divelab/Sys2Bench huggingface dataset:
Question: A baker filled with a measuring cup with 1/4 cup water. He poured 1/2 of the water into the batter, and then spilled 1/8 of the water on the floor. How much water will the baker needed to add what is left in the cup to have 50% more than what he started with?
Options:
A)1/8 cup
B)3/8 cup
C)1/4 cup
D)1/2 cup
E)7/8 cup
Rationale: B
1/4 is the original water in cup .half in batter.So left is 1/8 out which 1/8 is spilled out.So again left with 0.
so 50% more than what he started was = 1/4+1/2*(1/4)=3/8
Amount of water needed to add = 3/8 - 0=3/8
B
Answer: B
Question: If two positive numbers are in the ratio 1/8 : 1/5, then by what percent is the second number more than the first?
Options:
A)67%.
B)70%.
C)60%.
D)68%.
E)80%.
Rationale: Given ratio = 1/8 : 1/5 = 5 : 8
Let first number be 5x and the second number be 8x.
The second number is more than first number by 3x.
Required percentage = 3x/5x * 100 = 60%.
Answer: C
Answer: C
Question: A shopkeeper sold 8articles at the cost price of 10 articles. Then find the profit% or lost%
Options:
A)10%
B)25%
C)20%
D)30%
E)50%
Rationale: here 8 articles selling price = 10 articles cost price
so the difference = 10-8 = 2
% of profit = 2*100/8 = 25%
correct option is B
Answer: B
Question: Compound interest earned on a sum for the second and the third years are Rs.1200 and Rs.1440 respectively. Find the rate of interest?
Options:
A)65% p.a
B)88% p.a
C)20% p.a
D)66% p.a
E)44% p.a
Rationale: Rs.1440 - 1200 = Rs.240 is the interest on Rs.1200 for one year.
Rate of interest = (100 * 240) / (100 * 1) = 20% p.a
Answer: C
Answer: C
Question: A certain rectangular window is (1/3) times as long as it is wide. If its perimeter is 28 feet, what are its dimensions in terms of length by width?
Options:
A)12 by 2
B)11 by 3
C)10.5 by 3.5
D)10 by 4
E)9 by 3
Rationale: 2x+2y=28
x+y=14
x+(1/3)x=14
4x=14*3
x=10.5
Answer C
Answer: C
Question: In how many years Rs 100 will produce the same interest at 5% as Rs. 200 produce in 2 years at 10%
Options:
A)8
B)10
C)9
D)12
E)11
Rationale: Explanation:
Clue:
Firstly we need to calculate the SI with prinical 200,Time 2 years and Rate 10%, it will be Rs. 40
Then we can get the Time as
Time = (100*40)/(100*5) = 8
Option A
Answer: A
Question: 5400 ÷ 9 ÷ 3 = ?
Options:
A)1800
B)900
C)450
D)300
E)None of these
Rationale: 5400 ÷ 9 ÷ 3 = ?
or, ? = 5400 × 19×3=200
Answer E
Answer: E
Question: A committee of three students has to be formed. There are seven candidates: Jane, Joan, Paul, Stuart, and Jessica. If Paul and Stuart refuse to be in the committee together and Jane refuses to be in the committee without Paul, how many committees are possible?
Options:
A)3
B)4
C)5
D)6
E)8
Rationale: Let's try a different problem with your approach. There are five people: A, B, C, D, E. Need to chose 3 for a committee. A and B cannot be chosen together. B and C cannot be chosen together. How many options?
Your approach: total 10 options, 5c3.
Now, assume the wrong scenario where A and B are chosen together. There are three such scenarios. (A and B are chosen, just need one more person.) So we have to subtract the three wrong options. Similarly, there are three wrong scenarios where B and C are chosen together.
This gives us 10-3-3=4 as the answer.
Yet this answer is wrong. There are five possibilities: ACD, ACE, ADE, BDE, CDE.
E
Answer: E
Question: A library has an average of 600 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is:
Options:
A)250
B)260
C)300
D)285
E)None
Rationale: Since the month begins with sunday,to there will be five sundays in the month
Average required = (600x5 + 240x25) /30) = 300
Answer: Option C
Answer: C
Question: What is the length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high?
Options:
A)7
B)9
C)11
D)13
E)None
Rationale: Explanation:
d2 = 122 + 42 + 32 = 13
D)
Answer: D
Question: At the faculty of Aerospace Engineering, 312 students study Random-processing methods, 222 students study Scramjet rocket engines and 112 students study them both. If every student in the faculty has to study one of the two subjects, how many students are there in the faculty of Aerospace Engineering?
