divelab/Sys2Bench huggingface dataset:
Question: Ramzi walked for 3 days. She walked 18 miles on the first day, walking 3 miles per hour. On the second day she walked for one less hour but she walked one mile per hour, faster than on the first day. On the third day she walked the same number of hours as on the first day, but at the same speed as on the second day. How many miles in total did she walk?
Options:
A)24
B)44
C)58
D)60
E)62
Rationale: Ramzi walked 18 miles on the first day, walking 3 miles per hour i.e. total time of walk on Day-1 = 18/3 = 6 Hours
Second day time of walk = 6-1 = 5 hours and Speed = 3+1=4 miles per hour i.e. Distance walked on second day = 5*4 = 20 miles
Third day time of walk = 6 hours and Speed = 4 miles per hour i.e. Distance walked on second day = 6*4 = 24 miles
Total Distance travelled on three days = 18+20+24 = 62
Answer: Option E
Answer: E
Question: Walking with 4/5 of my usual speed, I miss the bus by 5 minutes. What is my usual time?
Options:
A)35 min
B)30 min
C)25 min
D)20 min
E)40 min
Rationale: Explanation:
Speed Ratio = 1:4/5 = 5:4Time Ratio = 4:51 -------- 5 4 --------- ? è 20
ANSWER IS D
Answer: D
Question: Amit and Ananthu can do a work in 15 days and 60 days respectively. Amit started the work and left after 3 days. Ananthu took over and completed the work. In how many days was the total work completed?
Options:
A)38 days
B)40 days
C)43 days
D)45 days
E)51 days
Rationale: Amit’s one day’s work= 1/15
Amit’s 3 day’s work = 1/15 *3 = 1/5
Work left= 1-1/5 = 4/5
Ananthu’s one day’s work= 1/60
Ananthu can do work in = 4/5 *60 = 48 days
So total days = 48+3 = 51 days
ANSWER:E
Answer: E
Question: What approximate value should come in place of question mark (?) in the following equation
287.532 + 1894.029 – 657.48 = 543.095 + ?
Options:
A)870
B)790
C)980
D)770
E)890
Rationale: ? = 285 + 1895 – 655 – 545 or, ? = 980
Answer C
Answer: C
Question: If the cost price is 25% of selling price. Then what is the profit percent
Options:
A)238
B)278
C)300
D)166
E)129
Rationale: Explanation:
Let the S.P = 100
then C.P. = 25
Profit = 75
Profit% = (75/25) * 100 = 300%
Answer: C
Answer: C
Question: Two men A and B start from place X walking at 4 ½ kmph and 5 ¾ kmph respectively. How many km apart they are at the end of 3 ½ hours if they are walking in the same direction?
Options:
A)2 3/8 km
B)4 3/6 km
C)4 3/8 km
D)4 7/8 km
E)4 1/8 km
Rationale: RS = 5 ¾ - 4 ½ = 1 ¼
T = 3 ½ h.
D = 5/4 * 7/2 = 35/8
= 4 3/8 km
Answer:C
Answer: C
Question: Is y is a positive number? Statement–1: 2x+y > 27; Statement–2: x–3y < 24
Options:
A)22
B)62
C)28
D)16
E)11
Rationale: Answer:B
Answer: B
Question: A word consists of 9 letters; 5 consonants and 4 vowels.Three letters are choosen at random. What is the probability that more than one vowel will be selected ?
Options:
A)17/49
B)17/42
C)17/87
D)17/29
E)17/12
Rationale: Explanation:
3 letters can be choosen out of 9 letters in {\color{Black} {^9}C_3} ways.
More than one vowels ( 2 vowels + 1 consonant or 3 vowels ) can be choosen in {\color{Black} \left ( {^4}C_2\times {^5}C_1 \right )+{^4}C_3} ways
Hence,required probability = {\color{Black} \frac{\left ( {^4}C_2\times {^5}C_1 \right )+{^4}C_3}{{^9}C_3}} = 17/42
Answer: B) 17/42
Answer: B
Question: A goods train leaves a station at a certain time and at a fixed speed. After ^hours, an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmph. This train catches up the goods train in 4 hours. Find the speed of the goods train.
