divelab/Sys2Bench huggingface dataset:
Question: In how many ways can the letters of the word REGULATION be arranged such that all the vowels always appear together?
Options:
A)10!*5!
B)10!*6!
C)10!
D)6!*5!
E)5!*5!
Rationale: The 10 letters can be grouped into 5 consonants and one set of 5 vowels.
The number of ways to arrange 6 units is 6!
Then, for each arrangement, the 5 vowels can be arranged in 5! ways.
The total number of arrangements is 6!*5!
The answer is D.
Answer: D
Question: Each digit 1 through 5 is used exactly once to create a 5-digit integer. If the 3 and the24 cannot be adjacent digits in the integer, how many 5-digit integers are possible?
Options:
A) 48
B) 72
C) 76
D) 78
E) 90
Rationale: Number of arrangements using 5 distinct digits = 5!
Number of arrangements in which 3 and 4 are adjacent - consider 3 and 2 together as one group. Now you have 4 numbers/groups to arrange which can be done in 4! ways. In each of these arrangements, 3 and 2 can be arranged as 32 or 23.
Number of arrangements in which 3 and 4 are not adjacent = 5! - 2*4! = 72
Answer : B
Answer: B
Question: A girl has exactly 6 quarters, 8 dimes, and 10 nickels in her pocket. If she withdraws a number of these coins at random, how many coins would she have to withdraw to ensure that she has at least a 50 percent chance of withdrawing at least one quarter?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: When the probability of NOT drawing a quarter is 50% or less, then the probability of drawing a quarter is at least 50%.
P(not drawing a quarter with 2 coins) = 18/24 * 17/23 = 51/92 > 50%
P(not drawing a quarter with 3 coins) = 51/92 * 16/22 = 102/253 < 50%
The answer is C.
Answer: C
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:
Options:
A)20 years
B)30 years
C)60 years
D)40 years
E)35 years
Rationale: D
40 years
Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years = 90 years.
Sum of the present ages of wife and child = (20 x 2 + 5 x 2) years = 50 years.
Husband's present age = (90 - 50) years = 40 years.
Answer: D
Question: Two trains of equal lengths are running at speeds of 30 kmph and 60 kmph. The two trains crossed each other in 30 seconds when travelling in opposite direction. In what time will they cross each other when travelling in the same direction?
Options:
A)90
B)82
C)16
D)67
E)12
Rationale: Let the length of each train be x m.
(x + x) / (60 + 30)5/18 = (750 * 18) / (30 * 5)
= 90 sec.
Answer: A
Answer: A
Question: It is well known that a triangle’s area is √(p(p-a)(p-b)(p-c)),
when p=(a+b+c)/2, such that a, b, c are the lengths of sides of the triangle. If the triangle has 300, 300, and 360 as the side’s lengths, what is the triangle’s area?
Options:
A)34,200
B)36,200
C)43,200
D)42,200
E)38,200
Rationale: It is well known that a triangle’s area is √(p(p-a)(p-b)(p-c)),
when p=(a+b+c)/2,
-> P=(300+300+360)/2=480, area=√(480(480-300)(480-300)(480-360))=43,200. Therefore, the answer is C.
Answer: C
Question: My brother is 3 years elder to me.My father was 28 years of age when my sister was born while my mother was 26 years of age when I was born.If my sister was 4 years of age when my brother was born,then,what was the age of my father and mother respectively when my brother was born ?
Options:
A)32 yrs,23 yrs
B)32 yrs,29 yrs
C)35 yrs,29 yrs
D)35 yrs,33 yrs
E)None of these
Rationale: Solution
Clealy,my brother was born 3 years before I was born and 4 years after my sister was born.
So,father's age when brother was born =(28+4) years =32 years,
mother's age when brother was born =(26-3) years =23 years . Answer A
Answer: A
Question: Club X has more than 50 but fewer than 80 members. Sometimes the members sit at tables with 3 members at one table and 4 members at each of the other tables, and sometimes they sit at tables with 3 members at one table and 5 members at each of the other tables. If they sit at tables with 6 members at each table except one and fewer than 6 members at that one table, how many members will be at the table that has fewer than 6 members?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: The number of members is 4j+3 = 5k+3.
Let's start at 4(12)+3 = 51 and keep adding 4 until we find a number in the form 5k+3.
51, 55, 59, 63 = 5(12) + 3
The club has 63 members.
63/6 = 6(10) + 3
The answer is C.
Answer: C
Question: What is the smallest positive integer x, such that 7000x is a perfect cube?
