divelab/Sys2Bench huggingface dataset:
Question: A football matches has been organized in such a fashion, every participating team plays a match against every other team once and only once.
If 36 matches are totally played, how many teams participated?
Options:
A)7
B)8
C)9
D)10
E)11
Rationale: For a match u need 2 teams.
Suppose there are totally 'n'teams.
Now we have to choose 2 teams out of 'n' teams.
nC2 = 36;
Solve to get n=9.
n(n-1)/2 = 36
9(9-1)/2 = 36
9(8)/2 = 36
72/2 = 36
So, answer is 9 If 36 matches are totally played.
ANSWER:C
Answer: C
Question: A sum of salary is distributed among A,B,C,D in the proportion of 2:3:4:6. If D gets $700 more than C, what is the B's share?
Options:
A)$1050
B)$2500
C)$3000
D)$3400
E)$8000
Rationale: Let the shares of A,B,C,D are 2x,3x,4x,6x
6x-4x = 700
x = 350
B's share = 3x = $1050
Answer is A
Answer: A
Question: A rectangular cube has a volume of 6 cubic feet. If a similar cube is twice as long, twice as wide, and twice as high, then the volume, in cubic feet of such cube is?
Choices
Options:
A)24
B)48
C)64
D)80
E)100
Rationale: Lets say the sides of the rectangular cube are x, y and z. Problem states volume is 6.
i.e,
x*y*z = 6 .
If every side is increased twice as before. then new volume is
2x*2y*2z = 8*(x*y*z) = 8*6 = 48.
Answer is B
Answer: B
Question: Little John had $5.10. He spent $1.05 on sweets and gave to his two friends $1.00 each. How much money was left?
Options:
A)$2.15
B)$2.05
C)$2.45
D)$2.25
E)$2.85
Rationale: John spent and gave to his two friends a total of
1.05 + 1.00 + 1.00 = $3.05
Money left
5.10 - 3.05 = $2.05
Answer :B
Answer: B
Question: Every person at a birthday party either wants candy or a wants cake, but not both. The ratio of people who want cake to people who want candy is 9 to 6 . If 9 people decided they wanted candy instead of cake, the ratio of people who want cake to people who want candy will be 1 to 1. How many people could be at the party?
Options:
A)60
B)50
C)90
D)45
E)Both C and D
Rationale: By checking the answer choices:
Since we have an initial ratio of 9:6, the total count should be divisible by 15.
A. 60/15=4, Cake People = 36, Candy People = 24, Since 36-9 is not equal to 24+9 this can not be the answer.
B. Out, Since not divisible by 15.
C. 90/15=6, Cake People = 54, Candy People = 36, Since 54-9 is equal to 36+9, this is the correct answer.
D. 45/15=3, Cake People = 27, Candy People = 18, Since 27-9 is not equal to 18+9 this as well can not be the answer.
E. Since choice D is not correct, choice E is also not correct.
C is the correct answer.
Answer: C
Question: A man rows his boat 65 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
Options:
A)5 kmph
B)4 kmph
C)9 kmph
D)8 kmph
E)1 kmph
Rationale: Speed downstream = d/t = 65/(2 1/2) = 26 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (26 - 18)/2 = 4 kmph
Answer:B
Answer: B
Question: The volume of a rectangular swimming pool is 840 cubic meters and water is flowing into the swimming pool. If the surface level of the water is rising at the rate of 0.5 meters per minute, what is the rate T, in cubic meters per minutes, at which the water is flowing into the swimming pool?
Options:
A)0.125
B)0.25
C)0.5
D)0.75
E)Not enough information to determine the rate
Rationale: The correct answer is E.
There are not enough info to answer the question.
A 840 cubic meters rectangle is built from: height*length*width.
From the question we know the volume of the pool and the filling rate.
A pool can have a height of 10*width8.4*length10 and have a volume of 840 cubic meters, and it can have a height of 1 meter, width of 100 meters and length of 8.4. In both cases the pool will fill up in a different rate = E
Answer: E
Question: A big container is 40% full with water. If 28 liters of water is added, the container becomes 3/4 full. What is the capacity of the big container in liters?
Options:
A)68
B)72
C)76
D)80
E)84
Rationale: 28 liters is 35% of the capacity C.
28 = 0.35C
C = 28/0.35 = 80 liters.
The answer is D.
Answer: D
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 120 m and they cross each other in 6 sec, then the speed of each train is?
