overlaps) = 9
%of customers coming for exactly 2 of the 3 procedures = 21%
E
Answer: E
Question: Two goods trains each 500 m long are running in opposite directions on parallel tracks. Their speeds are 60 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
Options:
A)22
B)27
C)40
D)99
E)12
Rationale: Relative speed = 60 + 30 = 90 km/hr.
90 * 5/18 = 25 m/sec.
Distance covered = 500 + 500 = 1000 m.
Required time = 1000/25 = 40 sec.
Answer: C
Answer: C
Question: An unbiased die is tossed .find the probability of getting a multiple of 3
Options:
A)3/7
B)4/9
C)1/3
D)3/5
E)2/7
Rationale: Here S={1,2,3,4,5,6}
Let E be the event of getting the multiple of 3
then ,E={3,6}
P(E)=n(E)/n(S)=2/6=1/3
Ans: C
Answer: C
Question: Find a sum for first 8 prime number'ss?
Options:
A)25
B)28
C)77
D)60
E)32
Rationale: Required sum = (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19) = 77
Note: 1 is not a prime number
Option C
Answer: C
Question: There are 20 balls which are red, blue or green. If 7 balls are green and the sum of red balls and green balls is less than 13, at most how many red balls are there?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: Explanation :
GIVEN:
RED + GREEN + BLUE = 20
GREEN = 7
SOLUTION:
R + G < 13
THEREFORE R + 7 < 13
SO r < 6
ANS: AT most 5 red balls
B. 5
Hence (B) is correct.
Answer : B
Answer: B
Question: A dishonest dealer claims to sell a product at its cost price. He uses a counterfeit weight which is 20% less than the real weight. Further greed overtook him and he added 15% impurities to the product. Find the net profit percentage of the dealer?
Options:
A)46.85%
B)43.75%
C)50%
D)56.25%
E)36%
Rationale: The dealer uses weight which is 20% less than the real weight. or (1- 1/5) or 4/5 of real weight.
It means that he is selling $4 worth of product for $5.
The dealer then further added 20% impurities to the product.
It means that he is selling $5 worth of product for $5.75.
So his profit is $5.75-$4 = $1.75
and his profit percent is
(1.75/4)*100 = 43.75%
Answer:- B
Answer: B
Question: A train 240 m long passes a pole in 24 seconds. How long will it take to pass a platform 650 m long?
Options:
A)65 sec
B)89 sec
C)100 sec
D)150 sec
E)120 sec
Rationale: Speed =	240/24 m/sec = 10 m/sec.
Required time = (240 + 650)/10	sec = 89 sec.
Answer: Option B
Answer: B
Question: (4300231)-?=2535618
Options:
A)1865113
B)1775123
C)1764613
D)1675123
E)None of them
Rationale: Let 4300231-x=2535618
then x=4300231-2535618
=1764613
Answer is C
Answer: C
Question: A train 605 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
Options:
A)81
B)16
C)33
D)54
E)12
Rationale: Speed of train relative to man = 60 + 6 = 66 km/hr.
= 66 * 5/18 = 55/3 m/sec.
Time taken to pass the men = 605 * 3/55 = 33 sec.
Answer: C
Answer: C
Question: From the top of a 9 metres high building AB, the angle of elevation of the top of a tower CD is 30º and the angle of depression of the foot of the tower is 60º. What is the height of the tower?
Options:
A)11
B)12
C)88
D)27
E)10
Rationale: We have to find the value of CD. We use Sine rule to find the answer easily. Sine rule is aSinA=bSinB=cSinCaSinA=bSinB=cSinC
In triangle BDE, 9Sin60=xSin309Sin60=xSin30
So 93–√2=x12⇒x=93–√932=x12⇒x=93
In triangle BCD, CDSin30=93–√Sin60CDSin30=93Sin60
CD12=93–√3–√2⇒CD=3CD12=9332⇒CD=3
So height of the tower = 9 + 3 = 12
Answer:B
Answer: B
Question: If one person completes a journey in 10 hrs. He travels 1st half of the journey at the rate of 21 km/hr and 2nd half at therate of 24 km/hr. Find the total journey in km.
