divelab/Sys2Bench huggingface dataset:
Question: An ant walks an average of 500 meters in 12 minutes. A beetle walks 15% less distance at the same time on the average. Assuming the beetle walks at her regular rate, what is its speed in km/h?
Options:
A)2.215
B)2.5.
C)2.775
D)3.2
E)3.5
Rationale: the ant walks an average of 500 meters in 12 minutes
or,
500 meters in 1/5 hours
the beetle walks 15% less distance = 500-75=425 meters in 12 minutes
or,
0.425 km in 12/60 = 1/5 hours
speed = 0.425*5 = 2.125 km/h
Ans should be 2.125
ANSWER:A
Answer: A
Question: Father John forms a choir from the church attendants. 30 people attend John's church, and the choir has 28 spots available, with one person as the lead singer. How many different combinations does John have?
Options:
A)3005
B)4412
C)6544
D)12180
E)24366
Rationale: Pick the lead first - there are 30 choices. Now John has to pick 27 more choir members out of the 29 still available. The order of picking the other members does not matter, since they are not assigned different roles in the choir. Since John can't pick the same person twice, there is no repetition. Use the combinations formula for selecting 27 out of 29, no repetition, not ordered.
Now, there are 30 choices for the lead vocal - multiply the number of choices for the choir by 30, because you need a lead AND 27 other members: 30×29×14 choices
Hmmm. This is painful to calculate, but the solution is a number that ends with 0 (why? look at the unit's digit for each of the numbers that are multiplied: 0×9×4 = something that ends with 0).
12180 is the only answer that ends with 0. Hallelujah John!
Answer: D
Question: A department store perceived a run on a lower priced garment and raised the price by 20% to keep stock available until another shipment arrived. Customers fumed and the department store manager allowed them to purchase the garments at 80% of the new price to save face. What was the difference in the new retail price and the price the customers were allowed to pay instead?
Options:
A)4.0%
B)5.0%
C)6.0%
D)7.0%
E)8.0%
Rationale: Quantity X Rate = Price
1 X 1 = 1
0.8 X 1.20 = 0.960
Decrease in price = (0.040/1) Ã— 100 = 4.0%
Answer = Option A
Answer: A
Question: Find the least number must be subtracted from 427398 so that remaining no.is divisible by 15?
Options:
A)3
B)4
C)6
D)9
E)8
Rationale: On dividing 427398 by 15 we get the remainder 3, so 3 should be subtracted
A
Answer: A
Question: The least number which should be added to 4298 so that the sum is exactly divisible by 5, 6, 4 and 3 is?
Options:
A)12
B)22
C)32
D)42
E)52
Rationale: L.C.M. of 5, 6, 4 and 3 = 60.
On dividing 4298 by 60, the remainder is 38.
Number to be added = (60 - 38) = 22
B)
Answer: B
Question: A cistern is normally filled in 6 hours but takes two hours longer to fill because of a leak in its bottom. If the cistern is full, the leak will empty it in?
Options:
A)33
B)88
C)24
D)99
E)11
Rationale: 1/6 - 1/x = 1/8
x = 24
Answer: C
Answer: C
Question: Find the 37.5% of 976 ?
Options:
A)368
B)655
C)366
D)437
E)545
Rationale: 37.5 % of 976
= 37.5/100 * 976 = 375/1000 * 976 = 3/8 * 976
= 3 * 122 = 366.
Answer:C
Answer: C
Question: It takes a boat 3 hours to travel down a river from point A to point B, and 5 hours to travel up the river from B to A. How long would it take the same boat to go from A to B in still water?
Options:
A)9 hours and 45 minutes
B)3 hours and 45 minutes
C)1 hours and 45 minutes
D)6 hours and 45 minutes
E)8 hours and 45 minutes
Rationale: Let: S be the speed of the boat in still water, r be the rate of the water current and d the distance between A and B.
d = 3(S + r) : boat traveling down river
d = 5(S - r) : boat traveling up river
3(S + r) = 5(S - r)
r = S / 4 : solve above equation for r
d = 3(S + S/4) : substitute r by S/4 in equation B
d / S = 3.75 hours = Let: S be the speed of the boat in still water, r be the rate of the water current and d the distance between A and B.
d = 3(S + r) : boat traveling down river
d = 5(S - r) : boat traveling up river
3(S + r) = 5(S - r)
r = S / 4 : solve above equation for r
d = 3(S + S/4) : substitute r by S/4 in equation B
d / S = 3.75 hours = 3 hours and 45 minutes.
correct answer B
Answer: B
Question: At the faculty of Aerospace Engineering, 312 students study Random-processing methods, 232 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)424.