Options:
A)404
B)452
C)444
D)468
E)422
Rationale: 312 + 222 - 112 (since 112 is counted twice )= 422
E is the answer
Answer: E
Question: A shopkeeper buys two articles for Rs.1000 each and then sells them, making 15% profit on the first article and 15% loss on second article. Find the net profit or loss percent?
Options:
A)200
B)768
C)150
D)280
E)279
Rationale: Profit on first article = 150% of 1000 = 150.
This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.
Answer: C
Answer: C
Question: Find the invalid no.from the following series 2,3,12,37,86,166,288
Options:
A)2
B)3
C)166
D)12
E)288
Rationale: 3-2=1
12-3=9
37-12=25
86-37=49
166-86=80(this must be 81=167-86=81)
so wrong number in the sequence is 166
difference between two sucessive numbers sequence would be
1,9,25,49,81,121(square of 1,3,5,7,9,11)
C
Answer: C
Question: The volumes of two cones are in the ratio 1 : 12 and the radii of the cones are in the ratio of 1 : 3. What is the ratio of their heights?
Options:
A)A)3:4
B)B)2:7
C)C)2:2
D)D)2:1
E)E)2:9
Rationale: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/12 = (1)2h1/(3)2h2
=> h1/h2 = 3/4
i.e. h1 : h2 = 3: 4
Answer: A
Answer: A
Question: In a room there are 8 people. Each person shook hands with every other person. How many hand shakes were there?
Options:
A)26
B)28
C)30
D)32
E)34
Rationale: 8C2 = 28
The answer is B.
Answer: B
Question: The average (arithmetic man) of three integers a, b, and c is exactly four times the median. If a < b < c and a = 0, what is the value of c/b?
Options:
A)2
B)3
C)4
D)11
E)Cannot be determined from the information given.
Rationale: The average of three integers a, b, and c is exactly twice the median --> (a+b+c)/3=4b --> since a=0, then (0+b+c)/3=4b --> c=11b --> c/b=11.
Answer: D.
Answer: D
Question: If f(x)= 5x^2- 2x+6 and g(y)= 3y-4, then g(f(x))
Options:
A)82x^2-9x+38
B)15x^2-6x+14
C)58x^2-4x+58
D)87x^2-5x+96
E)98x^2-7x+94
Rationale: g(f(x))=3(5x^2-2x+6)-4
=15x^2-6x+18-4
=15x^2-6x+14
the answer is B
Answer: B
Question: In a village there are 150 men and 90 women in present time.if in next year population will be P=(a^2 +b^2)^1/2 , and in every year men are reduces 8%.what is population of after 2 year.
Options:
A)140
B)141
C)142
D)143
E)144
Rationale: next year total population=[150^2+90^2]^.5=174.92=175
man decreased by 8% so total man =150*.92=138
women will be= 175-138=37
so population after two years= [135^2+37^2]^.5=142.87=143
so population after two year= 143
ANSWER:D
Answer: D
Question: Ramesh spends 50% of his monthly salary on food, and saves 90% of the remaining amount. If his monthly salary is Rs.10,000, how much money does he save every month ?
Options:
A)Rs.2500
B)Rs. 4500
C)Rs.8000
D)Rs.3000
E)Rs.1000
Rationale: Explanation:
Ramesh's monthly income = Rs.10,000
He spends 50% on food.
The total money spent on food = 50/100 * 10000 = Rs. 5000
Now, his monthly remaining income = Rs.10000 – Rs.500 = Rs. 5000
Out of Rs. 5000, he saves 90%.
Amount saved = 90/100 * 5000 = Rs. 4500
ANSWER:B
Answer: B
Question: A rectangular room 14 m long, 12 m broad is surrounded by a varandah, 3 m wide. Find the area of the varandah?
Options:
A)170
B)180
C)190
D)210
E)150
Rationale: Area of varandah = (l+b+2p)2p
= (14 + 12 + 6 ) 6
= 180 m(power)2
Answer is B.
Answer: B
Question: What is the probability that a 3 person committee chosen at random from a group consisting of 6 men, 7 women, and 5 children contains exactly 1 woman?
Options:
A)77/204
B)77/832
C)11/77
D)385/816
E)22/832
Rationale: Total possible selections = 3 out of 18 group members = 18C3
Favorable selections = 1 out of 7 women and 2 out of 11 (= 6 men + 5 children) = 7C1 * 11C2
Thus the required probability = 7C1*11C2 / 18C3 = 385/816. Thus D is the correct answer.