Options:
A)189 km
B)210 km
C)224 km
D)256 km
E)274 km
Rationale: distance = speed x time
Let time taken to travel the first half = x hr
then time taken to travel the second half = (10 - x) hr
Distance covered in the the first half = 21x
Distance covered in the the second half = 24(10 - x)
But distance covered in the the first half = Distance covered in the the second half
=> 21x = 24(10 - x)
=> 21x = 240 - 24x
=> 45x = 240
=> 9x = 48
=> 3x = 16
⇒x=163Hence Distance covered in the the first half = 21x=21×163=7×16=112 kmTotal distance = 2×112=224 km
C
Answer: C
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 6 sec. What is the length of the fast train?
Options:
A)27 7/6
B)27 7/5
C)277/2
D)300/9
E)27 7/1
Rationale: Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 6 = 300/9
= 300/9 m.
Answer:D
Answer: D
Question: If each of 4 subsidiaries of Corporation R has been granted a line of credit of $626,500 and each of the other 3 subsidiaries of Corporation R has been granted a line of credit of $112,000, what is the average (arithmetic mean) line of credit granted to a subsidiary of Corporation R?
Options:
A) $1,568,000
B) $448,000
C) $406,000
D) $313,600
E) $116,000
Rationale: My take is C.
(626500*4 + 112000*3)/7 = 406000
Answer: C
Question: A rainstorm increased the amount of water stored in State J reservoirs from 160 billion gallons to 200 billion gallons. If the storm increased the amount of water in the reservoirs to 40 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?
Options:
A)260
B)280
C)325
D)340
E)355
Rationale: Let total capacity be x
we know 200 = 0.40x
x = 200/0.40 = 500
Prior to storm, we had 160 bn gallons
500-160 = 340
Answer : D
Answer: D
Question: The average weight of 8 person’s increases by 2.5 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)76 kg
B)76.5 kg
C)85 kg
D)Data inadequate
E)None of these
Rationale: EXPLANATION
Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg.
Answer C
Answer: C
Question: Each week the forensics teams at Roslyn High School and Manchester High School debate each other. Each team has several members, and each week three are selected to debate. Whenever Aviva debates for Roslyn, Roslyn wins; and whenever Zachary debates for Roslyn, Roslyn wins. Whenever Josh debates for Roslyn, Manchester wins.
Options:
A)287
B)268
C)26
D)17
E)191
Rationale: Explanation:
It is clear that if Josh debates for Rosln, Manchester wins. So Option A is correct.
Answer: A
Answer: A
Question: If x is the sum of six consecutive integers, then x is divisible by which of the following: I. 12 II. 3 III. 6
Options:
A)I only
B)II only
C)III only
D)I and III
E)I, II, and III
Rationale: We're told that X is the SUM of 6 CONSECUTIVE INTEGERS. We're asked what X is divisible by....
Let's TEST VALUES....
IF we use the 6 consecutive integers: 7,8,9,10,11 and 12, then the sum = 57.
57 is divisible by 3
57 is NOT divisible by 6
57 is NOT divisible by 12
There's only one answer that 'fits' with these facts, so Answer : B
Answer: B
Question: if x:y = 1:2, then find the value of
(7x+3y):(2x+y)
Options:
A)13:4
B)15:5
C)16:5
D)17:5
E)None of these
Rationale: Explanation:
let x = 1k and y = 2k, so
=7(k)+3(2k)/ 2(k)+1(2k)
=13k/4k
=13:4
Option A
Answer: A
Question: A bat and a ball cost one dollar and ten cents in total. The bat costs a dollar more than the ball. How much does the ball cost?