B)428.
C)430.
D)432.
E)436
Rationale: Students studying Random-processing methods = 312
Students studying Scramjet rocket engines = 232
Students studying them both = 112
Therefore ;
Students studying Only Random processing methods = 312 - 112 = 200
Students Studying Only Scramjet Rocket engines = 232 - 112 = 120
Students Studying Both = 112
Students Studying None = 0 (As mentioned in question that every student in the faculty has to study one of the two subjects)
Total Students in faculty of Aerospace Engineering = Students of Only Random processing methods + Students of Only Scramjet Rocket engines + Both + None
Total number of Students = 200 + 120 + 112 + 0 = 432 ....
Answer D
Answer: D
Question: There were two candidates in an election. Winner candidate received 62% of votes and won the election by 300 votes. Find the number of votes casted to the winning candidate?
Options:
A)456
B)744
C)912
D)1200
E)775
Rationale: W = 62% L = 38%
62% - 38% = 24%
24% -------- 300
62% -------- ? => 775
ANSWER:E
Answer: E
Question: Two numbers N and 16 have LCM = 48 and GCF = 8. Find N.
Options:
A)35
B)56
C)76
D)87
E)24
Rationale: The product of two integers is equal to the product of their LCM and GCF. Hence.
16* N = 48 * 8
N = 48*8 / 16 = 24 correct answer E
Answer: E
Question: Of 21 applicants for a job, 14 had at least 5 years of prior work experience, 12 had advanced degrees, and 6 had at least 5 years of prior work experience and advanced degrees. How many of the applicants had neither 5 years of prior work experience nor advanced degrees?
Options:
A)1
B)3
C)5
D)7
E)9
Rationale: Had advanced degrees and 5 years work experience: 6
Only had 5 years work experience: 14-6 = 8
Only had advanced degrees: 12-6 = 6
21-6-8-6=1
Answer: A
Answer: A
Question: Last month, John rejected 0.5% of the products that he inspected and Jane rejected 0.6 percent of the products that she inspected. If total of 0.75 percent of the products produced last month were rejected, what fraction of the products did Jane inspect?
Options:
A)1/4
B)1/2
C)5/8
D)5/6
E)15/16
Rationale: X - fraction of products Jane inspected
(1 - X) - fraction of products John inspected
0.6(X) + 0.5(1-X) = 0.75
0.1X = 0.75 - 0.5
X = 0.25/0.1
X = 1/4
Therefore the answer is A: 1/4.
Answer: A
Question: A person divided his total amount into two parts in the ratio of 3:2. He invested the first part in a bank which gives simple interest at the rate of 10% pa and the second part in another bank which gives simple interest at the rate of 20%. If after 3 years the total interest received by him from both the banks is 42% of the total amount he deposited in both the banks together, what is the total amount he deposited ?
Options:
A)Rs. 16000
B)Rs. 18000
C)Rs. 20000
D)Cannot be determined
E)Data is not sufficient
Rationale: Explanation :
Data is not sufficient to find the answer
Answer : Option D
Answer: D
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)9kmph
B)52kmph
C)13kmph
D)36kmph
E)45kmph
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.
Ans: D
Answer: D
Question: What is the twenty-sixth decimal to the right in the fraction 21/22?
Options:
A)1
B)3
C)5
D)7
E)9
Rationale: 21/22 = 0.9545454545454545
The even-numbered decimal places are 5.
The answer is C.
Answer: C
Question: What is the thousandths digit in the decimal equivalent of 57/5000?
Options:
A)0
B)1
C)3
D)5
E)6
Rationale: 57/5000 = 57 /(5*10^3)
= (57/5) *10^-3
=11.4 * 10^-3
=.0114
Thousandths digit = 1
Answer B
Answer: B
Question: A bag contains 2 red, 3 green and 2 blue balls. Two balls are drawn at random. What is the probability that none of the balls drawn is blue?
Options:
A)11/21
B)10/21
C)3/5
D)2/7
E)5/7
Rationale: Total number of balls =7
Let S be the sample space.
Then, n(S)	= Number of ways of drawing 2 balls out of 7= 7C2 =(7 x 6)(2 x 1)= 21.