Options:
A)30
B)31
C)72
D)25
E)24
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (120 + 120)/6 => x = 20
Speed of each train = 20 m/sec.
= 20 * 18/5 =72km/hr.
Answer: Option C
Answer: C
Question: In a certain series, each term is m greater than the previous term. If the 19th term is 760 and the 16th term is 700, what is the first term?
Options:
A)200
B)300
C)400
D)450
E)500
Rationale: a + 18m = 760 (17th term)
a + 15m = 700 (16th term)
You get a = 400 and m = 20
Answer: C
Answer: C
Question: Working at a constant rate, P can finish a job in 4 hours. Q, also working at a constant rate, can finish the same job in 20 hours. If they work together for 3 hours, how many more minutes will it take P to finish the job, working alone at his constant rate?
Options:
A)12
B)15
C)20
D)21
E)24
Rationale: Each hour they complete 1/4 + 1/20 = 3/10 of the job.
In 3 hours, they complete 3(3/10) = 9/10 of the job.
The time for P to finish is (1/10) / (1/4) = (2/5) hour = 24 minutes
The answer is E.
Answer: E
Question: 7+2+2^2+2^3+2^4+2^5=？
Options:
A)(2^3-1)(2^3+1)
B)2^6+5
C)2^5-1
D)2^5+1
E)2^5-2
Rationale: From 7+2+2^2+2^3+2^4+2^5=69,
2^6+5=69
the correct answer is B.
Answer: B
Question: Q-1) Of the 84 parents who attended a meeting at a
school, 35 volunteered to supervise children during
the school picnic and 11 volunteered both to supervise
children during the picnic and to bring refreshments to
the picnic. If the number of parents who volunteered
to bring refreshments was 3 times the number of
parents who neither volunteered to supervise children
during the picnic nor volunteered to bring
refreshments, how many of the parents volunteered to
bring refreshments?
Options:
A)25
B)36
C)22
D)42
E)45
Rationale: i used the following formula: total = group1 + group2 + neither - both
using the information from the question stem, we have:
84 total people
35 who supervise (group1)
x who neither supervise nor bring refreshments
3x people who bring refreshments (group2)
11 who supervise AND bring refreshments (both)
therefore...
84 = 35 + 3x + x - 11
solving, we get x = 15.
since we want the value of those who bring refreshments AND supervise:
1.5(15) = 22
answer is C
Answer: C
Question: A student committee that must consists of 4 members is to be formed from a pool of 8 candidates. How many different committees are possible
Options:
A)5
B)8
C)70
D)56
E)336
Rationale: Out of 8 people, any 4 can be selected for a committee. So 8c4=70 is the answer
C
Answer: C
Question: A car travelling with 5/7 of its actual speed covers 42 km in 1 hr 40 min 48 sec. Find the actual speed of the car.
Options:
A)55 km/hr.
B)25 km/hr.
C)65 km/hr.
D)35 km/hr.
E)45 km/hr.
Rationale: D
35 km/hr.
Time taken = 1 hr 40 min 48 sec = 1 hr 40 4/5 min. = 126/75 hrs.
Let the actual speed be x km/hr.
Then, (5/7)x X 126/75 = 42
--> x = 35 km/hr.
Answer: D
Question: In an election between the two candidates, the candidates who gets 70% of votes polled is winned by 280 vote’s majority. What is the total number of votes polled?
Options:
A)750
B)700
C)800
D)850
E)None of these
Rationale: Explanation:
Note: majority (40 %) = difference in votes polled to win (70 %) & defeated candidates (30 %)
40 % = 70 % - 30 %
40% -----> 280 (40*7 = 280)
100% -----> 700 (100*7 = 700)
Answer: Option B
Answer: B
Question: If $120 invested at a certain rate of simple interest amounts to $240 at the end of 3 years,How much will $150 amount to at the same rate of interest in 6 years?
Options:
A)$190
B)$180
C)$200
D)$340
E)$450
Rationale: 120 amounts to 240 in 3 years.
i.e (principal + interest ) on 120 in 3 years = 240
120 + 120*(r/100)*(3) = 240 => r = 100/3
150 in 6 years = principal + interest
= 150 + 150*(r/100)*(6)
= 450
Answer is E.
