divelab/Sys2Bench huggingface dataset:
Question: In a division sum, the divisor is ten times the quotient and five times the remainder. If the remainder is 40, the dividend is:
Options:
A)A)5322
B)B)5330
C)C)4040
D)D)5340
E)E)5342
Rationale: Divisor = (5 * 40) = 200
= 10 * Quotient = Divisor
=> Quotient = 200/10 = 20
Dividend = (Divisor * Quotient) + Remainder
Dividend = (200 * 20) + 40 = 4040.
C
Answer: C
Question: How many of the positive factors of 36 , 84 and how many common factors are there in numbers?
Options:
A)2
B)4
C)3
D)5
E)6
Rationale: factors of 36 - 1, 2, 3, 4, 6, 9, 12, 18, 36
factors of 84 - 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Comparing both, we have six common factors of 36 and 84- 1,2,3,4,6,12,
Answer(E)
Answer: E
Question: A train running at the speed of 60 km/hr crosses a pole in 12 sec. What is the length of the train?
Options:
A)120 m
B)200 m
C)324 m
D)Cannot be determined
E)None of these
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 12 = 200 m
ANSWER:B
Answer: B
Question: X and Y started a business with capitals Rs. 20000 and Rs. 25000. After few months Z joined them with a capital of Rs. 30000. If the share of Z in the annual profit of Rs. 50000 is Rs. 14000, then after how many months from the beginning did Z join?
Options:
A)1
B)5
C)6
D)8
E)9
Rationale: Investments of X, Y and Z respectively are Rs. 20000, Rs. 25000 and Rs. 30000
Let investment period of Z be x months.
Ratio of annual investments of X, Y and Z is (20000 * 12) : (25000 * 12) : (30000 * x)
= 240 : 300 : 30x = 8 : 10 : x
The share of Z in the annual profit of Rs. 50000 is Rs. 14000.
=> [x/ (18 + x)] 50000 = 14000 => [x/ (18 + x)] 25 = 7
=> 25x = 7x + (18 * 7) => x = 7 months.
Z joined the business after (12 - 7) months. i.e., 5 months.Answer: B
Answer: B
Question: Which one of the following is not a prime number?
Options:
A)88
B)60
C)73
D)91
E)82
Rationale: D
91
91 is divisible by 7. So, it is not a prime number.
Answer: D
Question: The average of non-zero number and its square is 5 times the number. The number is?
Options:
A)9
B)8
C)6
D)4
E)3
Rationale: Let the number be x. Then,
(x + x2)/2 = 5x => x2 - 9x = 0
=> x(x - 9) = 0
=> x = 0 or x = 9
So, the number is 9.
Answer:A
Answer: A
Question: Out of 7 constants and 4 vowels how many words of 3 consonants and 2 vowels can be formed?
Options:
A)210
B)25000
C)25200
D)250
E)20000
Rationale: Number of ways of selecting (3 consonants out of 7) and (2 vowels out of 4)
= 7C3 * 4C2
= 210
Number of groups each having 3 consonants and 2 vowels = 210
Each group contains 5 letters
Number of ways of arranging 5 letters among themselves
= 5! = (5 * 4 * 3 * 2 * 1)
= 210
Required number of words = (210 * 210)
= 25200
ANSWER C 25200
Answer: C
Question: Pradeep has to obtain 40% of the total marks to pass. He got 200 marks and failed by 20 marks. The maximum marks are
Options:
A)300
B)600
C)550
D)1000
E)900
Rationale: Explanation :
Let their maximum marks be x.
Then, 40% of x = 200 + 20
=>40/100x= 220
x = (22000/40)
x= 550.
Answer : C
Answer: C
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?
Options:
A)87 sec
B)89 sec
C)17 sec
D)18 sec
E)97 sec
Rationale: Speed = 240/24
= 10 m/sec.
Required time
= (240 + 650)/10
= 89 sec.