Let E = Event of drawing 2 balls, none of which is blue.
n(E)	= Number of ways of drawing 2 balls out of (2 + 3) balls.
n(E)= 5C2=(5 x 4)(2 x 1)= 10.
P(E) =n(E)=10.
n(S)	21
Let E = Event of drawing 2 balls, none of which is blue.
n(E)	= Number of ways of drawing 2 balls out of (2 + 3) balls.= 5C2=(5 x 4)(2 x 1)= 10.
P(E)=N(E)/N(S)=10/21
So the answer is option B
Answer: B
Question: Find the odd man out. 12, 21, 32, 45, 60, 77, 95
Options:
A)45
B)95
C)32
D)21
E)95
Rationale: 12 + 9 = 21
21 + 11 = 32
32 + 13 = 45
45 + 15 = 60
60 + 17 = 77
77 + 19 = 96
Hence, 95 is wrong. 96 should have come in place of 95
Answer is B
Answer: B
Question: A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours will be the true time when the clock indicates 1 p.m. on the following day?
Options:
A)48 min. past 12
B)48 min. past 17
C)48 min. past 13
D)48 min. past 11
E)48 min. past 16
Rationale: Time from 8 a.m. on a day to 1 p.m. on the following day = 29 hours.
24 hours 10 min. of this clock = 24 hours of the correct clock.
hrs of this clock = 24 hours of the correct clock.
29 hours of this clock = hrs of the correct clock
= 28 hrs 48 min of the correct clock.
Therefore, the correct time is 28 hrs 48 min. after 8 a.m.
This is 48 min. past 12.
Answer: A
Answer: A
Question: The average marks of 20 students in a class is 100. But a student mark is wrongly noted as 50 instead of 10 then find the correct average marks?
Options:
A)78
B)82
C)98
D)91
E)85
Rationale: correct avg marks = 100+(10-50)/20
avg = 100-2 = 98
Answer is C
Answer: C
Question: The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
Options:
A)22
B)35
C)77
D)54
E)23
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle = 2.5 * 28/2
= 35 cm2
Answer:E
Answer: E
Question: Because he’s taxed by his home planet, Mork pays a tax rate of 45% on his income, while Mindy pays a rate of only 20% on hers. If Mindy earned 4 times as much as Mork did, what was their combined tax rate?
Options:
A)22%
B)25%
C)28%
D)31%
E)34%
Rationale: Let x be Mork's income, then Mindy's income is 4x.
The total tax paid is 0.45x + 0.8x = 1.25x
1.25x / 5x = 0.25
The answer is B.
Answer: B
Question: A 6% stock yields 8%. The market value of the stock is:
Options:
A)Rs. 48
B)Rs. 75
C)Rs. 96
D)Rs. 133.33
E)Rs. 143.33
Rationale: Let the face value of the stock is Rs.100
It yields Rs.6
Market value of the stock=(6/8)*100=Rs.75
ANSWER:B
Answer: B
Question: A boat can travel with a speed of 13 km/hr in still water. If the speed of the stream is 4 km/hr. find the time taken by the boat to go 80 km downstream?
Options:
A)2 hours
B)3 hours
C)4 hours
D)5 hours
E)None
Rationale: Solution
Speed Downstream	= (13 + 4) km/hr
= 17 km/hr.
Time taken to travel 80 km downstream	=(80 / 17)hrs
= 4 hrs 42 minutes.
Answer E
Answer: E
Question: What percent is 70 of 280?
Options:
A)25 %
B)30%
C)35%
D)40%
E)42%
Rationale: 70/280 = 1/4
1/4 × 100 = 25 %
A)
Answer: A
Question: A, B and C invests Rs.6000, Rs.5000 and Rs.3000 in a business. After one year C removed his money; A and B continued the business for two more year. If the net profit after 3 years be Rs.4206, then C's share in the profit is?
Options:
A)276
B)289
C)400
D)350.5
E)300
Rationale: 6*36 : 5*36 : 3*12
6: 5: 1
1/12 * 4206 = 350.50
Answer: D
Answer: D
Question: The angle between the minute hand and the hour hand of a clock when the time is 9.30, is
Options:
A)35°
B)65°
C)45°
D)105°
E)95°
Rationale: Angle between hands of a clock
When the minute hand is behind the hour hand, the angle between the two hands at M minutes past H 'o clock
=30(H−M/5)+M/2 degree
When the minute hand is ahead of the hour hand, the angle between the two hands at M minutes past H 'o clock
=30(M/5−H)−M/2 degree
Here H = 9, M = 30 and minute hand is behind the hour hand.
