divelab/Sys2Bench huggingface dataset:
Question: What is the present worth of Rs. 187 due in 2 years at 5% simple interest per annum?
Options:
A)288
B)266
C)120
D)277
E)170
Rationale: Let the present worth be Rs. x. Then,
S.I. = (187 - x)
(x * 5 * 2) / 100 = (187 - x)
10x = 18700 - 100x
110x = 18700 => x = 170.
Answer: E
Answer: E
Question: If a real number x is chosen at random in the interval [0,5] and a real number y is chosen at random in the interval [0,6], what is the probability that x < y?
Options:
A)2/3
B)3/5
C)5/12
D)7/12
E)11/15
Rationale: Since x is in [0,5] and y is in [0,6] we can draw a rectangle in the coordinate plane with vertices (0, 0), (5, 0), (0, 6), and (5, 6).
The points above the line y=x satisfy x < y.
The part of the rectangle below y=x has an area of 12.5
The whole rectangle has an area of 30.
P(x < y) = (30-12.5)/30 = 17.5/30 = 35/60 = 7/12
The answer is D.
Answer: D
Question: In a certain boys camp, 20% of the total boys are from school A and 30% of those study science. If there are 49 boys in the camp that are from school A but do not study science then what is the total number of boys in the camp?
Options:
A)70
B)245
C)150
D)35
E)350
Rationale: Since 30% of the boys from school A study science, then 70% of the boys from school A do NOT study science and since 20% of the total number of boys are from school A, then 0.2*0.7 = 0.14, or 14% of the boys in the camp are from school A and do not study science.
We are told that this number equals to 49, so 0.14*{total} = 49 --> {total} = 350.
Answer: E.
Answer: E
Question: A merchant purchased a jacket for $54 and then determined a selling price that equalled the purchase price of the jacket plus a markup that was 40 percent of the selling price. During a sale, the merchant discounted the selling price by 20 percent and sold the jacket. What was the merchant’s gross profit on this sale?
Options:
A) $0
B) $3
C) $4
D) $12
E) $18
Rationale: Actual Cost = $54
SP = Actual Cost + Mark up
= Actual Cost + 40% SP
= 54*100/60
on sale SP = 80/100(54*100/60) = 72
Gross profit = $18
Answer is E
Answer: E
Question: On the xy co-ordinate plane, point C is (3,-2) and point D is (-1,2.5). The point on line segment CD that is twice as far from C as from D is:
Options:
A)(1,-1)
B)(1,1)
C)(2,0.25)
D)(3,0.5)
E)(3,1)
Rationale: We want the point on the line that is twice as far from C as it is from D. We can examine the x and y coordinates separately since they are independent.
*It should be noted that there are two solutions to this problem, one point between C and D, and another point with D in the middle of C and the point. We can quickly look at the answer choices and see that all the points are between C and D, therefore we can search for that point using the following method:
Taking the x-coordinate first, the distance between C and D is |(x-coordinate of C) - (x-coordinate of D)|= |5 - (-1)| = 6
The x-coordinate that is twice as far from C as it is from D (and in between C and D) will be 4 units from C and 2 units from D. So the x coordinate of the point we're looking for is 5-4 = 1, or (-1)+2 = 1.
Now looking at the y-coordinate, we do the same thing. The distance between C and D is |(-2) - 2.5| = 4.5
The y-coordinate that is twice as far from C as it is from D (and in between C and D) will be 3 units from C and 1.5 units from D. So the y coordinate of the point we're looking for is (-2)+3 = 1, or 2.5-1.5 = 1.
So now we have our coordinates of the point on the line that is twice as far from C as it is from D: (3,0.5)
Answer: D
Answer: D
Question: A batsman makes a score of 87 runs in the 17th inning and thus increases his avg by 3. Find his average after 17th inning.
Options:
A)24
B)52
C)39
D)36
E)85
Rationale: Sol. Let the average after 17th inning = x.
Then, average after 16th inning = (x - 3).
16 (x - 3) + 87 = 17x or x = (87 - 48) = 39.
Ans: C
Answer: C
Question: There are 7 books on a shelf, of which 2 are paperbacks and 5 are hardbacks. How many possible selections of 4 books from this shelf include at least one paperback?
Options:
A)a) 30
B)b) 45
C)c) 50
D)d) 55
E)e) 60
Rationale: approach 1
at-least 1 paper back = total - no paper back
7c4-5c4 = 30
approach 2
at-least 1 paper back = 1 paper back , 3 hard back or 2 paper back 2 hard back
= 2c1*5c3+2c2*5c2 = 30
Answer is A
Answer: A
Question: If 4 men can color 48 m long cloth in 2 days, then 6 men can color 36 m long cloth in
Options:
A)2 days
B)1 day
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.