Answer: D
Question: If you multiply all the numbers on your mobile phone except 0, what is the answer?
Options:
A)256485
B)362880
C)125425
D)0
E)125826
Rationale: We have to multiply 1 to 9 to find the answer.
Therefore 1*2*3*4*5*6*7*8*9=362880
Answer is B
Answer: B
Question: The variable x is inversely proportional to the square of the variable y. If y is divided by 2a, then x is multiplied by which of the following?
Options:
A)1/4a
B)1/4a^2
C)1/2a
D)4a
E)4a^2
Rationale: initially - did x= 1/y^2
But this yielded the wrong answer,
I then re examined the question and tried y^2/x =1
Which I then got y = SQR(X)
subbing into y/2a I got answer E)
Answer: E
Question: 9 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 12 cm height. What is the diameter of each sphere?
Options:
A)4 cm
B)6 cm
C)8 cm
D)10 cm
E)12 cm
Rationale: Volume of cylinder = pi*r^2*h
Volume of a sphere = 4*pi*R^3 / 3
9*4*pi*R^3 / 3 = pi*r^2*h
R^3 = r^2*h / 12 = 64 cm^3
R = 4 cm
D = 8 cm
The answer is C.
Answer: C
Question: In how many ways Chief Minister and Minister be elected froma team of 12 members?
Options:
A)126
B)128
C)132
D)146
E)147
Rationale: To do this, if captain is elected first, then we have 12 ways of doing this.
For election of vice-captain, we have only 11 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 12*11 = 132 ways.
C
Answer: C
Question: If 20% of a = b, then b% of 20 is the same as :
Options:
A)4% of a
B)6% of a
C)8% of a
D)10% of a
E)12% of a
Rationale: Explanation:
20% of a = b =>20/100 a=b
b% of 20 =b/100 x 20 =20 a/100 x 1/100 x 20 =4a/100 =4% of a.
ANSWER IS A
Answer: A
Question: The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m
95 cm is
Options:
A)16cm
B)25cm
C)15cm
D)35cm
E)45cm
Rationale: Explanation:
So by now, you must be knowing this is a question of HCF, right.
H.C.F. of (700 cm, 385 cm, 1295 cm) = 35 cm.
Answer: Option D
Answer: D
Question: The boat moves downside 100km and upside 20km in 2 hours each. Then find the boat speed in still water?
Options:
A)15km/hr
B)25km/hr
C)30km/hr
D)20km/hr
E)40km/hr
Rationale: Down stream = 100/2 = 50km/hr
Up stream = 20/2 = 10km/hr
speed of boat in still water = 60/2 = 30km/hr
Answer is C
Answer: C
Question: Find the odd man out
253, 136, 352, 326, 631, 244
Options:
A)326
B)136
C)352
D)631
E)531
Rationale: The sum all three digits comes to 10 except 326
ANSWER:A
Answer: A
Question: When four fair dice are rolled simultaneously, in how many outcomes will at least one of the dice show 3?
Options:
A)238
B)671
C)297
D)200
E)211
Rationale: When 4 dice are rolled simultaneously, there will be a total of 6 x 6 x 6 x 6
= 1296 outcomes.
The number of outcomes in which none of the 4 dice show 3 will be 5 x 5 x 5 x 5
= 625 outcomes.
Therefore, the number of outcomes in which at least one die will show 3 = 1296 – 625
= 671
Answer: B
Answer: B
Question: Eight persons participated in a shooting competition. The top score in the competition is 85 points. Had the top score been 92 points instead of 85 points, the average score would have been 84. Find the number of points actually scored in the competition.
Options:
A)645
B)655
C)665
D)636
E)656
Rationale: Let the actual number of points scored be x,
Then [ x + (92 –85 )] /8 = 84, ( x + 7) /8 = 84 , x = ( 84*8 )- 7,
= 672 - 7 = 665
ANSWER:C
Answer: C
Question: Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is
Options:
A)5/18
B)5/12
C)5/15
D)5/14
E)5/11
Rationale: Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9) = 5/12.Answer:B
Answer: B
Question: In May, Xiang sold 15 used cars. For these 15 cars, the range of the selling price was $15,000 and the lowest selling price was $4,500. In June, Xiang sold 10 used cars. For these 10 cars, the range of the selling prices was $16,500 and the lowest selling price was $6,500. What was the range of the selling prices of the 25 used cars sold by Xiang in May and June?
