divelab/Sys2Bench huggingface dataset:
Question: The average age of husband, wife and their child 3 years ago was 26 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is
Options:
A)22
B)40
C)38
D)21
E)37
Rationale: Explanation:
Sum of the present ages of husband, wife and child = (26 x 3 + 3 x 3) years = 87 years.
Sum of the present ages of wife and child (20 x 2 + 5 x 2) years = 50 years.
Husband's present age = (87 - 50) years = 37 years.
Answer: E
Answer: E
Question: The percentage increase in the area of a rectangle, if each of its sides is increased by 20% is
Options:
A)38%
B)40%
C)44%
D)48%
E)50%
Rationale: Let original length = x metres and original breadth = y metres.
Original area = (xy) m2.
New length = 120 x m = 6 x m.
100 5
New breadth = 120 y m = 6 y m.
100 5
New Area = 6 x x 6 y m2 = 36 xy m2.
5 5 25
The difference between the original area = xy and new-area 36/25 xy is
= (36/25)xy - xy
= xy(36/25 - 1)
= xy(11/25) or (11/25)xy
Increase % = 11 xy x 1 x 100 % = 44%.
25 xy
C)
Answer: C
Question: The average (arithmetic mean) of the even integers from 0 to 40 inclusive is how much greater than the average (arithmetic mean) of the even integers from 0 to 20 inclusive?
Options:
A)10
B)20
C)5
D)30
E)15
Rationale: So, according to A mean of a set of even numbers from 0 to 40 =(0+40)/2=20 and mean of a set of even numbers from 0 to 20 =(0+20)/2=10
Difference=20-10=10
Answer: A.
Answer: A
Question: A can do a piece of work in 4 hours; B and C together can do it in 3 hours, which A and C together can do it in 2 hours. How long will B alone take to do it?
Options:
A)15 hours
B)14 hours
C)12 hours
D)74 hours
E)79 hours
Rationale: A's 1 hour work = 1/4;
(B + C)'s 1 hour work = 1/3;
(A + C)'s 1 hour work = 1/2
(A + B + C)'s 1 hour work = (1/4 + 1/3) = 7/12
B's 1 hour work = (7/12 + 1/2) = 1/12
B alone will take 12 hours to do the work.
Answer:C
Answer: C
Question: A tyre has two punctures. The first puncture alone would have made the tyre flat in 9 minutes and the second alone would have done it in 4 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat ?
Options:
A)3 1/5min
B)2 10/13min
C)3 3/5min
D)3 4/5min
E)3 min
Rationale: Explanation:
Do not be confused, Take this question same as that of work done question's. Like work done by 1st puncture in 1 minute and by second in 1 minute.
Lets Solve it:
1 minute work done by both the punctures =
(1/9+1/4)=(13/36)
So both punctures will make the type flat in
(36/13)mins=2 10/13mins
Option B
Answer: B
Question: A man can swim in still water at 9 km/h, but takes twice as long to swim upstream than downstream. The speed of the stream is?
Options:
A)1.7
B)1.4
C)3
D)1.5
E)1.9
Rationale: M = 9
S = x
DS = 9+ x
US = 9 + x
9 + x = (9 - x)2
9+ x = 18 -2x
3x = 9
x = 3
Answer:C
Answer: C
Question: If 5x^2 has two different prime factors, at most how many different prime factors does x have?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: x cannot have more than 2 prime factors, because in this case 5x^2 would also have more than 2 prime factors.
Can x have 2 prime factors? Yes, consider x=2*5=10 (in this case 5x^2 still has 2 prime factors).
Answer: B.
Answer: B
Question: How many different ways can you select a pilot and a co pilot if you have 30 people to choose from?
Options:
A) 199
B) 200
C) 398
D) 4950
E) 870
Rationale: You are not just choosing two from 30. Each of the two people chosen fills a particular slot. The first filling the pilot slot and the second filling the copilot slot is different from the first filling the copilot slot and the second filling the pilot slot.