B
Answer: B
Question: Given a set of numbers {5,6,7,8,9,10}, what is the probability that is two numbers are selected randomly that their sum will be greater than 12?
Options:
A)13/15
B)9/12
C)13/12
D)13/11
E)13/16
Rationale: First problem is 6C2 = 12 .. Not 20..
Point 2, your sum should be greater than 12, so these are the following possibilities you have
({5,8},{5,9},{5,10},{6,7},{6,8},{6,9},{6,10},{7,8},{7,9},{7,10},{8,9},{8,10},{9,10}) which leads to 13 pairs
So the probability is 13 on 12 or 13/12..
ANSWER:C
Answer: C
Question: If x/y = 7/3, then (x + y)/(x - y) = ?
Options:
A)5
B)5/2
C)-1/6
D)-1/5
E)-5
Rationale: Any x and y satisfying x/y = 7/3 should give the same value for (x + y)/(x - y).
Say x=7 and y=3, then (x + y)/(x - y) = (7 + 3)/(7-3) = 5/2.
Answer: B.
Answer: B
Question: If the sum of three consecutive even numbers is 50 more than the average of these numbers, then the largest of these numbers is?
Options:
A)20
B)24
C)22
D)26
E)27
Rationale: Explanation:
Let the smallest of these number be x. The other two numbers are (x + 2) and (x + 4).
x + (x + 2) + (x + 4) = (X + (X+2) + (x+4)) / 3 + 50
3x + 3*(x + 2) + 3*(x + 4) = x + (x + 2) + (x + 4) + 150
9x + 18 = 3x + 156
6x = 138
x = 23
Therefore, the largest number is 27.
ANSWER E
Answer: E
Question: In one hour, a boat goes 7 km along the steram and 5 km against the stream. The speed of the boat in still waer (in km/hr) is:
Options:
A)2
B)4
C)6
D)12
E)15
Rationale: Sol.
Speed in still water = 1/2 (7+5) kmph = 6 kmph.
Answer C
Answer: C
Question: A contest will consist of n questions, each of which is to be answered eithertrueorfalse. anyone who answers all n questions correctly will be a winner. what is the least value of n for which the probability is less than 1/10 that a person who randomly guesses the answer to each question will be a winner?
Options:
A)5
B)10
C)50
D)100
E)1000
Rationale: A contest will consist of n questions, each of which is to be answered eithertrueorfalse. anyone who answers all n questions correctly will be a winner. what is the least value of n for which the probability is less than 1/1000 that a person who randomly guesses the answer to each question will be a winner?
A.5
B.10
C.50
D.100
E.1000
Soln: ans is B
Probability that one question is answered right is 1/2.
Now for minimum number of questions needed to take probability less than 1/1000 is
=> (1/2)^n < 1/1000
n = 10 satisfies this.
D
Answer: D
Question: In a colony of 70 resident s, the ratio of the number of men and women is 4:3. Among the women, the ratio of the educated to the uneducated is 1:4. If the ratio of the number of education to uneducated persons is 8:27, then find the ratio of the number of educated and uneducated men in the colony?
Options:
A)1:9
B)1:6
C)1:3
D)1:1
E)1ratio 3
Rationale: Number of men in the colony = 4/7 (70) = 40
Number of women in the colony = 3/7 (70) = 30
Number of educated women in the colony = 1/5 (30) = 6
Number of uneducated women in the colony = 4/5 (30) = 24
Number of educated persons in the colony = 8/35 (70) = 16
As 6 females are educated, remaining 10 educated persons must be men.
Number of uneducated men in the colony = 40 - 10 = 30
Number of educated men and uneducated men are in the ratio 10:30 => 1:3
Answer: E
Answer: E
Question: A card is drawn from a pack of 52 cards. The probability of not getting a face card?
Options:
A)9/13
B)5/12
C)3/13
D)6/17
E)1/13
Rationale: Clearly in the 52 cards other than face cards = 52-16 = 36
probability of not getting a face card = 36/52 = 9/13
correct option is A
Answer: A
Question: How many 3-digit positive integers are there, where each digit is positive, and no 3 adjacent digits are same?
Options:
A)1236
B)504
C)4096
D)4608
E)6561
Rationale: First digit.. 9 posibilities
Second digit, 8 possibilities
third digit, 7 possibilities
9*8*7 = 504.
B
Answer: B
Question: Starting from his house one day, a student walk at a speed of 2 kmph and reaches his school 10 minutes late. Next he increased his speed by 1 kmph and reaches the school 10 minutes early. How far is the school from his house?
Options:
A)1km
B)2km
C)3km
D)4km
E)5km
Rationale: Let the distance be x km
Difference in timings = 20 min = 20/60 = 1/3 hr
x/2-x/3 = 1/3
x = 2km
Answer is B
Answer: B
Question: Calculate how many seconds it eill take for 4 bells to toll together again, given that they begin to toll together respectively at the intervals of 2, 5, 8 and 11 seconds. ?