Answer:B
Answer: B
Question: Consider a right triangle YBC with length of sides being x,y and z where y represents the hypotenuse , Which of these represent the radius of the circle which is inscribed in triangle YBC
Options:
A)[A] x+y+z/3
B)[B] x-y+z/3
C)[C] x-y+z/2
D)[D] (x^2 + y^2 + z^2)/3
E)[E] cannot be determined
Rationale: Radius of a circle inscribed in the right triangle YBC r = (x + z - y)/2 where y is the hypotenuse and x and y are other two sides.
Answer: C
Answer: C
Question: Ram and Shyam have a cube each. Ram paints four faces of cube with red color and rest with blue color. Ram asks Shyam to paint his cube as well with some sides red and some side blue. They now start rolling the cubes simultaneously. After doing this for very long Ram observes that probability of both cubes coming up with same color is 1/3. How many faces of his cube did Shyam paint red ?
Options:
A)0
B)2
C)3
D)4
E)5
Rationale: Explanation :
Let Shyam paints n faces of the cube red. So faces painted blue = (6-n)
Probability that both show up same color is: (probability both show red) + (probability both show blue)
= 4/6 * n/6 + 2/6 * (6-n)/6
= (2n + 6)/18
But as given, (2n + 6)/18 = 1/3 => n = 0
So Shyam hasn't painted any of the face with red color.
Answer : A
Answer: A
Question: CP of 2 buffaloes are $30,000. By selling 1 at a loss of 15% and other at a profit of 19%, he foundthat SP of both buffaloes is the same. Find the CP of each?
Options:
A)$9,500
B)$10,500
C)$11,500
D)$12,000
E)$12,500
Rationale: Let the C.P of 1st buffalo = x
∴C.P of 2nd buffalo = 30,000 - x
S.P of 1st buffalo = ( 100 - loss% )
------------------- x C.P
100
S.P = 100 - 15x
-----------= 85x/ 100
100
S.P of 2nd buffalo = ( 100 - Profit%)
--------------------- x C.P
100
S.P = (100 + 19)(30,000- x) 119(30,000 -x)
-------------------- = ----------------
100 100
S.P of 1st buffalo = S.P of 2nd buffalo
85x/ 100 = 119 ( 30,000 - x)/ 100
⇒ 85x = 119(30,000 - x)
⇒ 85x = 3,570,000 - 119x
⇒ 85x + 119 x = 3,570,000
⇒ 204x = 3,570,000
⇒ x = 3,570,000 / 204
⇒ x = $17,500
C.P of 1st buffalo = $17,500
C.P of 2nd buffalo = 30,000 - 17,500 = $12,500
E
Answer: E
Question: A person goes to his office at 1/3rd of the speed at which he returns from his office. If the avg speed during the whole trip is 12m/h. what is the speedof the person while he was going to his office?
Options:
A)8km/h
B)9km/h
C)10km/h
D)11km/h
E)13km/h
Rationale: u = k , v= 3k
\inline \therefore \frac{2uv}{u+v}\: \: \Rightarrow \frac{2\times k\times 3k}{(k+3k)}=12
\inline \Rightarrow 1.5k = 12
\inline \Rightarrow k=8km/h
A
Answer: A
Question: An unbiased die is tossed.Find the probability of getting a multiple of 3.
Options:
A)1/3
B)1/9
C)1/2
D)7/3
E)1/0
Rationale: Explanation:
Here S = {1,2,3,4,5,6}
Let E be the event of getting the multiple of 3
Then, E = {3,6}
P(E) = n(E)/n(S) = 2/6 = 1/3
Answer: A) 1/3
Answer: A
Question: 1234+123+12+X=1221.Find the value of X.