Options:
A)1. $15,600
B)2. $15,750
C)3. $16,820
D)4. $18,500
E)5. $19,200
Rationale: Edited the question as there was a typo.
Range = Highest Value - Lowest Value.
Range in May was 15,000 and the lowest price in May was 4,500, thus the highest price in May was 15,000+4,500=19,500.
Range in June was 16,500 and the lowest price in June was 6,500, thus the highest price in June was 16,500+6,500=23,000.
Lowest price of a car in May-June was 4,500 (May) and the highest price of a car in May-June was 23,000, thus the range for May-June is 23,000-4,500=18,500.
Answer: D.
Answer: D
Question: Three candidates contested an election and received 1130, 7630 and 15620 votes respectively. What percentage of the total votes did the winning candidate get?
Options:
A)57%
B)60%
C)64%
D)90%
E)80%
Rationale: total votes are 24380 ( sum of votes obtained by 3 candidates)
percentage of the total votes recd by the winning candidate = 100*15620/24380 = 64%
ANSWER:C
Answer: C
Question: What least value should be replaced by * in 2551112* so the number become divisible by 6
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: Explanation:
Trick: Number is divisible by 6, if sum of all digits is divisible by 3 and 2, so (2+5+5+1+1+1+2+*) = 17+* should be divisible by ,
17+1 will be divisible by 3,
but we can't take this number because 1 is not dividable by 2(2 only dividable by those numbers who contain even number at last position)
so that least number is 4.
Answer: Option B
Answer: B
Question: A new condo development is offering buyers the option to choose from 4 different counter top styles, 5 floor types and 4 colors of paint. In order to keep costs to the minimum, the buyer would like to choose from the lower cost options. In how many ways can 3 styles of counter tops, 2 colors floor types, and 3 colors of paint be selected from the given group?
Options:
A)112 ways
B)99 ways
C)80 ways
D)64 ways
E)12 ways
Rationale: The number of ways of selecting three styles of counter tops, two floors and three colors of paint is:
= ⁴C₃ * ⁵C₂ * ⁴C₃
= (4 * 3 * 2)/(3 * 2 * 1) * (5 * 4)/(2 * 1) * (4 * 3)/(3 * 2 * 1)
= 4 * 10 * 2
= 80 ways.
Answer: C
Answer: C
Question: An inspector rejects 0.08% of the meters as defective. How many will he examine to reject 2?
Options:
A)1200
B)1240
C)1852
D)3200
E)2500
Rationale: Then, 0.08% of x = 2
(8/100)*(1/100)x = 2
x = (2*100*100)/8 = 2500
Answer is E
Answer: E
Question: A certain sum of money is divided among A, B and C such that A gets one-third of what B and C together get and B gets two-seventh of what A and C together get. If the amount received by A is $30 more than that received by B, find the total amount shared by A, B and C.
Options:
A)$1080
B)$1180
C)$1280
D)$1380
E)$1480
Rationale: A = 1/3 (B+C) => C = 3A - B ---(1)
B = 2/7 (A+C) => C = 3.5 B - A --(B)
A-B = $30
A = 30+B
(1)===> C = 90+3B - B = 2B+90 ==> 2B-C = -90 ---(3)
(2)===> C = 3.5 B - B-30 = 2.5B-30==>2.5B-C = 30---(4)
from (4) and (3) 0.5B = 120
B = $240
A= $270
C =810-240=$570 Total amount = 270+240+570 = $1080
Answer: A
Answer: A
Question: How many prime numbers are between 51/13 and 89/9?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: 51/13= 4-
89/9= 10-
Prime numbers between 4 and 10 are 5 and 7
- sign signifies that the number is marginally less .
Answer C
Answer: C
Question: If the area of a square with sides of length 4 centimeters is equal to the area of a rectangle with a width of 4 centimeters, what is the length of the rectangle, in centimeters?
Options:
A)14
B)8
C)12
D)4
E)18
Rationale: Let length of rectangle = L
4^2 = L*4
=> L = 16/4 = 4
Answer D
Answer: D
Question: If 144/0.144 = 14.4/x, then the value of x is:
Options:
A)0.144
B)1.44
C)0.0144
D)0.014
E)0.00144
Rationale: =144/0.144 = 14.4/x
=144 x 1000/144
=14.4/x
=x = 14.4/1000
= 0.0144
Answer is C.
Answer: C
Question: How much 45% of 60 is greater than 35% of 40?