Options:
A)26 kmph
B)16 kmph
C)36 kmph
D)46 kmph
E)13 kmph
Rationale: Let the speed of the goods train be x kmph.
Distance covered by goods train in 10 hours= Distance covered by express train in 4 hours
10x = 4 x 90 or x =36.
So, speed of goods train = 36kmph.
Option C
Answer: C
Question: How many seconds will a 400 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
Options:
A)24 sec
B)30 sec
C)27 sec
D)28 sec
E)29 sec
Rationale: Speed of train relative to man = 63 - 3
= 60 km/hr.
= 60 * 5/18
= 50/3 m/sec.
Time taken to pass the man = 400 * 3/50
= 24 sec.
Answer:A
Answer: A
Question: Each person who attended a company meeting was either a stockholder in the company, an employee of the company, or both. If 60 percent of those who attended the meeting were stockholders and 47 percent were employees, what percent were stockholders who were not employees?
Options:
A)53
B)54
C)55
D)56
E)57
Rationale: 60+47=107 so 7% were both stockholders and employees.
The percent who were stockholders but not employees is 60-7=53%
The answer is A.
Answer: A
Question: A and B invests Rs.3000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
Options:
A)8:8
B)9:8
C)9:9
D)9:5
E)9:1
Rationale: (3*6 + 6*6): (4*12)
54:48 => 9:8
Answer: B
Answer: B
Question: A woman bought books at 30% discount on its original price. He sold it at a 90% increase on the price he bought it. What percent of profit did he make on the original price?
Options:
A)33%
B)22%
C)44%
D)55%
E)66%
Rationale: Original price = 100
CP = 70
S = 70*(190/100) = 133
100 - 133 = 33%
Answer: A
Answer: A
Question: A towel, when bleached, lost 20%20% of its length and 10%10% of its breadth. What is the percentage decrease in area?
Options:
A)30%
B)28%
C)32%
D)26%
E)28%
Rationale: Explanation:
Let original length =10
original breadth =10
Then, original area =10×10=100
Lost 20%20% of length
⇒ New length =10−2=8 (∵ 2 is 20% of 1010)
Lost 10% of breadth
⇒ New breadth =10−1=9 (∵ 1 is 10% of 10)
New area =8×9=72
Decrease in area
= original area - new area
=100−72=28
Percentage decrease in area
=decrease in area /original area×100
=28/100×100=28%
Answer: Option B
Answer: B
Question: Alfred started a business investing Rs. 45,000. After 3 months, Peter joined him with a capital of Rs. 60,000. After another 6 months, Ronald joined them with a capital of Rs. 90,000. At the end of the year, they made a profit of Rs. 16,500. Find the lire of each.
Options:
A)2300
B)3300
C)4300
D)1300
E)None of them
Rationale: Clearly, Alfred invested his capital for 12 months, Peter for 9 months and Ronald for 3 months.
So, ratio of their capitals = (45000 x 12) : (60000 x 9) : (90000 x 3)
= 540000 : 540000 : 270000 = 2 : 2 : 1.
Alfred's share = Rs. (16500 x (2/5)) = Rs. 6600
Peter's share = Rs. (16500 x (2/5)) = Rs. 6600
Ronald's share = Rs. (16500 x (1/5)) = Rs. 3300.
Answer is B.
Answer: B
Question: On a scale of map,0.6 cm represent 6.6 km.If the distance between the points on the map is 80.5 cm,the actual distance between these points is :
Options:
A)9 km
B)72.5 km
C)190.75 km
D)885.5 km
E)None of these
Rationale: Solution
Let the actual distance be x km.Then,
More distance on the map,More is the actual distance (Direct Proportion)
∴ 0.6 : 80.5 : : 6.6 : x ⇔ 0.6x = 80.5 × 6.6 ⇔ x = ⇔ x = 80.5x6.6/0.6=x=885.5. Answer D
Answer: D
Question: The security lock requires a five-digit lock code. If the lock code must consist only of digits from 1 through 6, inclusive, with no repeated digits, and the first and last digits of the code must be odd, how many lock codes are possible?