Answer: E
Question: A man bought an article and sold it at a gain of 5 %. If he had bought it at 5% less and sold it for Re 3 less, he would have made a profit of 10%. The C.P. of the article was
Options:
A)344
B)218
C)200
D)600
E)211
Rationale: Explanation:
Let original Cost price is x
Its Selling price = (105/100) * x = 21x/20
New Cost price = (95/100) * x = 19x/20
New Selling price = (110/100 )* (19x/20 )= 209x/200
[(21x/20) - (209x/200)] = 3
=> x = 600
Answer: D) Rs 600
Answer: D
Question: Find the least number of five digits which is exactly divisible by 12, 15 and 18?
Options:
A)10080
B)1080
C)10025
D)10050
E)10024
Rationale: LCM = 180
180) 10000 (55
9900
---------
100
10000 + 180 - 100 = 10080
ANSWER A
Answer: A
Question: A sum fetched a total simple interest of $4151.25 at the rate of 9 p.c.p.a. in 5 years. What is the sum?
Options:
A)$8829
B)$2840
C)$6578
D)$7782
E)$8928
Rationale: E
8928
Principal
= $100 x 4151.25/9 x 5
= $415125/45
= $8928.
Answer: E
Question: You have only 1 kg weight. You have to weight 31kg. Min number of measurements you have to done ?
Options:
A)21R
B)33R
C)35R
D)31R
E)38R
Rationale: You can do it in 5 steps.
1,2,4,8,16
Asume stone as S (Left Side) weight of 1kg as T (Right Side)
Move 1T to the same side as S and, Left Side is S+1T, Now weight 2T
Move 2T to the same side as S and, against S+3T, Now weight 4T
Move 4T to the same side as S and, against S+7T, weight 8T
Move 8T to the same side as S and, against S+15T, weight on right Side is 16T
15R + 16R = 31R.
ANSWER:D
Answer: D
Question: If a tire rotates at 400 revolutions per minute when the car is traveling 168km/h, what is the circumference of the tire?
Options:
A)2
B)1
C)7
D)3
E)5
Rationale: 400 rev / minute = 400 * 60 rev / 60 minutes
= 24,000 rev / hour
24,000 * C = 168,000 m : C is the circumference
C = 7 meters
correct answer C
Answer: C
Question: Every second Saturday and all Sundays are holidays. How many working days will be there in a
month of 30 days beginning on a Saturday?
Options:
A)24
B)23
C)18
D)21
E)22
Rationale: Explanation :
Mentioned month has begins on a Saturday and has 30 days
Sundays = 2nd, 9th, 16th, 23rd, 30th
=> Total Sundays = 5
Second Saturdays = 8th and 22nd
Total Second Saturdays = 2
Total Holidays = Total Sundays + Total Second Saturdays = 5 + 2 = 7
Total days in the month = 30
Total working days = 30 - 7 = 23
Answer : Option B
Answer: B
Question: A car runs 10,000 miles using 5 tyres interchangeably. to have equal worn out by all tyres,how many miles each tyre should have run?
Options:
A)5000
B)8000
C)4000
D)3000
E)2000
Rationale: for 5 tyres running interchangeably 10,000 miles the car runs
for 1 tyre=10000/5=2000
as you all know i suppose the car has 4 tyre
to have equal worn out by 4 tyres we need=2000*4=8000
ANSWER:B
Answer: B
Question: In a fuel station the service costs $1.75 per car, every liter of fuel costs 0.45$. Assuming that a company owns 12 cars and that every fuel tank contains 55 liters and they are all empty, how much money total will it cost to fuel all cars?
Options:
A)318$
B)380$
C)420$
D)450$
E)480$
Rationale: 12*1.75 + 0.45*12*55 = 318 hence - A
Answer: A
Question: Rs.2500 is divided into two parts such that if one part be put out at 5% simple interest and the other at 6%, the yearly annual income may be Rs.120. How much was lent at 5%?
Options:
A)2333
B)2777
C)3000
D)1000
E)2871
Rationale: (x*5*1)/100 + [(2500 - x)*6*1]/100 = 120
X = 3000
Answer: C
Answer: C
Question: January 1, 2007 was Monday. What day of the week lies on Jan. 1, 2008?
Options:
A)Monday
B)Tuesday
C)Wednesday
D)Friday
E)Sunday
Rationale: The year 2007 is an ordinary year. So, it has 1 odd day.
day of the year 2007 was Monday
day of the year 2008 will be 1 day beyond Monday
Hence, It will be Tuesday. answer : B
Answer: B
Question: What is 78% of 4/5?