Hence the angle
=30(H−M/5)+M/2
=30(9−30/5)+30/2
=30(9−6)+15
=30×3+15 =105°
Answer is D.
Answer: D
Question: If n and k are integers whose product is 2500, which of the following statements must be true?
Options:
A)n+k>0
B)n does not equal k
C)Either n or k is a multiple of 10
D)If n is even, then k is odd
E)If n is odd, then k is even
Rationale: If n is odd and k is odd, then the product is odd.
The answer is E.
Answer: E
Question: The total age of A and B is 14 years more than the total age of B and C. C is how many year younger than A
Options:
A)A)11
B)B)12
C)C)13
D)D)14
E)E)15
Rationale: Explanation:
Given that A+B = 14 + B + C
=> A – C = 14 + B – B = 14
=> C is younger than A by 14 years
Answer: Option D
Answer: D
Question: An art gallery owner is hanging paintings for a new show. Of the three paintings she has to choose from, she can only hang two on the main wall of the gallery. Assuming that she hangs as many as possible on that wall, in how many ways can she arrange the paintings?
Options:
A)6
B)30
C)64
D)120
E)216
Rationale: Arrangment means permutations questions..
3P2 = 3!/2! = 6.
IMO option A is correct answer..
Answer: A
Question: A man swims downstream 30 km and upstream 18 km taking 3 hours each time, what is the speed of the man in still water?
Options:
A)1
B)8
C)9
D)7
E)5
Rationale: 30 --- 3 DS = 10
? ---- 1
18 ---- 3 US = 6
? ---- 1 M = ?
M = (10 + 6)/2 = 8
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 126 grams of water?
Options:
A) 16
B) 72
C) 112
D) 128
E) 142
Rationale: Solution:
We are given that the ratio of hydrogen to oxygen in water, by mass, is 2 : 16. Using our ratio multiplier we can re-write this as 2x : 16x. We can now use these expressions to determine how much oxygen is in 126 grams of water.
2x + 16x = 126
18x = 126
x = 7
Since x is 7, we know that there are 16 x 7 = 112 grams of oxygen in 126 grams of water.
Answer C.
Answer: C
Question: If P and Q are positive integers related by the equation P = 10Q - 5, what is the remainder when P is divided by 5?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: This question asks what IS...(the answer), so we know that the answer will be definite. As such, we can TEST VALUES to quickly get the solution.
We're told that P and Q are POSITIVE INTEGERS and P = 10Q - 5. We're asked for the REMAINDER when P is divided by 5.
IF....
Q = 1
P = 5
5/5 = 1 remainder 0
Final Answer:
A
Answer: A
Question: If the selling price of 60 articles is equal to the cost price of 30 articles, then the loss or gain percent is:
Options:
A)55%
B)35%
C)66%
D)45%
E)50%
Rationale: Let C.P. of each article be Re. 1.
Then, C.P. of 60 articles = Rs. 60;
S.P. of 60 articles = Rs. 30.
Loss % = 30/60 * 100 = 50%
ANSWER:E
Answer: E
Question: P and Q started a business investing Rs. 85,000 and Rs. 15,000 respectively. In what ratio the profit earned after 2 years be divided between P and Q respectively ?
Options:
A)3 : 4
B)3 : 5
C)15 : 23
D)None of these
E)Data inadequate
Rationale: Explanation:
P : Q = 85000 : 15000 = 85 : 15 = 17 : 3.
ANSWER IS D
Answer: D
Question: A, B and C can do a work in 9, 30 and 45 days respectively. If they work together, in how many days will they complete the work?
Options:
A)5
B)6
C)7
D)8
E)11
Rationale: One days's work of A, B and C = 1/9 + 1/30 + 1/45
= (10 + 3 + 2)/90 = 1/6
A, B and C together can do the work in 6 days.
Answer:B
Answer: B
Question: The principal that amounts to Rs. 4913 in 3 years at 6 1/4 % per annum C.I. compounded annually, is?
Options:
A)Rs. 3096
B)Rs. 4076
C)Rs. 4085
D)Rs. 4096
E)Rs. 5096
Rationale: Principal = [4913 / (1 + 25/(4 * 100))3]
= 4913 * 16/17 * 16/17 * 16/17 = Rs. 4096.
ANSWER:D
Answer: D
Question: Due to reduction of 25% in price of oranges a customer can purchase 4 oranges more for Rs. 16. what is original price of an orange?