Options:
A)120
B)240
C)360
D)720
E)144
Rationale: X-X-X-X-X --> there are 3 odd digits from 1 to 6, inclusive thus options for the first and the last X's are: 3-X-X-X-2. Other X's can take following values: 3-4-3-2-2 --> 3*4*3*2*2=144.
Answer: E.
Answer: E
Question: Jamboree and GMAT Club Contest Starts
QUESTION #12:
How many words (with or without meaning) can be formed using all the letters of the word “SELFIE” so that the two E’s are not together?
Options:
A) 660
B) 600
C)400
D) 300
E) 240
Rationale: The question is asking the total number of arrangements possible with the letters of the word “SELFIE” where two E’s are not together.
Arrangements when two E’s are not together = Total arrangements - Arrangements when two E’s are together
In total there are 6 letters but two are identical. so we can arrange in 6! ways. but we divide for those objects that are identical. so divide by 2!. Hence,
Total arrangements = 6!/2!
Now two E's are coupled together. Consider this couple (EE) as one letter. apart from this there are 4 more letters. so we can arrange these 5 different objects in 5! ways.
Two E's can arrange themselves in 2! ways, but we divide for those objects that are identical. so divide by 2!. so arrangement for E's would be 2!/2!.
Hence, Arrangements when two E’s are together = 5! * (2!/2!)
Arrangements when two E’s are not together = 6!/2! - 5! = 5! * ( 6/2 -1 ) = 120 * 2 = 240.
Option C is correct!
Answer: C
Question: 23, 29, 31, 37, 41, 43, 47, 53, (...)
Options:
A)53
B)47
C)48
D)59
E)45
Rationale: Explanation :
All are prime numbers in their order, starting from 23
Hence, next number is 59
Answer : D
Answer: D
Question: If s and t are positive integers such that s/t = 58.32, which of the following could be the remainder when s is divided by t ?
Options:
A)22
B)42
C)18
D)40
E)45
Rationale: s/t= 58.32
s = 58.32t
s = (58 + 0.32)t
s = 58t + (32/100)t
s = 58t + (8/25)t
So remainder will be multiple of 8. The only multiple of 8 is 40.
Ans. D
Answer: D
Question: 2 men and 4 boys can complete a work in 4 days. 5 men and 6 boys can complete the same work in 3 days. The work done by 2 boys is equal to the work of how many men?
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: Exp: (2m + 4b)’s one day’s work = 1/4
(5m + 6b)’s one day’s work = 1/3
=> (8m + 16b)’s one day’s work = (15m + 18b) ’s one day’s work
=> 7 men’s work = 2 boy’s work
So, we should be employ 5 more men to be completed the work.
Answer: B
Answer: B
Question: A club wants to mix 10 pounds of candy worth $8.00 per pound with candy worth $5.00 per pound to reduce the cost of the mixture to $6.00 per pound. How many pounds of the $5.00 per pound candy should be used?
Options:
A)20
B)30
C)40
D)50
E)60
Rationale: Let number of pounds of 5$ candy to be used be w
6 = (10*8 + 5*w)/(10 +w)
=> 60 + 6w = 80 + 5w
=> w = 20
Answer A
Answer: A
Question: Six years ago, the ratio of ages of Kunal and Sagar was 6:5. Four years hence, the ratio of their ages will be 11:10. What is Sagar's age at present?
Options:
A)18
B)15
C)16
D)20
E)25
Rationale: [(6x + 6) + 4] / [(5x + 6) + 4] = 11/10
10(6x + 10) = 11(5x + 10) => x = 2
Sagar's present age = (5x + 6) = 16 years.
ANSWER C
Answer: C
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is:
Options:
A)230
B)244
C)245
D)238
E)236
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X = 245 m.