Options:
A)10
B)148
C)12
D)13
E)189
Rationale: x=1234+123+12-1221
x=148
CORRECT ANSWER : B
Answer: B
Question: One of the below words are odd one out. can you identify it?
first second third forth fifth sixth seventh eighth nine ten eleven twelve thirteen fourteen fifteen sixteen
Options:
A)forth. It should be spelled as fourth
B)4
C)14
D)15
E)16
Rationale: Correct Answer : A
forth. It should be spelled as fourth
Answer: A
Question: Together, 15 type A machines and 7 type B machines can complete a certain job in 4 hours. Together 8 type B machines and 15 type C machines can complete the same job in 11 hours. How many hours T would it take one type A machine, one type B machine, and one type C machine working together to complete the job (assuming constant rates for each machine)?
Options:
A) 22 hours
B) 30 hours
C) 44 hours
D) 60 hours
E) It cannot be determined from the information above.
Rationale: Say the rates of machines A, B and C are a, b, and c, respectively.
Together 15 type A machines and 7 type B machines can complete a certain job in 4 hours --> 15a + 7b = 1/4;
Together 8 type B machines and 15 type C machines can complete the same job in 11 hours --> 8b + 15c = 1/11.
Sum the above: 15a + 15b + 15c = 1/4 + 1/11 = 15/44 --> reduce by 15: a + b + c = 1/44 --> so, the combined rate of the three machines is 1/44 job/hour --> time is reciprocal of the rate, thus machines A, B and C can do the T job in 44 hours.
Answer: C.
Answer: C
Question: The area of a square is equal to five times the area of a rectangle of dimensions 125 cm * 64 cm. What is the perimeter of the square?
Options:
A)287
B)800
C)277
D)299
E)211
Rationale: Area of the square = s * s = 5(125 * 64)
=> s = 25 * 8 = 200 cm
Perimeter of the square = 4 * 200
= 800 cm.
Answer:B
Answer: B
Question: Three cars driven by Mike, Scott and Jenny start driving around a circular race course of length 540m from the same point simultaneously in the same direction at speeds of 9 m/s, 15 m/s and 27 m/s respectively. When will they meet for the first time after they started moving?
Options:
A)180 seconds
B)45 seconds
C)90 seconds
D)60 seconds
E)270 seconds
Rationale: If they all meet after T seconds, it means they covered the distances 9T, 15T, and 27T respectively.
Since they all arrive to the same spot, it means that the differences taken pairwise between the distances must be positive integer multiples of the length of the track, which is 540m. So, 6T, 12T, and 18T must all be multiples of 540. 6T multiple of 540 means T multiple of 90. The smallest T with this property is 90 and is on the list of answers.
Answer C.
Answer: C
Question: If the volume of the cube is 729, then the surface area of the cube will be
Options:
A)486
B)255
C)2866
D)265
E)872
Rationale: Explanation:
\inline \fn_jvn a^3=729; a=9
surface area= (6 x 9 x 9) = 486\inline \fn_jvn cm^2
Answer: A) 486 sq.cm
Answer: A
Question: Ravi can do a piece of work in 24 days while Prakash can do it in 40 days. In how many days will they finish it together?
Options:
A)15
B)16
C)17
D)18
E)10
Rationale: 1/24 + 1/40 = 1/15
15 days
Answer: A
Answer: A
Question: A man whose speed is 4.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 2.5 kmph, find his average speed for the total journey ?
Options:
A)3.1 kmph
B)5 kmph
C)6 kmph
D)4 kmph
E)7 kmph
Rationale: Explanation:
Speed of Man = 4.5 kmph
Speed of stream = 2.5 kmph
Speed in DownStream = 7 kmph
Speed in UpStream = 2 kmph
Average Speed = (2 x 7 x 2)/9 = 3.1 kmph.
Answer: A
Answer: A
Question: The sum of two numbers is 16 and their difference is 4. Find their product.
Options:
A)104
B)114
C)315
D)325
E)60
Rationale: Let the numbers be x and y.
Then x + y = 16 and x - y = 4
x = 10; y = 6
xy = 10 * 6 = 60
ANSWER: E
Answer: E
Question: A driver covers a certain distance by car driving at 40 km/hr and returns back to the starting point riding on a scooter at 10 km/hr. What was the average speed for the whole journey?