Options:
A)4
B)6
C)8
D)12
E)18
Rationale: Take out the factors of 7000x that will come 10^3*7. for perfect cube you need every no. raise to the power 3. for 7000x to be a perfect cube, need two 7 that means 49.
E is the answer.
Answer: D
Question: A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?
Options:
A)79.5
B)39.5
C)79.9
D)79.2
E)79.1
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 264)/20 = y
y = 22
Speed = 22 m/sec = 22 * 18/5 = 79.2 km/hr.
Answer:D
Answer: D
Question: In a college 1/5th of the girls and 1/8th of the boys took part in a social camp. What of the total number of student in the college took part in the camp ?
Options:
A)13/40
B)13/80
C)2/13
D)Data inadequate
E)None
Rationale: Answer
Out of the 5 girls, 1 took part in the camp. Out of the 8 boys, 1 took part in the camp.
∴ 2/13 of total number of students took part in the camp.
Correct Option: C
Answer: C
Question: A farming field can be ploughed by 6 tractors in 4 days. When 6 tractors work together, each of them ploughs 120 hectares a day. If two of the tractors were moved to another field, then the remaining 4 tractors could plough the same field in 5 days. How many hectares a day would one tractor plough then?
Options:
A)144
B)255
C)148
D)265
E)320
Rationale: If each of 66 tractors ploughed 120120 hectares a day and they finished the work in 44 days, then the whole field is: 120⋅6⋅4=720⋅4=2880120⋅6⋅4=720⋅4=2880 hectares. Let's suppose that each of the four tractors ploughed xx hectares a day. Therefore in 5 days they ploughed
5⋅4⋅x=20⋅x5⋅4⋅x=20⋅x hectares, which equals the area of the whole field, 2880 hectares.
So, we get 20x=288020x=2880
x=288020=144x=288020=144. Hence, each of the four tractors would plough 144 hectares a day.
correct answer is A)144
Answer: A
Question: Using all the letters of the word "NOKIA", how many words can be formed, which begin with N and end with A?
Options:
A)7
B)6
C)8
D)9
E)3
Rationale: There are five letters in the given word.
Consider 5 blanks ....
The first blank and last blank must be filled with N and A all the remaining three blanks can be filled with the remaining 3 letters in 3! ways.
The number of words = 3! = 6.
Answer:B
Answer: B
Question: Water consists of hydrogen and oxygen, and the approximate ratio, by mass, of hydrogen to oxygen is 2:16. Approximately how many grams of oxygen are there in 153 grams of water?
Options:
A) 16
B) 72
C) 112
D) 136
E) 142
Rationale: Since the ratio, by mass, of hydrogen to oxygen is 2:16, then oxygen is 16/(2+16)=8/9 of mass of water.
Therefore there are 153*8/9=136 grams of oxygen in 153 grams of water.
Answer: D.
Answer: D
Question: In a 240 meters race A beats B by 56 m or 7 seconds. A's time over the course is:
Options:
A)23 seconds
B)12 seconds
C)10 seconds
D)18 seconds
E)28 seconds
Rationale: B runs 56 m in 7 sec.
=> B runs 240 m in 7/56*240 = 30 seconds
Since A beats B by 7 seconds, A runs 240 m in (30-7) = 23 seconds
Hence, A's time over the course = 23 seconds
ANSWER:A
Answer: A
Question: a and b are positive integers less than or equal to 6. If a and b are assembled into the six-digit number ababab, which of the following must be a factor of ababab?
Options:
A)3
B)4
C)5
D)2
E)none of the above
Rationale: 242424 when divided by 2 gives the result 121212
CONCEPT: Rule of Divisibility of 2 isIf sum of the digits of the Number is divisible by 2 then the number will be divisible by 2
SUm of the digits of No. which is divisible by 2 hence the Number 242424 will be divisible by 2
D
Answer: D
Question: A watch which gains uniformly is 2 minutes low at noon on Monday and is 4 min. 48 sec fast at 2 p.m. on the following Monday. When was it correct?
Options:
A)2 p.m. on Tuesday
B)7 p.m. on Tuesday
C)8 p.m. on Tuesday
D)5 p.m. on Tuesday
E)1 p.m. on Tuesday
Rationale: 2 minutes slow at monday noon.
4 min 48 sec fast at 2 pm next monday.
It ran faster than normal time by 6 min 48 secs = 408 sec in 7 days 2 hours = 170 hours.
It was correct when it advanced 120 seconds than normal time.
The clock gains 408 seconds in 170 hours.