Options:
A)18
B)13
C)15
D)17
E)71
Rationale: (45/100) * 60 – (35/100) * 40
27 - 14 = 13
Answer: B
Answer: B
Question: For a certain alarm system, each code is comprised of 5 digits, but no digit can be used more than twice. How many codes can be made?
Options:
A)30,240
B)60,480
C)91,440
D)98,240
E)101,040
Rationale: Case 1: All digits distinct
Select 5 digits out of 10 in 10C5 ways and arrange them in 5! ways which gives us 10C5x5! = 30240
Case 2: Two digits are same, other 3 are distinct e.g. 45722
Select a digit which is to be repeated in 10C1 ways, select other 3 digits in 9C3 ways and arrange them in 5!/2! ways to get 10C1 x 9C3 x 5!/2! = 50400 ways
Case 3: Two digits repeated and one other digit e.g. 33448
Select 2 digits to be repeated in 10C2 ways, select the single digit in 8C1 ways and arrange them all in 5!/2!.2! ways to get 10C2 x 8C1 x 5!/2!.2! = 10800
Sum of all = 30240 + 50400 + 10800 = 91440 ways
ANS:C
Answer: C
Question: There are five newly appointed teachers in a college. The weight of first teacher is 200 kg and the weight of the 2nd teacher is 20% higher than the weight of the third teacher, whose weight is 25% higher than the first teacher's weight. The fourth teacher at 350 kgs is 30% lighter than the fifth teacher. Find the average weight of all the five teachers.
Options:
A)310
B)320
C)240
D)260
E)270
Rationale: Explanation :
Weight of first teacher = 200 kg
Weight of 3rd teacher = 250kg
=> Weight of 2nd teacher = 300 kg
Weight of 4th teacher = 350 kg
=> Weight of 5th teacher = 350/0.7 = 500 kg
Average weight = 1600/5 = 320 kg.
Answer : B
Answer: B
Question: A professional athlete was offered a three-year contract to play with Team K that provided for an annual salary of $100,000 in the first year, an increase in annual salary of 20% over the previous year for the next two years, and a bonus of $50,000 on signing. Team L offered a three-year contract providing for an annual salary of $150,000 in the first year, an increase in annual salary of 20% over the previous year for the next two years, and no signing bonus. If he accepts the offer of Team L and fulfills the three-year contract terms, the athlete will receive how much more money by choosing Team L over Team K ?
Options:
A)$132,000
B)$50,000
C)$82,500
D)$92,000
E)$100,000
Rationale: Team K's contract = $100,000 + $100,000*1.2 + $100,000*1.2*1.2 + $50,000 = $414,000
Team L's contract = $150,000 + $150,000*1.2 + $150,000*1.2*1.2 = $546,000
The difference = $132,000.
Answer: A.
Answer: A
Question: What is the length of the longest pole which can be kept in a room 12 m long, 4 m broad and 3 m high?
Options:
A)10 cm
B)12 cm
C)15 cm
D)13 cm
E)16 cm
Rationale: d2 = 122 + 42 + 32 = 13
ANSWER:D
Answer: D
Question: The table below shows how many coaches work with each of the major sports teams at Kristensen School. Although no single coach works with all three teams, 3 coaches work with both the Track and Tennis teams, 2 coaches work with both the Track and Baseball teams, and 1 coach works with both the Tennis and Baseball teams. How many different coaches work with these three teams?
Sports No of coaches
Track 7
Tennis 5
Baseball 4
Options:
A)6
B)10
C)11
D)12
E)17
Rationale: X = 7+ 5 + 4 - (3 + 2 + 1) = 10
Answer is B
Answer: B
Question: Braun invested a certain sum of money at 8% p.a. simple interest for 'n' years. At the end of 'n' years, Braun got back 5 times his original investment. What is the value of n?
Options:
A)50 years
B)25 years
C)12 years 6 months
D)37 years 6 months
E)40 years
Rationale: Explanatory Answer
Let us say Braun invested $100.
Then, at the end of 'n' years he would have got back $500.
Therefore, the Simple Interest earned = 500 - 100 = $400.
We know that Simple Interest = (Principal * number of years * rate of interest) / 100
Substituting the values in the above equation we get 400 = (100 * n * 8) / 100
Or 8n = 400
Or n = 50 years.
correct choice is (A)
Answer: A
Question: John makes $40 a week from his job. He earns a raise and now makes $70 a week. What is the % increase?
Options:
A)16%
B)16.66%
C)18%
D)21%
E)75%
Rationale: Increase = (30/40)*100 = 75%.