Answer: Option C
Answer: C
Question: Bill downloads the movieRevenge of the Avengersto his computer in 2.5 hours, using a download manager that downloads from 3 sources marked A, B and C. Each source provides download at a constant rate, but the rates of different sources are not necessarily identical. If the movie was downloaded from sources A and C alone, it would take 4 hours to complete the download. The next day, source B is available, but the other sources are inactive. How long will it take to download the trailer of the movie, a file that is 10 times smaller, from source B alone?
Options:
A)40 minutes
B)15 minutes
C)12 minutes
D)10 minutes
E)3 minutes
Rationale: Let the movie size be 400 u.
Given,A+C=4 hrs.
A+C=100 u/hr
And A+B+C=2.5 hrs or 400/2.5=160 u/hr
B alone=160-100=60 u/hr
Trailer=40 times smaller or400/10=40 u
B will take 40/60 hrs or 40 minutes.
Ans A
Answer: A
Question: A company has 3 directors and 5 managers. How many different committees with 5 people can be chosen having at least 1 director?
Options:
A)500
B)720
C)4500
D)25
E)55
Rationale: at least one means exactly one and more than one.
different committees with 5 people can be chosen having at least 1 director is
(3c1*5c4) + (3c2*5c3) + (3c3*5c2) = 55;
Hence E.
Answer: E
Question: The present age of a father is 3 years more than three times the age of his son.Three years hence,father as age will be 11 years more than twice the age of the son.Find the present age of the father.
Options:
A)36
B)77
C)33
D)44
E)55
Rationale: Explanation:
Let the present age be 'x' years. Then father's present age is 3x+3 years. Three years hence (3x+3)+3=2(x+3)+11 x=11 Hence father's present age = 3x+3 =[ (3 x 11) + 3] = 36 years.
Answer: A
Answer: A
Question: A starts a business with a capital of Rs. 85,000. B joins in the business with Rs.42500 after some time. For how much period does B join, if the profits at the end of the year are divided in the ratio of 3 : 1?
Options:
A)5 months
B)6 months
C)7 months
D)8 months
E)None of these
Rationale: Explanation :
Let B joins for x months. Then
A:B = 85000*12 : x* 42500 = 3 : 1
=> 850*12 : 425x= 3 : 1
=> 850*12/ 425x = 3/1 = 3
=> 850*4 /425x = 1
=> 2*4/x = 1
=> x = 8. Answer : Option D
Answer: D
Question: Which of the following expressions CANNOT be equal to 0 when x^2 − 8x = 15?
Options:
A)x^2 − 3x
B)x^2 − 3x -10
C)x^2 − 4x +5
D)x^2 − 4x - 5
E)x^2 − 2x - 3
Rationale: x^2 − 8x = 15
x^2 − 8x - 15= 0
x=3 or x=5
All other choices result in a possibility of 0 when you plug in 3 or 5 for x
Except x^2 − 4x +5
Answer is C
Answer: C
Question: Salad dressing P is made up of 30% vinegar and 70% oil, and salad dressing Q contains 10% vinegar and 90% oil. If the two dressings are combined to produce a salad dressing that is 18% vinegar, dressing P comprises what percentage of the new dressing?
Options:
A)20%
B)30%
C)40%
D)50%
E)60%
Rationale: Let x be the percentage of dressing P in the new dressing.
0.3x + 0.1(1-x) = 0.18
0.2x = 0.08
x = 0.4 = 40%
The answer is C.
Answer: C
Question: A man can row upstream at 20 kmph and downstream at 28 kmph, and then find the speed of the man in still water?
Options:
A)24
B)37
C)30
D)27
E)18
Rationale: US = 20
DS = 28
M = (28 + 20)/2 = 24
Answer:A
Answer: A
Question: Which among 2^1/2, 3^1/3, 4^1/4 , 6^1/6 and 12^1/12 is the largest ?