Options:
A)3
B)4
C)5
D)6
E)8
Rationale: Explanation: When you read the math problem, you probably saw that the bat and the ball cost a dollar and ten cents in total and when you processed the new information that the bat is a dollar more than the ball, your brain jumped to the conclusion that the ball was ten cents without actually doing the math. But the mistake there is that when you actually do the math, the difference between $1 and 10 cents is 90 cents, not $1. If you take a moment to actually do the math, the only way for the bat to be a dollar more than the ball AND the total cost to equal $1.10 is for the baseball bat to cost $1.05 and the ball to cost 5 cents.
The ball costs 5 cents.
correct answer is C)5
Answer: C
Question: A train leaves Mumabai at 9 am at a speed of 40 kmph. After one hour, another train leaves Mumbai in the same direction as that of the first train at a speed of 50 kmph. When and at what distance from Mumbai do the two trains meet?
Options:
A)267
B)2667
C)200
D)269
E)265
Rationale: When the second train leaves Mumbai the first train covers 40 * 1 = 40 km
So, the distance between first train and second train is 40 km at 10.00am
Time taken by the trains to meet
= Distance / relative speed = 40 / (50 -40) = 4 hours
So, the two trains meet at 2 p.m. The two trains meet 4 * 50
= 200 km away from Mumbai.
Answer:C
Answer: C
Question: Four persons enter the lift of a four storey building at the ground floor. In how many ways can they get out of lift on any floor other than ground floor
Options:
A)81
B)129
C)154
D)182
E)250
Rationale: Each person out of 4 has 3 floors (options) to get out of (since no one gets out on the ground floor), hence total ways is 3*3*3*3=3^4=81.
Answer: A.
Answer: A
Question: The R students in a class agree to contribute equally to buy their teacher a birthday present that costs y dollars. If r of the students later fail to contribute their share, which of the following represents the additional number of dollars that each of the remaining students must contribute in order to pay for the present?
Options:
A) y/R
B) y/(R-x)
C) xy/(R-x)
D) ry/(R(R-r))
E) y/(R(R-x))
Rationale: y/(R-r)- y/R
if we simplify this we get choice D, which is the correct answer.
Answer: D
Question: In the first round of the elections, the only two candidates got exactly the same number of votes. During the second round, 22,000 votes switched from the first candidate to the second one. The total number of votes remained the same in both rounds, and no other votes switched sides. If, in the second round, the winning candidate got five times as many votes as the other candidate, how many people have voted in each round?
Options:
A)15,000
B)66,000
C)40,000
D)50,000
E)60,000
Rationale: Let A be the first candidate and B be the second one.
Given x+22000 = 5(x-22000) => x = 33000
2x = 66000
IMO option B.
Answer: B
Question: A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of other variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:
Options:
A)No profit, no loss
B)5%
C)8%
D)10%
E)None of these
Rationale: C.P. of 56 kg rice = Rs. (26 x 20 + 30 x 36) = Rs. (520 + 1080) = Rs. 1600.
S.P. of 56 kg rice = Rs. (56 x 30) = Rs. 1680.
Gain =80/1600x100% = 5%.
Answer: Option B
Answer: B
Question: Find how many positive integers less than 10,000 are there suchthat the sum of the digits of the no. is divisible by 3?
Options:
A)2345
B)2445
C)2653
D)3334
E)3456
Rationale: If sum of the digits is divisible by 3, the number is divisible by 3.
Therefore, required number of non-negative integers is equal to count of numbers less than 10,000 which are divisible by 3.
Such numbers are (3, 6, 9, ... , 9999) (arithmetic progression with first term=3, last term=9999, common difference=3).
Count of such numbers =
9999
3
=
3333
99993=3333
But zero is also divisible by 3.
This makes our total count 3334
D
Answer: D
Question: At a certain company, each employee has a salary grade s that is at least 1 and at most 5. Each employee receives an hourly wage p, in dollars, determined by the formula p = 9.50 + 0.25(s – 1). An employee with a salary grade of 5 receives how many more dollars per hour than an employee with a salary grade of 3?