So the answer is in a sense (30C2) x 2 = 870E
Answer: E
Question: A big container is 30% full with water. If 27 liters of water is added, the container becomes 3/4 full. What is the capacity of the big container?
Options:
A)36 liters
B)40 liters
C)45 liters
D)54 liters
E)60 liters
Rationale: A big container is 30% full with water and after 27 liters of water is added, the container becomes 75% full. Hence these 27 liters account for 45% of the container, which means that the capacity of it is 27/0.45=60 liters.
OR: if the capacity of the container is x liters then: 0.3x+27=0.75x --> x=60 liters.
Answer: E.
Answer: E
Question: A person bought a certain quantity of rice at the rate of Rs. 150/quintal. 10% of the rice was spoiled. At what rate(per quintal) should he sell the remaining rice to earn 20% profit.
Options:
A)Rs. 180
B)Rs. 200
C)Rs. 210
D)Rs. 220
E)NONE
Rationale: Solution: Suppose he buy 1 quintal of Rice in Rs.150.
10% is spoiled so he now have to sell of 90 kg remaining)
.But he has to make a profit of 20%,so he will sell
90kg for Rs. 180
This means his selling price is Rs. 200 per quintal.
Answer: Option B
Answer: B
Question: By selling an article at Rs.800, a shopkeeper makes a profit of 25%. At what price should he sell the article so as to make a loss of 30%?
Options:
A)448
B)480
C)267
D)288
E)276
Rationale: SP = 800
Profit = 25%
CP = (SP)*[100/(100+P)]
= 800 * [100/125]
= 640
Loss = 25% = 25% of 640 = Rs.192
SP = CP - Loss = 640 - 192 = Rs.448
Answer: A
Answer: A
Question: If 7log(4*5^2) = x, find x
Options:
A)12
B)11
C)10
D)14
E)13
Rationale: 7(log2^2*5^2)=x
7log(5*2)^2=x
7*2log(5*2)=x
14log10=x
log10 base 10=1
so
14*1=x
x=14
ANSWER:D
Answer: D
Question: There is 2/5 chance it will rain today.
There is a probability of 1/2 I will find the love of my life today.
What is the probability I will find the love of my life in the rain today?
Options:
A)2/5
B)3/5
C)3/10
D)1/5
E)7/10
Rationale: In order to find the answer we need to multiply the probabilities - 2/5*1/2=1/5
Answer:D
Answer: D
Question: The speed of a boat in still water is 20 km/hr and the rate of current is 5 km/hr. The distance travelled downstream in 27 minutes is:
Options:
A)9.25
B)5.25
C)7.25
D)6.25
E)11.25
Rationale: Explanation:
Speed downstream = (20+5) kmph = 25 kmph
Distance travelled = (25*(27/60)) km = 11.25 km.
ANSWER:E
Answer: E
Question: A particular library has 75 books in a special collection, all of which were in the library at the beginning of the month. These book are occasionally loaned out through an inter-library program. If, by the end of the month, 65 percent of books that were loaned out are returned and there are 61 books in the special collection at that time, how many books of the special collection were loaned out during that month?
Options:
A)20
B)30
C)35
D)40
E)55
Rationale: The total number of books is 75.
Let x be the number of books which were loaned out.
65% of books that were loaned out are returned.
35% of books that were loaned out are NOT returned.
Now, there are 61 books, thus the number of un-returned books is 75-61 = 14 books.
0.35x = 14
x = 40
The answer is D.
Answer: D
Question: Which of the following CANNOT be weighed using a balance scale and these unit weights: 1, 4, 7, and 10
Options:
A)14
B)15
C)17
D)21
E)20
Rationale: A. 13 (can be weighed by keeping weights of 10 and 4)
B. 15 (can be weighed by keeping weights of 10,4 and 1 kg)
C. 17 (can be weighed by keeping weights of 10 and 7 kg)
D. 21 (can be weighed by keeping weights of 10, 7 and 4 kg)
E. 19(cannot be weighed)
E
Answer: E
Question: The distance from City A to City B is 180 miles. While driving from City A to City B, Cara drives at a constant speed of 30 miles per hour. Dan leaves City A 60 minutes after Cara. What is the minimum constant speed in miles per hour that Dan must exceed in order to arrive in City B before Cara?