Options:
A)1.39
B)1.33
C)1.31
D)1.32
E)1.38
Rationale: Explanation:
Recall it is based on inverse proportion or product constancy concept.
Reducion in price increase in amount
25% \inline \left ( \frac{1}{4} \right )
\inline \left ( \frac{1}{3} \right ) 33.33% = 4 oranges
It means original number of oranges = 4 x 3 = 12
\therefore original price of oranges = \inline \frac{16}{12} = Rs. 1.33
Answer: B) Rs 1.33
Answer: B
Question: The time taken by a man to row his boat upstream is twice the time taken by him to row the same distance downstream. If the speed of the boat in still water is 42 kmph, find the speed of the stream?
Options:
A)15 kmph
B)17 kmph
C)14 kmph
D)18 kmph
E)19 kmph
Rationale: The ratio of the times taken is 2:1.
The ratio of the speed of the boat in still water to the speed of the stream = (2+1)/(2-1) = 3/1 = 3:1
Speed of the stream = 42/3 = 14 kmph.
Answer: C
Answer: C
Question: The cost price of 7 articles is equal to the selling price of 5 articles. What is the profit percent?
Options:
A)10%
B)20%
C)30%
D)40%
E)50%
Rationale: 5*SP = 7*CP
SP = 1.4*CP
The profit percent is 40%.
The answer is D.
Answer: D
Question: If paint costs $3.20 per quart, and a quart covers 60 square feet, how much will it cost to paint the outside of a cube 10 feet on each edge?
Options:
A)$ 1.60
B)$ 32.00
C)$ 96.00
D)$108.00
E)$196.00
Rationale: total surface area = 6a^2 = 6*10*10 = 600
each quart covers 20 sqr ft
thus total number of quarts = 600/60 = 10
cost will be 10*3.2 = $32
Ans: B
Answer: B
Question: Sandy gets 3 marks for each correct sum and loses 2 marks for each incorrect sum. Sandy attempts 30 sums and obtains 55 marks. How many sums did Sandy get correct?
Options:
A)19
B)21
C)23
D)25
E)27
Rationale: Let x be the correct sums and (30-x) be the incorrect sums.
3x - 2(30-x) = 55
5x = 115
x = 23
The answer is C.
Answer: C
Question: A certain telescope increases the visual range at a particular location from 90 kilometers to 150 kilometers. By what percent is the visual range increased by using the telescope ?
Options:
A)30%
B)33 1/2%
C)40%
D)60%
E)66 2/3%
Rationale: Original visual range = 90 km
New visual range = 150 km
Percent increase in the visual range by using the telescope
= (150-90)/90 * 100%
= 2/3 * 100%
= 66.67 %
Answer E
Answer: E
Question: If P : Q = 3 : 4 and Q : R = 5 : 6, then P : Q : R is:
Options:
A)3 : 4 : 6
B)3 : 5 : 6
C)15 : 20 : 24
D)5 : 6 : 3
E)None
Rationale: P:Q=3:4, Q:R=5:6, P:Q:R=3×5:5×4:6×4
⇒ 15:20:24
Answer: C.
Answer: C
Question: At the end of the first quarter, the share price of a certain mutual fund was 30 percent higher than it was at the beginning of the year. At the end of the second quarter, the share price was 75 percent higher than it was at the beginning of the year. What was the percent increase in the share price from the end of the first quarter to the end of the second quarter?
Options:
A)20%
B)25%
C)30%
D)34.6%
E)40%
Rationale: Another method is to use the formula for 2 successive percentage changes:
Total = a + b + ab/100
75 = 30 + b + 30b/100
b = 34.6
Answer (D)
Answer: D
Question: A train 1200 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
Options:
A)288 m
B)256 m
C)100 m
D)278 m
E)287 m
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (1200 + x)/60
= 65/3
x = 500 m.
Answer:C
Answer: C
Question: A tank is 25m long 12m wide and 6m deep. The cost of plastering its walls and bottom at 45 paise per sq m is
Options:
A)Rs. 234.80
B)Rs. 334.80
C)Rs. 434.80
D)Rs. 534.80
E)None of these
Rationale: Explanation:
Area to be plastered = [2(l + b) Ã— h] + (l Ã— b)
= [2(25 + 12) Ã— 6] + (25 Ã— 12) = 744 sq m
Cost of plastering = 744 Ã— (45/100) = Rs.334.80 Answer: B
Answer: B
Question: The total of company C's assets in 1994 was 400% greater than the total in 1993, which in turn was 400% greater than the total in 1992. If the total of company C's assets in in 1992 was N dollars, which one of the following represents company C's assets in 1994:
Options:
A)7N
B)8N
C)9N
D)12N
E)25N
Rationale: Let's use actual numbers. Starting in 1992, let's say company C had $100 in assets.