The clock gains 1 second in 170/408 hours
The clock gains 120 seconds in 170408×120170408×120 hours = 50 hours = 2 days 2 hours.
So the clock shows correct time on Wednesday 2 pm..
Answer:A
Answer: A
Question: By selling 12 toffees for a rupee, a man loses 20%. How many for a rupee should be sell to get a gain of 20%?
Options:
A)2
B)8
C)9
D)7
E)6
Rationale: Explanation:
Let S.P. of 12 toffees be Rs. x.
Then, 80:1 = 120:x or x = 120/180 = 3/2
For Rs. 3/2, toffees sold = 12.
For Re. 1, toffees sold = 12 * 2/3 = 8
Answer:B
Answer: B
Question: Four extra-large sandwiches of exactly the same size were ordered for m students, where m > 6. Three of the sandwiches were evenly divided among the students. Since 4 students did not want any of the fourth sandwich, it was evenly divided among the remaining students. If Carol ate one piece from each of the four sandwiches, the amount of sandwich that she ate would be what fraction of a whole extra-large sandwich?
Options:
A)(4m-15)/[m(m-5)]
B)(4m-15)/[m(m-8)]
C)(4m-18)/[m(m-5)]
D)(4m-20)/[m(m-5)]
E)(5m-15)/[m(m-5)]
Rationale: Three of the sandwiches were evenly divided among the students
i.e. Amount of Sandwiches with each students = 3/m
Amount of 4th Sandwich with remaining (m-6) students = 1/(m-6)
The amount of Sandwich that carol ate = 3/m + 1/(m-6) = (3m-18+m)/[m(m-5)] = (4m-15)/[m(m-5)]
Answer: A
Answer: A
Question: In one alloy there is 12% chromium while in another alloy it is 8%. 15 kg of the first alloy was melted together with 40 kg of the second one to form a third alloy. Find the percentage of chromium in the new alloy.
Options:
A)8.8%
B)9%
C)9.2%
D)9.1%
E)8.4%
Rationale: The amount of chromium in the new 15+40=55 kg alloy is 0.12*15+0.08*40=5 kg, so the percentage is 5/55*100=9.1%.
Answer: D.
Answer: D
Question: The cost price of an article is 64% of the marked price. Calculate the gain percent after allowing a discount of 12%?
Options:
A)37.5%
B)37.6%
C)38.5%
D)17.5%
E)37.2%
Rationale: Let marked price = Rs. 100.
Then, C.P. = RS. 64, S.P. = Rs. 88
Gain % = 24/64 * 100 = 37.5%.
Answer: A
Answer: A
Question: Running at the same constant rate, 5 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?
Options:
A) 648
B) 1,800
C) 2,160
D) 10,800
E) 64,800
Rationale: 5 machines produce 270 bottles per minute;
1 machine produces 270/5=54 bottles per minute;
10 machines produce 54*10=540 bottles per minute;
In 4 minutes 10 machines produce 540*4=2,160 bottles.
Answer: C.
Answer: C
Question: A man saves a certain portion of his income during a year and spends the remaining portion on his personal expenses. Next year his income increases by 35% but his savings increase by 100%. If his total expenditure in 2 years is double his expenditure in 1st year, What %age of his income in the first year did he save?
Options:
A)25%
B)28%
C)30%
D)32.5%
E)35%
Rationale: 1st year Income= I
1st year savings= S
1st year Expense= E1
2nd year Income = 1.35I
2nd year savings= 2S (100% increase)
2nd Year expense= E2
E1+ E2= 2E1
E2=E1
That means Expenses are same during both years. With increase of 35% income the savings increased by 100%.
or S= .35I
or S= 35% of Income
E is the answer
Answer: E
Question: An empty wooden vessel weighs 14% of its total weight when filled with paint. If the weight of a partially filled vessel is one half that of a completely filled vessel, what fraction of the vessel is filled.
Options:
A)6/13
B)5/9
C)1/24
D)4/9
E)2/5
Rationale: An empty wooden vessel weighs 14% of its total weight when filled with paint:
Vessel = 0.14(Vessel + Paint);
14V = V + P (so the weight of completely filled vessel is 14V)
P = 13V (so the weight of the paint when the vessels is completely filled is 13V).
The weight of a partially filled vessel is one half that of a completely filled vessel:
V + P' = 1/2*14V;
P' = 6V (so the weight of the paint when the vessels is partially filled is 6V).
What fraction of the vessel is filled?