Options:
A)12 km/h
B)14 km/h
C)16 km/h
D)18 km/h
E)20 km/h
Rationale: time 1 = d / 40
time 2 = d / 10
total time = d/40 + d/10 = d/8
average speed = total distance / total time = 2d / (d/8) = 16 km/h
The answer is C.
Answer: C
Question: At a certain restaurant, the ratio of the number of cooks to the number of waiters is 3 to 11. When 12 more waiters are hired, the ratio of the number of cooks to the number of waiters changes to 1 to 5. How many cooks does the restaurant have?
Options:
A)4
B)6
C)9
D)12
E)15
Rationale: Originally there were 3k cooks and 11k waiters.
The new ratio is 1:5 which equals 3:15.
15k = 11k+12
k=3
There are 9 cooks.
The answer is C.
Answer: C
Question: A sum of money place at compound interest doubles itself in 4 years. In how many years will it amount to eight times itself?
Options:
A)33
B)77
C)12
D)88
E)11
Rationale: 100 ---- 200 ---- 4
400 ---- 4
800 ---- 4
------
12 years
Answer: C
Answer: C
Question: How long does a train 150 m long running at the speed of 72 km/hr takes to cross a bridge 132 m length?
Options:
A)14.1 sec
B)12.1 sec
C)16.1 sec
D)13.1 sec
E)12.15sec
Rationale: Speed = 72 * 5/18 = 20 m/sec
Total distance covered = 150 + 132 = 282 m.
Required time = 282/20 = 14.1 sec.
Answer:A
Answer: A
Question: The probability of rain showers in Barcelona on any given day is 0.6. What is the probability that it will rain on exactly one out of three straight days in Barcelona?
Options:
A)0.144
B)0.072
C)0.432
D)0.72
E)0.288
Rationale: IMO This is just for first day! It can rain on 2nd day or 3 rd day (and not rain on other days) in 3 consecutive days!
Hence,
0.6*0.4*0.4 + 0.4*0.6*0.4+ 0.4*0.4*0.6 = 0.288
Option - E
Answer: E
Question: How many days are there in x weeks x days ?
Options:
A)7x2
B)8x
C)14x
D)7
E)8
Rationale: Solution
x weeks x days = (7x+x) days = 8x days. Answer B
Answer: B
Question: In year Y imported machine tools accounted for 25 percent of total machine - tool sales in the United States, and Japanese imports accounted for 50 percent of the sales of imported machine tools. If the total sales of machine tools imported Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?
Options:
A)8X/1
B)13X/20
C)80/9X
D)20X/13
E)80X/9
Rationale: IMT = 0.25T
JI = 0.50 IMT
0.50 IMT = $x b
IMT = $x/(0.50) b
T = 4*IMT = 4x/0.50 = 4x*100/50 = 8x/1
Ans: "A"
Answer: A
Question: The average height of 50 pupils in a class is 150 cm. Five of them whose height is 142 cm, leave the class and five others whose average height is 156 cm, join. The new average height of the pupils of the class (in cm) is ?
Options:
A)287 cm
B)151 cm
C)151.4 cm
D)287 cm
E)297 cm
Rationale: Total height = 150 * 50 = 7500 cm.
New average = [7500 - 5 * 142 + 5 * 156 ] / 50
= 151.4 cm.
Answer:C
Answer: C
Question: Juan is a gold medalist in athletics. In the month of May, if Juan takes 10 seconds to run y yards, how many seconds will it take him to run x yards at the same rate?
Options:
A)10x/y
B)11x/y
C)9x/y
D)12x/y
E)13x/y
Rationale: velocity=distance/time;
since he ran at same rate both d tyms,
y/10=x/t
so t=10x/y
ANSWER:A
Answer: A
Question: The average weight of 29 students is 28 kg. By the admission of a new student, the average weight is reduced to 27.8 kg. The weight of the new student is
Options:
A)22 kg
B)21.6 kg
C)22.4 kg
D)21 kg
E)None of these
Rationale: Exp . The total weight of 29 students = 29* 28
The total weight of 30 students = 30* 27.8
Weight of the new student = ( 30*27.8 – 29*28)
= 834 - 812 = 22
Answer:A
Answer: A
Question: On rainy mornings, Mo drinks exactly N cups of hot chocolate (assume that N is an integer). On mornings that are not rainy, Mo drinks exactly 4 cups of tea. Last week Mo drank a total of 42 cups of tea and hot chocolate together. If during that week Mo drank 14 more tea cups than hot chocolate cups, then how many rainy days were there last week?