In 1993, the total assets were 400% GREATER, which means 1992 PLUS 400% of 1992:
$100 + 4x$100 = $100 + $400 = $500
In 1994, the total assets were 400% GREATER than they were in 1993, which means 1993 PLUS 400% of 1993:
$500 + 4x$500 = $500 + $2000 = $2500
This is 25 times the 1992 number, so the correct answer is 25N.
E
Answer: E
Question: 30 square stone slabs of equal size were needed to cover a floor area of 120 sq.m. Find the length of each stone slab?
Options:
A)120cm
B)200cm
C)88cm
D)666cm
E)776cm
Rationale: Area of each slab
=120/30m2=4m2
Length of each slab √4=2m=200cm
B
Answer: B
Question: For what value of x between − 5 and 5, inclusive, is the value of x^2 − 10x + 16 the greatest?
Options:
A)− 5
B)− 2
C)0
D)2
E)4
Rationale: we can see from the statement that two terms containing x, x^2 will always be positive and -10x will be positive if x is -ive..
so the equation will have greatest value if x is -ive, and lower the value of x, greater is the equation.
so -5 will give the greatest value..
ans A
Answer: A
Question: In a rectangular coordinate system, what is the area of a rhombus whose vertices have the coordinates (0, 3.5), (9, 0), (0, -3.5), (-9, 0)?
Options:
A)56
B)88
C)112
D)116
E)63
Rationale: Area of rhombus= 1/2* D1 *D2
Length of 1st diagonal = 9+9= 18
Length of 2nd diagonal= 3.5+3.5= 7
Area= 1/2*18*7= 63
E is the answer
Answer: E
Question: 1397 x 1397
Options:
A)1951609
B)1981709
C)18362619
D)2031719
E)None of these
Rationale: 1397 x 1397	= (1397)2
= (1400 - 3)2
= (1400)2 + (3)2 - (2 x 1400 x 3)
= 1960000 + 9 - 8400
= 1960009 - 8400
= 1951609.
Answer: Option A
Answer: A
Question: How many 9's are there preceded by 5 but not followed by 1?
5 9 3 2 1 7 4 2 5 9 7 4 6 1 3 2 8 7 4 1 3 8 3 5 9 1 7 4 3 9 5 8 2 0 1 8 7 4 6 3
Options:
A)4
B)2
C)6
D)8
E)9
Rationale: 5 9 3
5 9 7
Only at these places 2 is preceded by 5 but not followed by 1
Answer: B
Answer: B
Question: A man sells a horse for Rs.740 and loses something, if he had sold it for Rs.980, his gain would have been double the former loss. Find the cost price of the horse?
Options:
A)587
B)679
C)767
D)820
E)998
Rationale: CP = SP + 1CP = SP - g
740 + x = 980 - 2x
3x = 240 => x
= 80
CP = 740 + 80
= 820
Answer:D
Answer: D
Question: Every year Taylor goes to the same carnival, and he attempts to shoot a basketball into a small hoop, hoping that he will win a ten-foot tall teddy bear. If the probability that Taylor does not make a basket is 1/3, what is the probability that Taylor makes exactly one basket in three tries?
Options:
A)1/9
B)2/9
C)2/5
D)3/5
E)3/7
Rationale: Probability of basket = 2/3
Probability of no basket = 1/3
Required probability=3* 2/3*1/3*1/3
= 2/9
B is the answer .
Answer: B
Question: 100 people are standing in a circle. The person standing at number 1 is having a sword. He kills the person next to him with the sword and then gives the sword to the third person. This process is carried out till there is just one person left.
Can you find out who survives?
Options:
A)93
B)73
C)90
D)75
E)87
Rationale: B
The person on 73rd number will survive.
Till the number is the power of 2, the last person to survive will be the one who started it. But since the number here is not the power of 2, we will take the greatest power of 2 that is less than the number which is 64.
100 - 64 = 36
36 people are killed as 2, 4, 6, ..., 72. Thus the sword will now be given to the 73rd person. Now he is the first person to start in the remaining 64 people. Thus he will be the one to survive.
Answer: B