So, we need to find the ratio of the weight of the paint when the vessel iscompletely filledto the weight of the paint when the vessel ispartially filled:
P'/P = 6V/13V = 6/13.
Answer: A.
Answer: A
Question: 2 numbers are there in the ratio 3:4. If 3 is to be added to both of the numbers the ratio will become 7:9 then find initial numbers?
Options:
A)18,24
B)15,12
C)3,2
D)21,22
E)40,12
Rationale: Let 2 numbers are 3x,4x
after adding 3 on both numbers 3x+3, 4x+3
3x+3:4x+3 = 7:9
9(3x+3) = 7(4x+3)
x = 6
Intial numbers = 3x,4x = 18,24
Answer is A
Answer: A
Question: Two trains of equal lengths take 10 sec and 14 sec respectively to cross a telegraph post. If the length of each train be 120 m, in what time will they cross other travelling in opposite direction?
Options:
A)10
B)12
C)13
D)11.7
E)15
Rationale: Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/14 = 8.6 m/sec.
Relative speed = 12 + 8.6 = 20.6 m/sec.
Required time = (120 + 120)/20.6 = 11.7 sec.
Answer: Option D
Answer: D
Question: In a zoo, the ratio of the number of cheetahs to the number of pandas is 1 : 3 and was the same five years ago. If the increase in the number of cheetahs in the zoo since then is 6, then what is the increase in the number of pandas?
Options:
A) 18
B) 3
C) 5
D) 10
E) 15
Rationale: One short cut to solve the problem is
c:p = 1:3
c increased to 7
=> 1:3 = 7:x
=> x = 21
=>p increased by 18
A is the answer
Answer: A
Question: A watch which gains uniformly is 2 minutes low at noon on Monday and is 4 min. 48 sec. fast at 2 p.m. on the following Monday. When was it correct?
Options:
A)2 p.m. on Tuesday
B)2 p.m. on Wednesday
C)3 p.m. on Thursday
D)1 p.m. on Friday
E)None of these
Rationale: Time from 12 p.m. on Monday to 2 p.m. on the following Monday = 7 days 2 hours = 170 hours.
∴ The watch gains (2 + 44⁄5) min.
or 34⁄5 min. in 170 hrs.
Now, 34⁄5 min. are gained in 170 hrs.
∴ 2 min. are gained in (170 × 5⁄34 × 2)hrs. = 50 hrs
∴ Watch is correct 2 days 2 hrs. after 12 p.m. on Monday i.e. it will be correct at 2 p.m. on Wednesday.
Answer B
Answer: B
Question: Seven machines at a certain factory operate at the same constant rate. If six of these machines, operating simultaneously, take 35 hours to fill a certain production order, how many fewer hours does it take all seven machines, operating simultaneously, to fill the same production order?
Options:
A)4
B)5
C)7
D)10
E)12
Rationale: The total work is 6*35 = 210 machine hours
The time required for seven machines is 210/7 = 30 hours, thus 5 fewer hours.
The answer is B.
Answer: B
Question: A student got twice as many sums wrong as he got right. If he attempted 75 sums in all, how many did he solve correctly ?
Options:
A)25
B)16
C)18
D)24
E)26
Rationale: Explanation:
Suppose the boy got x sums right and 2x sums wrong.
Then, x + 2x = 75 3x = 75 x = 25.
Answer:A
Answer: A
Question: A does a work in 10 days and B does the same work in 30 days. In how many days they together will do the same work ?
Options:
A)5.5 days
B)6.5 days
C)7.5 days
D)8.5 days
E)None of these
Rationale: Explanation:
Firstly we will find 1 day work of both A and B, then by adding we can get collective days for them,
So,
A's 1 day work = 1/10
B's 1 day work = 1/30
(A+B)'s 1 day work =
(1/10+1/30)=2/15
So together they can complete work in 7.5 days.
Answer: C
Answer: C
Question: Winners will be announced the following day at 9 AM Pacific/1 PM Eastern Time.
If A, X, Y, and Z are unique nonzero digits in the equation:
XY
*YX
____
AYZ
And Y > X, the 2-digit number XY = ?
Options:
A)13
B)21
C)23
D)24
E)25
Rationale: The reasoning is as follows:-
B) can't be answer because Y<X
D) can't be answer because it XY x YX will give 4 digit number. Thus wrong
E) can't be answer because it XY x YX will give 4 digit number. Thus wrong
A) can't be answer because it XY x YX will give 3 digit number but the middle digit will not be equal to Y. Thus wrong
C) is the correct answer because Y>xwill give 3 digit numbermiddle digit is Y
A
Answer: A
Question: The distance from City A to City B is 180 miles. While driving from City A to City B, Ed drives at a constant speed of 30 miles per hour. Flora leaves City A 2 hours after Ed. What is the minimum constant speed in miles per hour that Flora must exceed in order to arrive in City B before Ed?