Options:
A)0
B)4
C)5
D)6
E)7
Rationale: T= the number of cups of tea
C= the number of cups of hot chocolate
T+C = 42 T-C=14 -> T= 28. C=14.
Mo drinks 4 cups of tea a day then number of days that are not rainy = 28/4= 7
So number of rainy days = 7-7 = 0
A is the answer.
Answer: A
Question: 5% people of a village in Sri Lanka died by bombardment, 15% of the remainder left the village on account of fear. If now the population is reduced to 2553, how much was it in the beginning?
Options:
A)2988
B)2776
C)4400
D)2871
E)3162
Rationale: X * (95/100) * (85/100) = 2553
X = 3162
Answer:E
Answer: E
Question: Look at this series: 0.7, 2.1, ____, 18.9, 56.7, ... What number should fill the blank?
Options:
A)6.3
B)5.3
C)6.2
D)6.1
E)4.3
Rationale: This is a simple multiplication series. Each number is 3 times greater than the previous number.
Answer: A
Answer: A
Question: There are 11 software engineers and 7 civil engineers in a company. Theyare selecting member for row. In how many ways can they be seated in a row so that no two of the civil engineers will sit together?
Options:
A)10!×11!/5!
B)9!×11!/4!
C)11!×12!/5! ways
D)9!×5!/4!
E)5!×6!/7!
Rationale: 11 software engineers can be arranged in 11! ways. ...(A)
Now we need to arrange civil engineers such that no two civil engineers can be seated together. i.e., we can arrange 7 civil engineers in any of the 12 (=11+1) positions marked as * below.
* 1 * 2 * 3 * 4 * 5 * 6 * 7 * 8 * 9 * 10 * 11 *
(where 1, 2… 11 represent software engineers)
This can be done in 12P7 ways. ... (B)
From (A) and (B),
required number of ways
= 11! × 12P7
=11!×12!/5!
C
Answer: C
Question: A train 1100 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)200 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, (1100 + x)/60
= 65/3
x = 200 m.
Answer:C
Answer: C
Question: A man had 38 sheep. he wanted to divide them equally among his 6 children. How many sheep shall he keep to himself, so as to equally divide remaining sheep among his 6 children?
Options:
A)6
B)5
C)4
D)2
E)8
Rationale: Since he has 38 sheep and 6 children. The nearest number divisible by 6 is 36. So he would keep 2 sheep for himself and give 6 sheep to each child. So option D is correct.
Answer: D
Question: From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?
Options:
A)624
B)702
C)756
D)812
E)832
Rationale: Total men are 7
Total women are 6 so we select 5 peoples in both and at least 3 are men
7c3*6c2+7c4*6c1+7c5*6c0 then we get the 756
ANSWER:C
Answer: C
Question: How many keystrokes are needed to type numbers from 1 to 1000?
Options:
A)2704
B)2890
C)2893
D)3001
E)None of these
Rationale: 1-9
9 digits
10-99
There are 90 2-digit numbers
(90)(2) = 180 digits
100-999
There are 900 3-digit numbers
(900)(3) = 2700 digits
1000
4 digits
9 + 180 + 2700 + 4 = 2893
Answer: C
Answer: C
Question: If x is an integer, then x(x – 1)(x – k) must be evenly divisible by seven when k is any of the following values EXCEPT
Options:
A)-4
B)-2
C)-1
D)2
E)5
Rationale: We have the product of 3 integers: (x-1)x(x-k).