Options:
A)6.9
B)69.0
C)0.6845
D)0.624
E)0.69
Rationale: 78%*(4/5)=0.78*0.8=0.624
Answer :D
Answer: D
Question: Addison High School’s senior class has 300 boys and 240 girls. If 30% of the boys did not attend the college then 70% of the total class attended college, what percentage of the girls class did not attend college?
Options:
A)70
B)45
C)50
D)46
E)30
Rationale: % of boy attending the college = 100-30 = 70%
Number of boys attending the college : 0.70*300 = 210
Total people = 300+240 = 540
Total number of students attending the college: 0.70*540 = 378
number of girls attending the college = 378-210 = 168
number of girls not attending the college = 240-168 = 72
% of girls not attending = 72/240 = 30%. E is the correct answer
Answer: E
Question: The radius of a wheel is 22.4 cm. What is the distance covered by the wheel in making 300 resolutions.
Options:
A)421 m
B)422 m
C)423 m
D)424 m
E)425 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 300 resolutions.
= 300 * 2 * 22/7 * 22.4
= 42200 cm
= 422 m
Answer: B
Answer: B
Question: A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime. The product of all the possible units digits of Sophie Germain primes greater than 4 is
Options:
A)3
B)7
C)189
D)227
E)234
Rationale: In that case, the Sophie prime numbers greater than 5 are 7,11,23,47,59, .. which yields units digit as 1,3,7 and 9
Product would be 1 x 3 x 7x9 =189 Answer should be C.
Answer: C
Question: If 0 < e< 1 < f, which of the following must be true?
Options:
A)1 < 1/e< 1/f
B)1/e< 1 < 1/f
C)1/e< 1/f< 1
D)1/f< 1 < 1/e
E)1/f< 1/e< 1
Rationale: 0<e<1<f. Let e=1/2 and f=2
Substituting values:
A. 1<2<1/2 ---Wrong
B. 2<1< 1/2 ---Wrong
C. 2<1/2<1 ---Wrong
D. 1/2<1<2 ---Correct
E. 1/2<2<1 ---Wrong
Hence answer is D
Answer: D
Question: Andrew started saving at the beginning of the year and had saved $180 by the end of the year. He continued to save and by the end of 2 years had saved a total of $540. Which of the following is closest to the percent increase in the amount Andrew saved during the second year compared to the amount he saved during the first year?
Options:
A)11%
B)25%
C)44%
D)56%
E)100%
Rationale: Percent increase in the amount Andrew saved during the second year compared to the amount he saved during the first year.
Percentage Change = ( Change in value / Original value ) * 100
Percentage Change = [ (Saving in 2nd year - Saving in 1st year ) / Saving in 1st year ] * 100
Saving in 2nd year + Saving in 1st year = 540
Saving in 2nd year + 180 = 540
Saving in 2nd year = 540 - 180 = 360
Change in Value = 360 - 180 = 180
Original Value = 180
Percentage Increase = (180 / 180 ) * 100 = 100%..... Answer E......
Answer: E
Question: A rectangular field has to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?
Options:
A)95
B)92
C)82
D)88
E)97
Rationale: AREA OF FIELD = 680 SQ FEET
LENGTH OF ADJ SIDES 20 FEET AND 680/20 = 34 FEET
REQ LENGTH OF THE FENCING = 20 + 34 + 34 = 88 FEET
ANSWER D
Answer: D
Question: 7 people meet for a business lunch. Each person shakes hands once with each other person present. How many handshakes take place?
Options:
A)30
B)21
C)18
D)15
E)10
Rationale: the formula to count handshakes is n(n−1)2n(n−1)2
Where n is the number of people
=> 7(7-1)/2 = 7*6/2 = 42/2 = 21
=> the answer is B(21)
Answer: B
Question: A, B and C enter into a partnership by investing $15000, $21000 and $27000 respectively. At the end of 8 months, B receives $1540 as his share. Find the share of A.
Options:
A)$800
B)$900
C)$1000
D)$1100
E)$1200
Rationale: The ratio of capital of A, B and C = 15000 : 21000 : 27000 = 5 : 7 : 9
A's share = (5/7)*1540 = $1100
The answer is D.
Answer: D
Question: In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples?
Options:
A)5/21
B)5/23
C)5/29
D)5/12
E)5/92
Rationale: Number of ways of (selecting at least two couples among five people selected) = (⁵C₂ * ⁶C₁)
As remaining person can be any one among three couples left.