Options:
A)35
B)40
C)45
D)50
E)55
Rationale: The time it takes Ed to drive to City B is 180 / 30 = 6 hours.
Flora needs to take less than 4 hours for the trip.
Flora needs to exceed a constant speed of 180 / 4 = 45 miles per hour.
The answer is C.
Answer: C
Question: Find the circumference and area of radius 4 cm.
Options:
A)24 cm²
B)44 cm²
C)50 cm²
D)84 cm²
E)94 cm²
Rationale: Area of circle = πr²
= 22/7 × 4 × 4 cm²
= 50 cm²
ANSWER:C
Answer: C
Question: If A:B = 1/2: 1/3 B:C = 1/2:1/3 then A:B:C?
Options:
A)2:4:5
B)1:2:7
C)9:6:4
D)3:6:9
E)None
Rationale: Answer: Option C
A:B = 1/2:1/3 = 3:2
B:C = 1/2:1/3 = 3:2
A:B:C = 9:6:4
Answer: C
Question: A bookseller sells his books at a 25% markup in price. If he sells a book for $12.5, how much did he pay for it?
Options:
A)$14.40
B)$14.00
C)$11.00
D)$9.60
E)$10.00
Rationale: Let the cost price of book = x
Selling price of book = 12.5$
Markup % = 25
(125/100)x = 12.5
=> x = 10
Answer E
Answer: E
Question: Raman mixed 44 kg of butter at Rs. 150 per kg with 36 kg butter at the rate of Rs. 125 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction?
Options:
A)129.25
B)287.25
C)194.25
D)188.25
E)112.25
Rationale: Explanation:
CP per kg of mixture = [44(150) + 36(125)]/(44 + 36) = Rs. 138.75
SP = CP[(100 + profit%)/100]
= 138.75 * [(100 + 40)/100] = Rs. 194.25
Answer:C
Answer: C
Question: A contractor hires 100 men to finish a job in 50 days. After 36 days, n men leave. After some more days, the contractor hires 2n more men to complete the job on time. For how many days did these 2n men work?
Options:
A)20
B)18
C)16
D)12
E)7
Rationale: Step1: Find Each day what % of work is finished ; it requires 50 days to complete which means each day 1/50= 2% work will be completed.
Step 2 : After 36 Days = 36* 2= 72% of work is finished. remaining is 28% ( which means if same 100 men were about to complete the job they would have required 14 more days)
Step3: Let us assume all people have left job. therefore contractor hires 2n people. initially it was taking 14 days to compete for n people. at present 2n people are present to finish job. hence 7 more days.
E
Answer: E
Question: One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is a face card?
Options:
A)1/13
B)4/13
C)1/4
D)9/52
E)None
Rationale: Solution
Clearly, there are 52 cards, out of which there are 16 faces cards.
Therefore, P(getting a face card)
= 16/52
‹=›4/13.
Answer B
Answer: B
Question: Two pens and one eraser cost Rs. 35 and 3 pencil and four erasers cost Rs. 65. Find the cost of pencil and eraser separately.
Options:
A)5,15
B)15,5
C)5,10
D)10,5
E)20,5
Rationale: Let pen be x and eraser be y
Then 2x + y = 35 ……………(i)
And 3x + 4y = 65 ……………(ii)
Multiplying equation (i) by 4, and subtracting we get
5x = 75
x = 15
Substituting the value of x = 15 in equation (i) 2x + y = 35 we get;
2 × 15 + y = 35
30 + y = 35
y = 35 – 30
y = 5
Therefore, the cost of 1 pen is Rs. 15 and the cost of 1 eraser is Rs. 5. correct ans is B
Answer: B
Question: What is the decimal equivalent of (1/4)^5?
Options:
A)0.0016
B)0.0625
C)0.0001
D)0.25
E)0.5
Rationale: (1/4)^5 = 1/1024 =0.0001
Answer : C
Answer: C
Question: A sells his house to B at a profit of 10% who in turn sells it to C at a profit of 15% who in turn Sells it to D at a profit of 25% and D sells it to E at 35% profit. If cost price of E’s house is Rs 35,00,000, what is the approximate cost price of A’s house?