Note that the product of 3 integers is divisible by 3 if at least one multiple is divisible by 7. Now, to guarantee that at least one integer out of x, (x – 1), and (x – k) is divisible by 7 these numbers must have different remainders upon division by 7, meaning that one of them should have remainder of 1, another reminder of 2 and the last one remainder of 0, so be divisible by 7.
Next, if k=2 then we'll have (x-1)x(x-2)=(x-1)x(x-2) --> which means that (x-1) and (x-2) will have the same remainder upon division by 7. Thus for k=2 we won't be sure whether (x-1)x(x-k) is divisible by 7.
Answer: E.
Answer: E
Question: The ratio, by weight, of coffee to mate to water in a certain cup of coffee is 6:2:15. The coffee is altered so that the ratio of coffee to mate is halved while the ratio of coffee to water is doubled. If the altered coffee will contain 16 grams of mate, how many grams of water does it contain after alteration?
Options:
A)12
B)15
C)30
D)60
E)100
Rationale: c:m:w = 6:2:15
new c:m = 1/2(6/2) = 3:2
new c:w = 2(6:15) = 12:15 = 4:5
so new m:c:w = 2:3
4:5
= 8:12:15 ( notice how i combined the two ratios by multiplication by 3 and 4 of respective ratios)
m = 16 g
Let T = total amount of c + m + w then
8 / (8+12+15)T = 16 x 35/8 = 70g
then w = 15/35 x 70 = 30g
Answer C
Answer: C
Question: A 210 m long train running at the speed of 120 km/hr crosses another train running in opposite direction at the speed of 80 km/hr in 9 sec. What is the length of the other train?
Options:
A)290
B)280
C)270
D)260
E)250
Rationale: Relative speed = 120 + 80 = 200 km/hr.
= 200 * 5/18 = 500/9 m/sec.
Let the length of the other train be x m.
Then, (x + 210)/9 = 500/9 => x = 290.
Answer: Option A
Answer: A
Question: A and B are two multiples of 14, and Q is the set of consecutive integers between A and B, inclusive. If Q contains 10 multiples of 14, how many multiples of 7 are there in Q?
Options:
A)20
B)19
C)18
D)17
E)16
Rationale: Halfway between the multiples of 14, there will be another multiple of 7.
The total number of multiples of 7 is 10+9 = 19.
The answer is B.
Answer: B
Question: The price of stock decreased by 8% last year and rose by 10% this year. What is the net percentage change in the price of the stock?
Options:
A)0.2%
B)0.8%
C)1.2%
D)1.6%
E)2%
Rationale: (100% - 8%) * (100% + 10%) = 0.92 * 1.10 =1.012 = 101.2%.
The net percentage change in the price of the stock is (+) 1.2%
The answer is C
Answer: C
Question: A train is 360 meter long is running at a speed of 50 km/hour. In what time will it pass a bridge of 140 meter length.
Options:
A)26 seconds
B)36 seconds
C)46 seconds
D)56 seconds
E)None of these
Rationale: Explanation:
Speed = 50 Km/hr = 50*(5/18) m/sec
= 125/9 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
=500/125/9 = 36 seconds
Answer: B
Answer: B
Question: Some people went for vacation. unfortunately it rained for 13 days when they were there. But whenever it rained in the morning, they had clean afternoon and vice versa. In all they enjoyed 11 morning and 12 afternoons. How many days did they stay there totally
Options:
A)16 days
B)17 days
C)18 days
D)19 days
E)15 days
Rationale: Whenever it rains, it only rains half a day.... so look at this problem in half days.The family was rained on for 13 {half days}, but they also had 11 + 12 {half days} of sun.So, 13 + 11 + 12 = 36 half days = 18 days
ANSWER:C
Answer: C
Question: 400 students took a mock exam in Delhi, 60% of the boys and 80% of the girls cleared the cut off in the examination. If the total percentage of students qualifying is 65%, how many girls appeared in the examination?