Options:
A)2^1/2
B)3^1/3
C)4^1/4
D)6^1/6
E)12^1/12
Rationale: 2^1/2, 3^1/3, 4^1/4 , 6^1/6 and 12^1/12
Multiply each number raised to the power of 12
So,
2^1/2 = 2^6 = 64
3^1/3 = 3^4 = 81
4^1/4 = 4^3 = 64
6^1/6 = 6^2 = 36
12^1/12 = 12^1 = 12
So, the greatest is 3^1/3
ANSWER:B
Answer: B
Question: Susan, John, Daisy, Tim and Kim need to be seated in 5 identical chairs in straight line so that Susan is seated always left to Tim. How many such arrangements are possible ?
Options:
A)360
B)120
C)80
D)240
E)60
Rationale: Total # of arrangement of 5 people is 5!.
In half of the cases Susan will be seated left to Tim and in half of the cases Susan will be seated right to Tim (why should one seating arrangement have more ways to occur than another?).
So, # of arrangements to satisfy the given condition is 5!/2=60.
Answer: E.
Answer: E
Question: If a / b is an integer, which of the following statements must be true?
Options:
A)q is an integer
B)a = nb where n is an integer
C)both a and b are integers
D)b / a is an integer
E)either a or b is negative
Rationale: Let a = 1/4; b = 1/8 --> a/b = 2
a = nb where n is an integer --> 1/4 = 2*(1/8) --> Correct
Answer: B
Answer: B
Question: Boy sells a book for Rs. 450 he gets a loss of 10%, find CP of the book?
Options:
A)Rs.350
B)Rs.400
C)Rs.500
D)Rs.550
E)Rs.620
Rationale: Find cost price
Let C.P. of book = x and S.P. = Rs. 450
S.P. of book = C.P. – (10% of C.P.)
S.P. = x – (0.10x)
450 = 0.9 x
x i.e cost price = Rs.500
C
Answer: C
Question: there are two kind of professional in a company software & personal. If the personal are 15% of the total .a party is going .in a party if 50% of the total professional left and all are software then what is the ratio of the software professional left to total software professional.
Options:
A)7:15
B)7:16
C)7:17
D)7:18
E)7:19
Rationale: let there are 100 professionals.
15 are personal 85 are software
in party 50% left means 50 professionals are there and all are software.
85-50=35 have gone then ratio
35:85
7:17
ANSWER:C
Answer: C
Question: The smallest number which when diminished by 7, is divisible 12, 16, 18, 21 and 28 is:
Options:
A)1008
B)1015
C)1022
D)1032
E)None of these
Rationale: EXPLANATION
Required number = (L.C.M. of 12,16, 18, 21, 28) + 7
= 1008 + 7
= 1015
Answer B
Answer: B
Question: A library branch originally contained 18365 volumes, 30% of which were fiction novels. 1/3 of the volumes were transferred to another location and 1/3 of the volumes transferred were fiction novels. What percent of the remaining collection was fiction novels?
Options:
A)2.5%
B)17.67%
C)28.3%
D)45.2%
E)73.6%
Rationale: Fiction Novels = 5,509
Transferred to another location = 6,121
Transferred fiction novels = 2,040
Non Transferred Fiction Novels = 3,469
Percent of the remaining collection was fiction novels = 3469/(18365 - 6121 ) * 100 => 28.332...%
Hence answer will be (C)
Answer: C
Question: A drink vendor has 40 liters of Maaza, 144 liters of Pepsi and 368 liters of Sprite. He wants to pack them in cans, so that each can contains the same number of liters of a drink, and doesn't want to mix any two drinks in a can. What is the least number of cans required?
Options:
A)35
B)37
C)42
D)50
E)69
Rationale: The number of liters in each can = HCF of 40, 144 and 368 = 8 liters.
Number of cans of Maaza = 40/8 = 5
Number of cans of Pepsi = 144/8 = 18
Number of cans of Sprite = 368/8 = 46
The total number of cans required = 5 + 18 + 46 = 69 cans.
ANSWER:E
Answer: E
Question: Find the third proportional to 4 and 16?