Options:
A)42
B)44
C)46
D)36
E)50
Rationale: The time it takes Cara to drive to City B is 180 / 30 = 6 hours.
Dan needs to take less than 5 hours for the trip.
Dan needs to exceed a constant speed of 180 / 5 = 36 miles per hour.
The answer is D.
Answer: D
Question: At a school dance, 40% of the students had a date, 70% of the remaining students arrived at the dance with a group. What percentage of the students arrived alone?
Options:
A)40% of the students arrived alone.
B)10% of the students arrived alone.
C)42% of the students arrived alone.
D)18% of the students arrived alone.
E)None of these.
Rationale: Explanation:Let total number of students be 100,Then, number of students with a date = 40.Number of students arriving with a group= 70% of 60 = 42.Total number of students arriving alone = 100 – (40 + 42) = 18.Thus, 18% of the students are arriving alone.Answer: Option D.
Answer: D
Question: With both inlets open, a water tank will be filled with water in 24 minutes. The first inlet alone would fill the tank in 2 hours. If in every minutes the second inlet admits 50 cubic meters of water than the first, what is the capacity of the tank ?
Options:
A)2,000
B)10,500
C)11,750
D)12,000
E)13,000
Rationale: The work Done by Inlet A and B together in 1 min = 1/24
The work Done by Inlet A (First Inlet) in 1 min = 1/120
The work Done by Inlet B (Second Inlet) in 1 min = (1/24)- (1/120) = 1/30
DIfference of Work done by B and A = B - A = 50 Cubic meter
i.e. (1/30)- (1/120) = 50 Cubic meter
i.e. Tank = 40*50 = 2000 Cubic Meter
Answer: option A
Answer: A
Question: By selling 8 pencils for a rupee a man loses 10%. How many for a rupee should he sell in order to gain 10%?
Options:
A)6.54
B)9.45
C)7.34
D)6.67
E)5.09
Rationale: 90% --- 8
110% --- ?
90/110 * 8 = 6.54
Answer: A
Answer: A
Question: The credit card and a global payment processing companies have been suffering losses for some time now. A well known company recently announced its quarterly results. According to the results, the revenue fell to $48.0 billion from $69.0 billion, a year ago. By what percent did the revenue fall?
Options:
A)20.8
B)30.4
C)31.8
D)32.5
E)33.8
Rationale: $69-$48=21$
(21/69)*100=30.434%
ANSWER:B
Answer: B
Question: If x+1/x=5 then find out the value of x^5+1/x^5=?
Options:
A)2515
B)2525
C)2535
D)2545
E)2555
Rationale: given,(x+ 1/x) = 5
x^2 + 1/x^2 = (x+ 1/x)^2 - 2*x*1/x = 5^2 - 2 = 23 -------(1)
x^3 + 1/x^3 = (x+ 1/x)^3 - 3*x*1/x*(x+ 1/x) = 5^3 - 3*5 = 110 -------(2)
multiplying (1)& (2), we get
=>(x^2+ 1/x^2)*(x^3+ 1/x^3) = 23*110
=> x^5 + 1/x + x + 1/x^5 = 2530
=> x^5 + 1/x^5 + (x+ 1/x)= 2530
=> x^5 + 1/x^5 + 5 = 2530
=> (x^5+ 1/x^5)= 2525
ANSWER:B
Answer: B
Question: A basketball team scored x points per game in its first n games of the season, and in all the following games it scored an average (arithmetic mean) of y points per game. What was the average number of points per game in its first n + 4 games?