E
Answer: E
Question: Of the 20 guests at a party, 10 percent are women. How many men must leave in order to bring the number of women up to 50 percent of the guests?
Options:
A)18
B)14
C)16
D)4
E)2
Rationale: Now, there are 2 women (10% of 20) and 20-2=18 men at a party. We need there to be 2 women and 2 men, in this case there will be 50% women and 50% men.
Therefore 18-2=16 men must leave.
Answer: C.
Answer: C
Question: The entire contents of a full sack of flour can be used to make 15 cupcakes and 10 pizzas. The same full sack of flour can be used to make 7 cupcakes and 14 pizzas. If a full sack of flour is used to make only pizzas, how many pizzas can be made?
Options:
A)10
B)21 1/2
C)18 3/4
D)19
E)19 1/4
Rationale: 15x+10y=7x+14y
x=1/2y. Answer B
Answer: B
Question: A number consists of two digits. If 3/5 of 1/5 of the number is 9. Find the sum of its two digits?
Options:
A)28
B)189
C)17
D)12
E)01
Rationale: Explanation:
x * 3/5 * 1/5 = 9
x = 75 => 7 + 5 = 12
Answer: D
Answer: D
Question: Set S is the prime integers between 0 and 35. If three numbers are chosen randomly from set S, what is the probability that the sum of these three numbers is odd?
Options:
A)15/56
B)3/8
C)15/28
D)8/11
E)3/4
Rationale: Total number of combinations=11C3=165................(1)
Total number of combinations including 2 and two other numbers=10C2=45......................(2)
Therefore the difference ie. (1)-(2) is the set of 3 primes without 2=(165-45)=120
So, probability=120/165=8/11
D
Answer: D
Question: In wardrobe Karan has 3 trousers. One of them is grey the 2nd blue and the 3rd brown. In his wardrobe he also has 4 shirts. One of them is grey and the other 3are white. He opens his wardrobein the dark and pick out one shirttrouser pair without examination the color. What is the likelihood that neither the shirt nor the trouser is grey?
Options:
A)1/2
B)2/3
C)4/5
D)6/11
E)4/5
Rationale: Probability that trouser is not grey = 2/3
Probability that shirt is not grey = 3/4
∴ Required probability = 2/3 x 3/4 = 1/2
A
Answer: A
Question: If 12 ounces of a strong vinegar solution are diluted with 50 ounces of water to form a five-percent vinegar solution, what was the concentration of the original solution?
Options:
A)19.3%
B)25.8%
C)16.67%
D)15.5%
E)12.5%
Rationale: Let X be the quantity of non-vinegar in the strong vinegar solution
Thus vinegar quantity will be 12 - X
When 50 ounces of water were added the percentage of vinegar becomes 5%, thus (12 - X)/62 = 5/100
From this equation X = 8.9
Answer (12-8.9)/12 = 25.8%
ANSWER:B
Answer: B
Question: Lucy deposited $62500 in an investment fund that provided 24 percent annual return compounded half yearly.If she made no other transactions with the fund, in how much time, in years, did her investment earn a total interest of $10400?
Options:
A)0.5
B)1
C)3
D)6
E)6.1
Rationale: A = P + I = 62500 + 10400 = 72900
72900 = 62500(1 + 24/2*100)^(2t)
(676/625) = (112/100)^(2t)
(27/25)^2 = (27/25)^2t
t = 1yrs =
Answer: B
Answer: B
Question: 10 men and 15 women together can complete a work in 6 days. It takes 100 days for one man alone to complete the same work. How many days will be required for one woman alone to complete the same work?
Options:
A)90
B)125
C)145
D)225
E)None of these
Rationale: 1 man’s 1 day’s work = 1⁄100
(10 men + 15 women)’s 1 day’s work = 1⁄6
15 women’s 1 day’s work
= (1⁄6 - 10⁄100) = (1⁄6 - 1⁄10) = 1⁄15
∴ 1 woman’s 1 day’s work = 1⁄225
∴ 1 woman alone can complete the work in 225 days
Answer D
Answer: D
Question: Find the no.of ways of arranging the boy and 8 guests at a circular table so that the boy always sits in a particular seat?
Options:
A)5!
B)8!
C)9!
D)12!
E)11!
Rationale: Ans.(B)
Sol. Total number of persons = 9 Host can sit in a particular seat in one way. Now, remaining positions are defined relative to the host. Hence, the remaining can sit in 8 places in 8P8 = 8! Ways ... The number of required arrangements = 8! x 1= 8! = 8! ways
Answer: B