Options:
A)80
B)12
C)64
D)78
E)72
Rationale: Formula = Third proportional = (b × b)/a
A = 4 and B = 16
(16 × 16)/ 4 = 256/4 = 64
C
Answer: C
Question: A train 360 m long runs with a speed of 45 km/hr. What time will it take to pass a platform of 140 m long?
Options:
A)38 sec
B)35 sec
C)44 sec
D)40 sec
E)none of these
Rationale: Speed = 45 km/hr = 45 × (5/18) m/s
= 150/12 = 50/4 = 25/2 m/s
Total distance = length of the train + length of the platform
= 360 + 140 = 500 meter
Time taken to cross the platform = 500/(25/2) = 500 × 2/25 = 40 seconds
ANSWER:D
Answer: D
Question: A tank fills in the sequence of 10, 20, 40, 80.... (Means 10 litres in 1 hr, 20 litres in 2nd so on.). If at the 4th hour the tank is 1/4 full .When will it be full?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: At the 4th hour, it ll fill 80 litres
80 litres is 1/4th of a tank...then the full tank can have 80 * 4 = 320 litres
Given series 10, 20 ,40 ,80, (ie) each litre is double of previous litres
so at the 5th hour tank filled ll be 80 * 2 = 160liters
At the 6th hr it ll fill the full tank (ie) 160 * 2 = 320
So the tank ll be full at 6th hr
ANSWER:D
Answer: D
Question: A can do a piece of work in 24 days. When he had worked for 2 days B joins him. If the complete work was finished in 8 days. In how many days B alone can finish the work?
Options:
A)9
B)77
C)66
D)55
E)12
Rationale: 8/24 + 6/x = 1
X =9 days
Answer:A
Answer: A
Question: When tossing two coins once, what is the probability of heads on both the coins?
Options:
A)2/8
B)4/5
C)3/7
D)6/7
E)1/4
Rationale: Explanation :
Total number of outcomes possible when a coin is tossed = 2 (∵ Head or Tail)
Hence, total number of outcomes possible when two coins are tossed, n(S) = 2 × 2 = 4
E = event of getting heads on both the coins = {HH}
Hence, n(E) = 1
P(E)=n(E)/n(S)=1/4
Answer:E
Answer: E
Question: Whats the reminder when 54,879,856,985,421,547,895,689,874,525,826,547 is divided by 2
Options:
A)1
B)7.
C)2.
D)3
E)9
Rationale: A number ending in a 0 is divisible by 2.
Given the obscene number, you should immediately be convinced that you will need to focus on a very small part of it.
54,879,856,985,421,547,895,689,874,525,826,547 = 54,879,856,985,421,547,895,689,874,525,826,540+7
The first number is divisible by 16. You just have to find the remainder when you divide 5287 by 16. That will be the remainder when you divide the original number by 2.
7/16 gives remainder 1.
Answer (A)
Answer: A
Question: Two trains, one from Howrah to Patna and the other from Patna to Howrah, start simultaneously. After they meet, the trains reach their destinations after 9 hours and 16 hours respectively. The ratio of their speeds is?
Options:
A)4:7
B)4:3
C)4:11
D)4:9
E)4:13
Rationale: Let us name the trains A and B.
Then, (A's speed) : (B's speed)
= √b : √a = √16 : √9 = 4:3
Answer: B
Answer: B
Question: Twenty four years ago,a father was three times as old as his son.Now the father is only twice as old as his son. Then the sum of the present ages of the son and the father is :
Options:
A)144
B)76
C)108
D)105
E)86
Rationale: Let the present ages of the father and son be 2x and x years respectively.
then,(2x-24)=3 (x-24)
x=48.
Required sum =(2x+x)=3x=144 years.
Answer is A
Answer: A
Question: A shopkeeper buys mangoes at the rate of 5 a rupee and sells them at 3 a rupee. Find his net profit or loss percent?
Options:
A)66 1/4 %
B)66 9/3 %
C)66 2/3 %
D)66 1/5 %
E)66 1/3 %
Rationale: The total number of mangoes bought by the shopkeeper be 15.