Options:
A)x + 3y/(n + 3)
B)x + y/(n + 3)
C)(x + 3y)/(n + 3)
D)(nx + 3y)/(n + 4)
E)(3x + ny)/(n + 3)
Rationale: Total points in first n games = nx
Total marks in next 3 games is 3y
So, Average marks in n + 4 games = (nx+3y)/(n+4)
Hence, correct answer will be (D)
Answer: D
Question: Carol and Jordan draw rectangles of equal area. If Carol's rectangle measures 15 inches by 24 inches and Jordan's rectangle is 8 inches long, how wide is Jordan's rectangle, in inches?
Options:
A)30
B)35
C)40
D)45
E)50
Rationale: Area of first rectangle is 15*24=360 hence area of second would be 8x=360x
x=45
answer is D
Answer: D
Question: What is the unit digit in 14^100?
Options:
A)0
B)5
C)2
D)3
E)6
Rationale: Unit digit in 14^100 = unit digit in [(14^4)^25 ]But unit digit in 14^4=6unit digit 14^100= 6Answer is E
Answer: E
Question: Sandy invested a certain sum of money at 12% p.a. simple interest for 'n' years. At the end of 'n' years, Sandy got back 7 times the original investment. What is the value of n?
Options:
A)30
B)35
C)40
D)45
E)50
Rationale: n* 0.12 * principal + principal = 7 * principal
n * 0.12 = 6
n = 50 years
The answer is E.
Answer: E
Question: Prabhu purchased 30 kg of rice at the rate of 17.50 per kg and another 30 kg rice at a certain rate. He mixed the two and sold the entire quantity at the rate of 18.60 per kg and made 20 per cent overall profit. At what price per kg did he purchase the lot of another 30 kg rice?
Options:
A)14.5
B)12.5
C)15.5
D)13.5
E)None of these
Rationale: Let he purchase of x/kg.
∴ (525 + 30x) × 120⁄100 = 60 × 18.60
⇒ x = 13.5/kg.
Answer D
Answer: D
Question: A BOWLER CAN TAKE MAX. 3WICKETS IN A OVER.IF HE BOWLS 6OVERS IN AN INNINGS, HOW MANY MAXIMUM WICKETS CAN HE TAKE?
Options:
A)8
B)9
C)11
D)7
E)10
Rationale: 10 because after 10 wickets, the innings is complete.
ANSWER:E
Answer: E
Question: A and C can finish 100,000 piece of work in 15 days each. B can do 30% faster than A and B.Approximately how many days would it take to finish million piece of work with all three working simultaneously?
Options:
A)40
B)46
C)51
D)42
E)54
Rationale: since B is 30% faster , thus it will finish130,000 piece of work in 15 days
in 15 days total piece of work finish by all three will be :
100,000+100,000+130,000 = 330,000
in 30 days:
330,000+330,000 = 660,000
in 45 days:
660,000+330,000 = 990,000
now only 10,000 more piece of work are required to finish , which will take 1 day
thus in all 46 days.
Ans:B
Answer: B
Question: Find the missing in the series: 60, 54, 45, 41,___
Options:
A)22
B)287
C)267
D)2767
E)2771
Rationale: Answer:C
Answer: C
Question: A bag contains 6 red, 5 blue and 2 green balls. If 2 ballsare picked at random, what is the probability that both are red?
Options:
A)1/13
B)2/23
C)5/26
D)4/27
E)3/23
Rationale: P(Both are red),
=6C213C2=6C213C2
=5/26
C
Answer: C
Question: What is the total number of positive integers that are less than 500 and that have no positive factor in common with 500 other than 1?
Options:
A)50
B)100
C)200
D)300
E)400
Rationale: Since 500=2^2*5^3 then a number can not have 2 and/or 5 as a factor.
The odd numbers do not have 2 as a factor and there are 250 odd numbers from 1 to 500.
We then need to eliminate the 50 numbers that end with 5, that is 5, 15, 25,...,495.