Required probability
= (5C2 * 6C1)/10C5
= (10 * 6)/252 = 5/21
Answer: A
Answer: A
Question: Create 2 equivalent fractions with the numbers 4, 9, 2, and 18
Options:
A)2/9 and 5/18
B)2/9 and 4/18
C)3/9 and 4/18
D)2/9 and 6/18
E)None
Rationale: Solution:
We're searching for pairs of numbers which, when multiplied, have the same product. We observe that 4 x 9 = 18 x 2 = 36, so the fractions will be 2/9and4/18
Answer B
Answer: B
Question: The average age of 7 men increases by 4 years when two women are included in place of two men of ages 26 and 30 years. Find the average age of the women?
Options:
A)42
B)40
C)30
D)18
E)11
Rationale: Explanation:
26 + 30 + 7 * 4 = 84/2 = 42
Answer: A
Answer: A
Question: One fourth of a solution that was 10% sugar by weight was replaced by a second solution resulting in a solution that was 17 percent sugar by weight. The second solution was what percent sugar by weight?
Options:
A)34%
B)24%
C)22%
D)38%
E)8.5%
Rationale: Instead of using complex calculations and remembering formulae, why dont u directly get to weighted average.
3 parts of 10% + 1 part of x (unknown) % = 4 parts of 17%
=> x% = 68%-30% = 38%
ans D it is.
Answer: D
Question: xy=1 then what is (3^(x+y)^2) / (3^(x-y)^2)
Options:
A)81
B)4
C)8
D)16
E)32
Rationale: (x+y)^2 - (x-y)^2
(x+y+x-y)(x+y-x+y)
(2x)(2y)
4xy
4
3^4 = 81
Answer A
Answer: A
Question: There are 10 slate rocks, 15 pumice rocks, and 6 granite rocks randomly distributed in a certain field. If 2 rocks are chosen at random and without replacement, what is the probability that both rocks will be slate rocks?
Options:
A)2/19
B)3/31
C)4/37
D)5/41
E)6/53
Rationale: 10/31*9/30 = 3/31
The answer is B.
Answer: B
Question: Which of the following fractions is greater than 1/7?
Options:
A)1. 12/50
B)2. 3/11
C)3. 2/9
D)4. 4/17
E)5. 6/24
Rationale: 1. 12/50
12.5/50 = 1/4 thus 12/50 < 1/4
2. 3/11
3/12 = 1/4 thus 3/11 > 1/4
3. 2/9
2/8 = 1/4 thus 2/9 < 1/4
4. 4/17
4/16 = 1/4 thus 4/17 < 1/4
5. 6/24
6/24 = 1/4
A
Answer: A
Question: 3 men or 6 women can do a piece of work in 23 days. In how many days will 12 men and 8 women do the same work?
Options:
A)15/9 days
B)15/4 days
C)18/4 days
D)69/16 days
E)35/4 days
Rationale: 3M = 6W ---- 23 days
12M + 8W -----?
24W + 8 W = 32W ---?
6W ---- 23 32 -----?
6 * 23 = 32 * x => x = 69/16 days
Answer:D
Answer: D
Question: A train running at the speed of 72 km/hr crosses a pole in 9 seconds. What is the length of the train?
Options:
A)286
B)278
C)255
D)180
E)287
Rationale: Speed=(72 * 5/18) m/sec = (20) m/sec Length of the train
= (Speed x Time) = (20 * 9) m
= 180 m.
Answer:D
Answer: D
Question: Joshua and Jose work at an auto repair center with 3 other workers. For a survey on health care insurance, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that Joshua and Jose will both be chosen?
Options:
A)1/15
B)1/10
C)1/9
D)1/6
E)1/3
Rationale: Two Methods
1) Probability of chosing Josh first = 1/5
Probability of chosing Jose second = 1/4
total = 1/20
Probability of chosing Jose first = 1/5
Probability of chosing Josh second = 1/4
Total = 1/20
Final = 1/20 + 1/20 = 1/10
B
Answer: B
Question: If 4 men can colour 48 m long cloth in 2 days, then 6 men can colour 36 m long cloth in
Options:
A)1 day
B)2 days
C)3 days
D)4 days
E)5 days
Rationale: The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 6 = 1 day.
A
Answer: A
Question: All of the stocks on the over-the-counter market are designated by either a 8-letter or a 9-letter code that is created by using the 26 letters of the alphabet. Which of the following gives the maximum number of different stocks that can be designated with these codes?