If he buys 5 a rupee, his CP = 3
He selling at 3 a rupee, his SP = 5
Profit = SP - CP = 5 - 3 = 2
Profit Percent = 2/3 * 100 = 66 2/3 %
Answer:C
Answer: C
Question: In a theater, the first row has 14 seats and each row has 3 more seats than previous row. If the last row has 50 seats, what is the total number of seats in the theater?
Options:
A)404
B)408
C)412
D)416
E)420
Rationale: The number of seats in the theater is
14 + (14+3) + ...+ (14+36)=
13(14) + 3(1+2+...+12)=
13(14) + 3(12)(13)/2=
13(14+18) = 13(32) = 416
The answer is D.
Answer: D
Question: Solution A is 10% salt and Solution B is 80% salt. If you have 30 ounces of solution A and 60 ounces of solution B, in what ratio could you mix Solution A with Solution B to produce 50 ounces of a 50% salt solution?
Options:
A)6:4
B)6:14
C)3:4
D)4:6
E)3:7
Rationale: Forget the volumes for the time being.
You have to mix 20% and 80% solutions to get 50%. This is very straight forward since 50 is int he middle of 20 and 80 so we need both solutions in equal quantities. If this doesn't strike, use
w1/w2 = (A2 - Aavg)/(Aavg - A1)
w1/w2 = (80 - 50)/(50 - 10) = 3/4
So the volume of the two solutions will be equal. Answer has to be 3:4.
C
Answer: C
Question: Five percent of a certain grass seed is timothy. If the amount of the mixture needed to plant one acre contains 2 pounds of timothy, how many acres can be planted with 640 pounds of the seed mixture?
Options:
A)12
B)16
C)20
D)24
E)120
Rationale: If the mixture contains 2 pounds of timothy, the mixture must be 40 pounds.
Thus we need 40 pounds of mixture per acre.
640 / 40 = 16 acres
The answer is B.
Answer: B
Question: Which of the following fractions E has a decimal equivalent that is a terminating decimal?
Options:
A)10/189
B)15/196
C)16/225
D)25/144
E)39/128
Rationale: The fraction E will terminate if and only if the denominator has prime divisors only 2 and 5 or both.
A. 10/189 = 10/(3*3*3*7) Non-term.
B. 15/196 = 15/(2*2*7*7) Non-term.
C. 16/225 = 16/(5*5*3*3) Non-term.
D. 25/144 = 25/(2*2*2*7) Non-term.
E. 39/128 = 39/(2^7) Terminatingbecause only 2 in denominator.
Answer: E
Question: Claudia can choose any two of four different candles and any 8 of 9 different flowers for a centerpiece arrangement. Given these choices, how many candle + flower groupings can she select?
Options:
A)54
B)72
C)96
D)144
E)432
Rationale: 2 candles from 4 candles: 4C2: 6
8 flowers from 9 flowers: 9C8 : 9
So total grouping
9*6= 54.
Answer is A.
Answer: A
Question: A dealer purchases 15 articles for Rs. 25 and sells 12 articles for Rs. 30. Find the profit percentage?
Options:
A)58%
B)50%
C)20%
D)30%
E)70%
Rationale: L.C.M of 15 and 12 = 60
CP of 60 articles = Rs. 100 (25 * 4)
SP of 60 articles = Rs. 150 (30 * 5)
Profit percentage = (150 - 100)/100 * 100 = 50%
Answer:B
Answer: B
Question: Pipes A and B can fill a cistern in 8 and 24 minutes respectively. They are opened an alternate minutes. Find how many minutes, the cistern shall be full?
Options:
A)12 min
B)6 min
C)4 min
D)8 min
E)10 min
Rationale: 1/8 + 1/24 = 1/6
6 * 2 = 12
ANSWER A
Answer: A
Question: The average of 11 results is 60. If the average of first six results is 58 and that of the last six is 63, find the sixth result.
Options:
A)22
B)44
C)66
D)72
E)NOne
Rationale: Sol.
Sixth result = (58 x 6 + 63 x 6 - 60 x 11) = 6
Answer C
Answer: C