There are a total of 250 - 50 = 200 such numbers between 1 and 500.
The answer is C.
Answer: C
Question: Two women started running simultaneously around a circular track of length 1800 m from the same point at speeds of 10 km/hr and 20 km/hr. When will they meet for the first time any where on the track if they are moving in opposite directions?
Options:
A)72
B)74
C)76
D)78
E)80
Rationale: Time taken to meet for the first time anywhere on the track
= length of the track / relative speed
= 1800 / (30 + 60)5/18 = 1800* 18 / 90 * 5 = 72 seconds.
Answer:A
Answer: A
Question: Three people have $28, $72, and $98, respectively. If they pool their money then redistribute it among them, what is the maximum value for the median amount of money?
Options:
A)$72
B)$85
C)$99
D)$101
E)$202
Rationale: Solution -
Total money distributed is $198. In order to maximize median, one person has to accept $0 and remaining two people share $99 each. Hence median is $99.
ANS C
Answer: C
Question: Find the length of the altitude of an equilateral triangle of side 3√3 cm.
Options:
A)4.5cm
B)7.2cm
C)4.3cm
D)5.6cm
E)5.7cm
Rationale: Area of the triangle = (√3/4) x (3√3)2 = 27√3. Let the height be h.
Then, (1/2) x 3√3 x h = (27√3/4) X(2/√3) = 4.5 cm.
Ans: A
Answer: A
Question: A single discount equivalent to the discount series of 20%, 15% and 10% is?
Options:
A)31.8
B)31.1
C)38.8
D)31.2
E)31.9
Rationale: Explanation:
100*(80/100)*(85/100)*(90/100) = 61.2
100 - 61.2 = 38.8
Answer: C
Answer: C
Question: The ratio 15:25 expressed as percent equals to
Options:
A)70 %
B)60 %
C)30 %
D)75 %
E)None of above
Rationale: Explanation:
Actually it means 15 is what percent of 25, which can be calculated as,
(15/25)*100 = 15 * 4 = 60
Answer: Option B
Answer: B
Question: A store owner wants to mix cashews and almonds. Cashews cost 2 dollars per pound and almonds cost 5 dollars per pound. He plans to sell 150 pounds of a mixture. How many pounds of each type of nuts should be mixed if the mixture will cost 3 dollars?
Options:
A)30
B)40
C)50
D)60
E)70
Rationale: Let x be the number of pounds of cashews
So, 150 - x will represent the number of almonds
Since each pound of the mixture cost 3 dollars, 150 pounds will cost 3 × 150 = 450 dollars
Cost of cashews + cost of almonds = 450
2 × x + (150 - x) × 5 = 450
2x + 150 × 5 - x × 5 = 450
2x + 750 - 5x = 450
2x - 5x + 750 = 450
-3x + 750 = 450
-3x + 750 - 750 = 450 - 750
-3x = -300
-3x/-3 = -300/-3
x = 100
150 - x = 150 - 100 = 50.
Answer C
Answer: C
Question: How much is 80% of 60 is greater than 4/5 of 25?
Options:
A)15
B)28
C)16
D)12
E)73
Rationale: (80/100) * 60 â€“ (4/5) * 25
48 - 20 = 28
Answer: B
Answer: B
Question: If x⁄2 + 3⁄4 = 9⁄4, what is the value of x?
Options:
A)–2
B)–1
C)1
D)3
E)5
Rationale: x⁄2 + 3⁄4 = 9⁄4
Let's multiply both sides by 4.
2x + 3 = 9
2x = 6
x = 3
The answer is D.
Answer: D
Question: The MegaTek Corporation is displaying its distribution of employees by department in a circle graph. The size of each sector of the graph representing a department is proportional to the percentage of total employees in that department. If the section of the circle graph representing the manufacturing department takes up 180° of the circle, what percentage of MegaTek employees are in manufacturing?