Options:
A)$0.50
B)$1.00
C)$1.25
D)$1.50
E)$1.75
Rationale: Salary grade of 5 is p(5)=9.50+0.25(5–1)=9.50+0.25*4;
Salary grade of 3 is p(3)=9.50 + 0.25(3–1)=9.50+0.25*2;
p(5)-p(3)=9.50+0.25*4-9.50-0.25*2=0.5.
Answer: A.
Answer: A
Question: Rain is falling at a rate of 10 centimeters per hour all over North Carolina. Somewhere downtown in North Carolina a group of people are waiting for the rain to stop. If the rain filled a round puddle the with a base area of 300 square centimeters and a depth of 30 centimeters, how long did the people wait for the rain to stop?
Options:
A)4 hours
B)11 hours
C)7 hours 15 minutes
D)3 hours
E)14 hours
Rationale: Answer is : D, 3 hours
The volume of the puddle is irrelevant and only height matters since rain fell all over the city.
Thus, it takes only 30 / 10 = 3 hours of rain to fill the puddle
Answer: D
Question: C and D start a business with Rs.25000 and Rs.35000 respectively. Hoe should they share their profits at the end of one year?
Options:
A)5:7
B)7:5
C)4:7
D)7:4
E)3:7
Rationale: Explanation:
They should share the profits in the ratio of their investments.
The ratio of the investments made by C and D =
25000 : 35000 => 5:7
Answer:A
Answer: A
Question: Two trains 140 m and 210 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)12.6 sec
B)10.1 sec
C)10.6 sec
D)10.8 sec
E)10.2 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other
= 140 + 210 = 350 m.
Required time = 350 * 9/250
= 12.6 sec.
Answer:A
Answer: A
Question: The fourth proportional to 7, 9, 14 is:
Options:
A)10
B)12
C)14
D)16
E)18
Rationale: Let the fourth proportional to 7, 9, 14 be x.
Then, 7 : 9 : 14 : x
7x = (9 x 14)
x =	(9 x 14)/7
x=126/7 =18
Answer: Option C
Answer: C
Question: The Shopkeeper increased the price of a product by 25% so that customer finds it difficult to purchase the required amount. But somehow the customer managed to purchase only 70% of the required amount. What is the net difference in the expenditure on that product?
Options:
A)10%
B)11%
C)12.5%
D)13%
E)15%
Rationale: Quantity X Rate = Price
1 x 1 = 1
0.7 x 1.25 = 0.875
Decrease in price = (0.125/1) × 100 = 12.5%
C)
Answer: C
Question: The shopkeeper sale, all of the prices of the items sold were different. If the price of a radio sold at the shopkeeper sale was both the 9th highest price and the 14th lowest price among the prices of the items sold, how many items were sold at the shopkeeper sale?
Options:
A)23
B)22
C)32
D)26
E)17
Rationale: 8+13+1= 22
Answer: B
Answer: B
Question: What is the minimum percentage increase in the mean of set F {-4, -1, 0, 6, 9} if its two smallest elements are replaced with two different primes?
Options:
A) 25%
B) 50%
C) 75%
D) 100%
E) 200%
Rationale: Mean of F is (-4-1+0+6+9)/5=2;
In order the increase to be minimal we should replace two smallest elements of F, which are -4 and -1, with two smallest primes, which are 2 and 3. Hence our new set will be {2, 3, 0, 6, 9} --> new mean is (2+3+0+6+9)/5=4.
Percent increase=(4-2)/2*100=100%.
Answer: D.
Answer: D
Question: Judges will select 6 finalists from the 8 contestants entered in a singing competition. The judges will then rank the contestants and award prizes to the 3 highest ranked contestants: a blue ribbon for first place, a red ribbon for second place, and a yellow ribbon for third place. How many different arrangements of prize-winners are possible?
Options:
A)10
B)21
C)210
D)420
E)560
Rationale: First Select 5 from 7 contestants and then select top 3 from those 5 =
8C6*6C3 =28 * 20 = 560
ANS:E
Answer: E