Options:
A)50
B)100
C)120
D)140
E)180
Rationale: 60%*x+80%*(400-x)=65%*400
Ans=100
ANSWER:B
Answer: B
Question: List I: 3, 6, 8, 11
List II: x, 3, 6, 8, 11
Options:
A)5
B)6
C)7
D)8
E)9
Rationale: List I has even number of terms, thus its median is the average of two middle terms (when arranged in ascending/descending order), so median=(6+8)/2=7.
List II has odd number of terms, thus its median is the middle term (when arranged in ascending/descending order). As no other number in the list equal to 7, then x=7.
Answer: C.
Answer: C
Question: Solve the quickfire maths brain teaser âˆš16% = ?
Options:
A)30%
B)40%
C)85%
D)19%
E)29%
Rationale: âˆš16%
=> âˆš16/âˆš100
=> 4/10
=> 40/100
=> 40%
B
Answer: B
Question: In how many ways letters of the word LEADER be arranged?
Options:
A)5
B)78
C)69
D)58
E)120
Rationale: LEADER has 6 letters, out of which E repeated 2 times. Hence total ways = 6! / (2!) = 120 ways
E
Answer: E
Question: If S is the sum of the reciprocals of the consecutive integers from 91 to 100, inclusive, which of the following is less than S?
I. 1/8
II. 1/10
III. 1/11
Options:
A)None
B)I only
C)III only
D)II and III only
E)II only
Rationale: Since we summarize the reciprocals from 100 to 91, we can say also that we add ten numbers who are all (with one exception 1/100) greater than 1/100, so that the sum must be greater than 1/10.
On the other side we can say that we add the reciprocals from 91 to 100, so that the sum has to be less than the sum of ten times 1/91.
We can conclude that the sum has to be less than 1/9 but more than 1/10. That leaves us E as the only possible answer.
Answer: E
Question: If x = y+3+4.5x and y = x+24, what is the value of x/y ?
Options:
A)-6/5.
B)-7/20.
C)-1/2.
D)5/6.
E)1.5.
Rationale: (1) x = y + 3 + 4.5x
Substitute y for y = x + 24 (Eq. we are given)
x = x + 24 + 3 + 4.5x
Combine like terms
x = 5.5x + 27 --> -4.5x = 27--> x = -6
(2) y = x + 18
Substitute x for x = -6
y = (-6) + 18 = 12
(3) x/y = ?
Substitute x and y we found above
x/y = (-6) / (12) = -1/2
My answer: C
Answer: C
Question: For 2consecutive yrs, my incomes are in the ratio of 4:7 and expenses in the ratio of 3:5. If my income in the 2nd yr is Rs. 42000 & my expenses in the first yr in Rs.21000, my total savings for the two-year is
Options:
A)Rs. 9000
B)Rs. 9800
C)Rs. 9900
D)Rs. 9990
E)Rs. 10000
Rationale: Sol. Income in first year = * x 42000 = Rs. 24000
Expenses in second year = \ x 21000 = Rs. 35000 Total savings = Total income - Total expenses = (42000 + 24000)- (21000 + 35000)
= 66000 - S6000 = Rs. 10000
E
Answer: E
Question: If a2 - b2 = 5 and a*b = 2, find a4 + b4.
Options:
A)50
B)72
C)25
D)92
E)33
Rationale: a2 - b2 = 5 : given
a4 + b4 - 2a2b2 = 52 : square both sides and expand.
a*b = 2 : given
a2b2 = 22 : square both sides.
a4 + b4 - 2(4) = 25 : substitute
a4 + b4 = 33
correct answer E
Answer: E
Question: 8 red card number 1-8 put in one box， 8 blue card number 1-8，put in another box, take one card from each of the box，what is the probability that the number match each other?
Options:
A)1/2
B)1/4
C)1/8
D)1/16
E)1/64
Rationale: Probability to pick a number from the first box - any of the 8 = 1..
prob to pick the same number from the 2nd box = 1/8..
Prob = 1∗1/8=1/8
Answer:C
Answer: C