Options:
A)20%
B)25%
C)30%
D)35%
E)50%
Rationale: ANSWER: E
180° divided by 360° equals 0.5, therefore the sector is equal to 50% of the total
Answer: E
Question: if integer N has p factors ; how many factors will 6N have ?
Options:
A)p
B)2p
C)P+1
D)2p+1
E)Cannot be determined
Rationale: Case 1:
Let N = 6 => 2 x 3 (prime factorization) => p = 4;
6N = 36 => no. of factors = 9; (p+5)
Case 2:
Let N = 7 => p = 2;
6N = 42 => no of factors =8; (4p)
For different N different results are observed. So, shouldn't E be the right answer?
Answer: E
Question: Look at this series: 36, 34, 30, 28, 24, ... What number should come next?
Options:
A)2
B)22
C)23
D)26
E)30
Rationale: This is an alternating number subtraction series. First, 2 is subtracted, then 4, then 2, and so on
2.
24-2=22
Option B
Answer: B
Question: Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 42 minutes. The waste pipe can empty the full cistern in?
Options:
A)A)7
B)B)6
C)C)8
D)D)9
E)E)5
Rationale: 1/10 + 1/15 - 1/x = 1/42
x = 7
Answer:A
Answer: A
Question: A person saved $10 in buying an item on sale. If he spent $400 for the item, approximately how much percent he saved in the transaction?
Options:
A)8%
B)10%
C)2%
D)2.4%
E)6%
Rationale: Actual price = 400+10 = $410
Saving = 10/410 * 100 = 100/41 = 2.4% approximately
Answer is D
Answer: D
Question: A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?
Options:
A)5litres, 7 litres
B)7litres, 4 litres
C)6litres, 6 litres
D)4litres, 8 litres
E)8litres, 10 litres
Rationale: Explanation:
Solution 1
Let x and (12âˆ’x) litres of milk be mixed from the first and second container respectively.
Amount of milk in x litres of the the first container =.75x
Amount of water in x litres of the the first container =.25x
Amount of milk in (12âˆ’xlitres of the the second container =5(12âˆ’x)
Amount of water in (12âˆ’x)litres of the the second container =.5(12âˆ’x)
Ratio of water to milk
Since x=6,12âˆ’x=12âˆ’6=6
Hence 6 and 6 litres of milk should mixed from the first and second container respectively.
Answer IS C
Answer: C
Question: Vijay bought 160 shirts at the rate of Rs. 220 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?
Options:
A)s.225
B)s.288
C)s.485
D)s.279
E)s.282
Rationale: Total CP per shirt = 220 + 1400/160 + 1.75 + 320/160 = Rs. 232.5
SP = CP[(100 + profit%)/100]
= 232.5 * [(100 + 20)/100] = Rs.279.
Answer:D
Answer: D
Question: The average age of seven persons sitting in a row facing east is 28 years. If the average age of the first three persons is 25 years and the average age of the last three persons is 35 years, then find the age of the person sitting in the middle of the row?
Options:
A)9 years
B)29 years
C)18 years
D)19 years
E)16 years
Rationale: Total age seven persons = (28 * 7)years
Total age of the first three persons and the last three persons are (25 * 3) years and (35 * 3) years respectively.
Age of the person sitting in the middle of the row = 28 * 7 - 25 * 3 - 35 * 3 = 196 - 75 - 105 = 16 years.
ANSWER:E
Answer: E
Question: A certain factory produces buttons and buckles at a uniform weight. If the total weight of 2 buttons and 2 buckles is one third of 11 buckles and 3 buttons, then the weight of 3 buttons and 5 buckles is how many times that of 5 buckles and 6 buttons?
Options:
A)1/2
B)2/3
C)3/4
D)4/5
E)5/6
Rationale: Let x be the weight of a button and let y be the weight of a buckle.
2x + 2y = (1/3)(3x+11y)
3x = 5y
x = 5y/3
3x + 5y = a(6x+5y)
10y = a(15y)
a = 10/15 =2/3
The answer is B.