Options:
A)a. 27(26^8)
B)b. 26(26^4)
C)c. 27(26^4)
D)d. 26(26^5)
E)e. 27(26^5)
Rationale: no of different stocks for 8-letter code = 26^8
no of different stocks for 9-letter code = 26^9
total = 26^8 + 26^9 = 26^8(26+1) = 27(26^8)
[Reveal]Spoiler:
Option A
Answer: A
Question: The average (arithmetic mean) of 4 positive integers is 45. If the average of 2 of these integers is 45, what is the greatest possible value that one of the other 2 integers can have?
Options:
A)55
B)65
C)100
D)89
E)115
Rationale: a + b + c + d = 180
a + b = 90
c + d = 90
Greatest possible = 89 (Just less than 1)
Answer = D
Answer: D
Question: A certain characteristic in a large population has a distribution that is symmetric about the mean m. If 68 percent of the distribution lies within one standard deviation d of the mean, what percent W of the distribution is less than m +d ?
Options:
A)16%
B)32%
C)48%
D)84%
E)92%
Rationale: D
The prompt says that 68% of the population lies between m-d and m+d.
Thus, 32% of the population is less than m-d or greater than m+d.
Since the population is symmetric, half of this 32% is less than m-d and half is greater than m+d.
Thus, W=(68+16)% or (100-16)% of the population is less than m+d.
Answer: D
Question: Twelve men and six women together can complete a piece of work in four days. The work done by a women in one day is half the work done by a man in one day. If 12 men and six women started working and after two days, six men left and six women joined, then in hoe many more days will the work be completed?
Options:
A)2 (1/9)
B)2 (4/2)
C)5 (1/2)
D)2 (1/2)
E)2 (1/6)
Rationale: Work done by a women in one day = 1/2 (work done by a man/day)
One women's capacity = 1/2(one man's capacity)
One man = 2 women.
12 men = 24 women.
12 men + 6 women = 30 women
30 women can complete the work in four days. In the first 2 days they can complete 1/2 of the work. Remaining part of the work = 1/2. If 6 men leave and 6 new women join, then new work force = 30 women - 12 women + 6 women = 24 women.
Time taken by them to complete the remaining work = 1/2 (Time taken by 24 women to complete the work) = 1/2 * (30 * 4)/24 = 2 (1/2) days.
Answer: D
Answer: D
Question: If KING is coded as 17 and MASS is coded as 29 Then DOC is coded as
Options:
A)21
B)20
C)19
D)5
E)None
Rationale: KING = 11+9+14+7=41 i.e (4*4)+(1*1)=17
MASS = 13+1+19+19=52 i.e (5*5)+(2*2)=29
DOC = 4+14+3=21 i.e(2*2)+(1*1)=5
ANSWER:D
Answer: D
Question: The number 130 can be written as the sum of the squares of 2 different positive integers. What is the sum of these 2 integers?
Options:
A) 17
B) 16
C) 15
D) 14
E) 13
Rationale: 11^2 + 3^2 = 130 --> 11 + 3 = 14.
D
Answer: D
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 10 seconds. The speed of the train is?
Options:
A)28
B)50
C)88
D)22
E)12
Rationale: Speed of the train relative to man = (125/10) m/sec = (25/2) m/sec. [(25/2) * (18/5)] km/hr = 45 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5 = 45 ==> x
= 50 km/hr.Answer:B
Answer: B
Question: Which of the options is a two-digit number, which has a unit's digit that exceeds its ten's digit by 4 and the product of the given number and the sum of its digits is equal to 208.
Options:
A)15
B)37
C)55
D)26
E)73
Rationale: Using the elimination method the option that fits this description is 26
6-2 = 4 (unit's digit that exceeds its ten's digit by 3)
26*8 = 208 (the product of the given number and the sum of its digits is equal to 175)
answer :D
Answer: D
Question: Which of the following equations has a root in common with x^2−4x+4=0 ?
Options:
A)x^2-1=0
B)x^2-2=0
C)x^2-3=0
D)x^2-4=0
E)x^2-5=0
Rationale: If we carefully look at the given equation we can arrange it in the following manner:
(x-2)^2= 0
so the two root is 2.
Now put 2 in given equations. The equation in which one of them gives value 0, that will be our answer.
(A) putting 2: we get 3. Reject this option.
(B) putting 2: we get 2. Reject this option.
(C) putting 2: we get 1. Reject this option.
(D) putting 2: we get 0. This is the equation, no need to check other option.
D is the answer.
Answer: D