Correct Show Answer
Explanation:
Options:
A)Rs 15,40,000
B)Rs 15,10,000
C)Rs 15,00,000
D)Rs 16,40,000
E)Rs 17,40,000
Rationale: Let the cost price of A’s house = Rs X
Therefore, Cost price of E’s house
= 1.1 x 1.15 x 1.25 x 1.35 x X
Therefore, 3500000 = 1.1 x 1.15 x 1.25 x 1.35 x X
X = 3500000 / 1.1 x 1.15 x 1.25 x 1.35
= Rs 16,39,584.25
The nearest option is Rs 16,40,000.
ANSWER:D
Answer: D
Question: If the area of a circle is 64pi square feet, find its circumference.
Options:
A)65 pi feet
B)43 pi feet
C)42 pi feet
D)18 pi feet
E)16 pi feet
Rationale: The area is given by pi * r * r. Hence
pi * r *r = 64 pi
r *r = 64 ; hence r = 8 feet
The circumference is given by
2 *pi *r = 2 * pi * 8 = 16 pi feet
correct answer E
Answer: E
Question: If nn is a positive integer and (n+1)(n+3)(n+1)(n+3) is odd, then (n+2)(n+4)(n+2)(n+4) must be a multiple of which one of the following?
Options:
A)1
B)3
C)4
D)8
E)6
Rationale: (n+1)(n+3)(n+1)(n+3) is odd only when both (n+1)(n+1) and (n+3)(n+3) are odd. This is possible only when nn is even.
Hence, n=2mn=2m, where mm is a positive integer. Then,
(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)(n+2)(n+4)=(2m+2)(2m+4)=2(m+1)2(m+2)=4(m+1)(m+2)
=4 * (product of two consecutive positive integers, one which must be even)=4 * (product of two consecutive positive integers, one which must be even) =4 * (an even number), and this equals a number that is at least a multiple of 8=4 * (an even number), and this equals a number that is at least a multiple of 8
Hence, the answer is (D).
Answer: D
Question: The average age of a husband and his wife was 23 years at the time of their marriage. After five years they have a one-year old child. The average age of the family now is
Options:
A)76 years
B)11 years
C)19 years
D)15 years
E)12 years
Rationale: Explanation:
Sum of the present ages of husband, wife and child = (23 * 2 + 5 * 2) + 1 = 57 years.
Required average = (57/3) = 19 years.
Answer: C
Answer: C
Question: If 5/(4 + 1/x) = 1, then x =
Options:
A)3
B)1
C)1/3
D)-1/3
E)-3
Rationale: The expression 5/(4 + 1/x) = 1 should have been equal to something .
If 5/(4 + 1/x) = 1
=>5x/(4x + 1 ) = 1
=> 5x = 4x + 1
=> x = 1
Correct Option : B
Answer: B
Question: Find the next number in the series ?
2 3/4 5/7 7/10 11/13 13/16 ?
Options:
A)18/20
B)17/16
C)18/40
D)17/19
E)11/29
Rationale: D
17/19
series is 2/1 3/4 5/7 7/10 11/13 13/16
Numerator is prime number series 2-3-5-7-11-13-17
and Denominator is +3 series 1-4-7-10-13-16-19
Answer: D
Question: A tank is filled in 5 hours by three pipes A, B and C. The pipe C is twice as fast as B and B is twice as fast as A. How much time will pipe A alone take to fill the tank?
Options:
A)35
B)88
C)25
D)99
E)21
Rationale: Suppose pipe A alone takes x hours to fill the tank.
Then, pipes B and C will take x/2 and x/4 hours respectively to fill the tank.
1/x + 2/x + 4/x = 1/5
7/x = 1/5 => x = 35 hrs.
Answer: A
Answer: A
Question: The diluted wine contains only 8 liters of wine and the rest is water. A new mixture whose concentration is 30%, is to be formed by replacing wine. How many liters of mixture shall be replaced with pure wine if there was initially 32 liters of water in the mixture?
Options:
A)2
B)5
C)6
D)7
E)8
Rationale: Explanation:
Wine Water
8L 32L
1 : 4
20 % 80% (original ratio)
30 % 70% (required ratio)
In ths case, the percentage of water being reduced when the mixture is being replaced with wine.
so the ratio of left quantity to the initial quantity is 7:8
Therefore , \frac{7}{8}=\left [ 1-\frac{K}{40} \right ]
\Rightarrow \frac{7}{8}=\left [ \frac{40-K}{40} \right ] \Rightarrow K= 5 l
Answer: B) 5
Answer: B