Answer: B
Question: There are 10 pair of socks in a cupboard from which 4 individual socks are picked at random. The probability that there is at least one pair is:
Options:
A)195/323
B)99/323
C)198/323
D)185/323
E)115/323
Rationale: probability is 1-p(drawing four socks which ar different)
p(drawing four socks different) (20/20)*(18/19)*(16/18)*(14/17)=>224/323
so probability is 1-224/323=>99/323
ANSWER:B
Answer: B
Question: A teacher gave the same test to three history classes: W, B, and C. The average (arithmetic mean) scores for the three classes were 65, 80, and 77, respectively. The ratio of the numbers of students in each class who took the test was 4 to 6 to 5, respectively. What was the average score for the three classes combined?
Options:
A)74
B)75
C)76
D)77
E)78
Rationale: Ans : B (75)
lets say class W indeed has 4 children, B has 6 children and C has 5 children.
now, if the average of class W is 65, hence total marks awarded in the class = 65*4=260
Similarly,
class B = 80*6 = 480
class C = 77*5 = 385
total marks provided = W+B+C = 260+480+385 = 1125
avg. marks = 1125 / 15 (total no. of students) = 75=B
Answer: B
Question: If n=(81!  − 80!  + 79!)/(79!), which of the following could be subtracted from n so that √n is an integer?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: first lets find n.
n=(81! −80! +79!)/(79!)
n=81! /79!−80!/79! +79!/79!
n=81∗80−80+1=80(81−1)+1=80^2+1
so what should be subtracted from80^2+1, so that it becomes a perfect square ..
ans is 1, as 80^2−1+1=80^2
ANSWER:A
Answer: A
Question: A man has Rs. 320 in the denominations of one-rupee notes, five-rupee notes and ten-rupee notes. The number of notes of each denomination is equal. What is the total number of notes that he has ?
Options:
A)90
B)70
C)50
D)80
E)60
Rationale: Let number of notes of each denomination be x.
Then x + 5x + 10x = 320
16x = 320
x = 20.
Hence, total number of notes = 3x = 60.
Answer is E.
Answer: E
Question: 50 + 5 * 12 / (180/3) = ?
Options:
A)23
B)78
C)27
D)51
E)81
Rationale: Explanation:
50 + 5 * 12 / (180/3) = 50 + 5 * 12 / (60)
= 50 + (5 * 12)/60 = 50 + 1 = 51.
Answer:D
Answer: D
Question: The speed of light is approximately 1,76 * 10^5 miles per second. This approximate speed is how many miles per hour?
Options:
A) 1,11 * 10^7
B) 6,70 * 10^8
C) 1,11 * 10^8
D) 1,86 * 10^8
E) 6,70 * 10^7
Rationale: The easiest way to answer this question is by POE, it does not require any calculation (answered in 30seconds). In one hour there are 3600 seconds, therefore speed in miles/hour will be.
(1.76*10^5)*3600 = (1.76*10^5)*(3.6*10^3) = some number*10^8...
The key is realizing that thesome numberhas to be bigger thatn 1.76 (because 1.76*3.6), and the only answer that fits that is B
Answer: B
Question: In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 60 questions and secures 110 marks, the no of questions he attempts correctly is :
Options:
A)34
B)38
C)40
D)42
E)44
Rationale: Explanation:
Let the number of correct answers be X.
Number of incorrect answers = (60 – X).
4x – (60 – x) = 110
=> 5x = 170
=> x = 34
Answer: A
Answer: A
Question: 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4m3 , then the rise in the water level in the tank will be:
Options:
A)20 cm
B)25 cm
C)35 cm
D)50 cm
E)None of these
Rationale: Explanation:
Total volume of water displaced =(4 x 50) m3 = 200 m3
Rise in water level = 200/40×20= 0.25m = 25cm
Answer: B
Answer: B