Options:
A)440
B)420
C)410
D)442
E)422
Rationale: LCM of 2, 5, 8 and 11 is
440
LCM=440
ANSWER:A
Answer: A
Question: When two dice are tossed, what is the probability that the total score is a prime number?
Options:
A)1/6
B)3
C)5/12
D)7/12
E)9/12
Rationale: Total number of outcomes possible=36
probability of total score is a prime number=15
P(E) =15/36=5/12
ANSWER:C
Answer: C
Question: The compound interest earned by Sunil on a certain amount at the end of two years at the rate of6% p.a. was Rs.370.80. Find the total amount that Sunil got back at the end of two years in the form of principal plus interest earned.
Options:
A)Rs.3360.80
B)Rs.3370.80
C)Rs.3320.70
D)Rs.3230.80
E)Rs.3130.80
Rationale: Let the sum be Rs.P
P{ [ 1 + 6/100]2 - 1 } = 370.80
P(6/100)(2 +6/100) = 370.80 [a2 - b2 = (a - b) ( a + b)] P = 246 / (0.05)(2.05) = 3000. Amount =Rs.3370.80. Answer :B
Answer: B
Question: A team has to design a flag. The team has six blue strips of cloth and seven red strips of cloth that they must use as is to make the flag. How many different flags can the team design with the materials at hand?
Options:
A)42
B)120
C)720
D)1,716
E)5,040
Rationale: The # of permutations of total 6+7=13 strips where 6 are identical blue and 7 are identical red is 13!/(6!*7!)=1716 (note that they must use all the materials at hand, also I guess that the strips must be either only vertical or only horizontal).
Answer: D.
Answer: D
Question: The area of a rhombus is equal to the area of a rectangle whose length is 20cm and the breadth is 10cm. If one of the diagonals is 32cm what is the length of other diagonal?
Options:
A)10
B)12.5
C)15
D)16
E)17.5
Rationale: Area of rectangle=20x10=200cmÂ²
Let 'l' the length of other diagonal = 0.5x32xl = 200
which gives x=12.5cm
Answer: B
Answer: B
Question: An investor bought a 1-year $6,000 certificate of deposit that paid interest at an annual rate of 8 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?
Options:
A)$480
B)$489.60
C)$634.64
D)$800.32
E)$240
Rationale: 1.04*1.04*6000 = $6489.60
The answer is B.
Answer: B
Question: A boat takes 19 hours for travelling downstream from point A to point B and coming back to a point C midway between A and B. If the velocity of the stream is 4 kmph and the speed of the boat in still water is 14 kmph, what is the distance between A and B ?
Options:
A)160 km
B)180 km
C)200 km
D)220 km
E)None
Rationale: Solution
Speed Downstream	= (14 + 4) km/hr
= 18 km/hr.
Speed upstream	=(14 - 4) km/hr
= 10 km/hr..
Let the distance b/w A and B
be xkm.Then	=(x/18+ x/2 / 10)
= 19
= 19x / 180 = 19
x= 180.
Answer B
Answer: B
Question: The distance between two towns is 380 km. At the same moment, a passenger car and a truck start moving towards each other from different towns. They meet 4 hours later. If the car drives 5 km/hr faster than the truck, what are their speeds?
Options:
A)50 and 45
B)45 and 50
C)30 and 35
D)35 and 30
E)40 and 50
Rationale: The main idea used in this kind of problems is that the distance equals speed multiplied by time S=V⋅t
V (km/hr) t (hr) S (km)
Car x + 5 4 4(x +5)
Truck X 4 4x
4(x+5)+4x=380
4x+4x=380−20
8x=360
x=3608
x=45
Therefore the truck's speed is 45 km/hr, and the car's speed is 50 km/hr.
So answer is B.
Answer: B
Question: Fred can fill K cans of water in 5 minutes. If there are T cans of water in one gallon, how many gallons can Fred fill in 35 minutes?
Options:
A)7K/T
B)7KT
C)7T/K
D)35KT
E)35T/K
Rationale: Fred can fill this number of cans in 35 minutes: (35/5)K = 7K.
One can is 1/T gallons.
Fred can fill 7K*(1/T) = 7K/T gallons of water in 35 minutes.
The answer is A.
Answer: A
Question: The speeds of three asteroids were compared. Asteroids X-13 and Y-14 were observed for identical durations, while asteroid Z-15 was observed for 2 seconds longer. During its period of observation, asteroid Y-14 traveled three times the distance X-13 traveled, and therefore Y-14 was found to be faster than X-13 by 8000 kilometers per second. Asteroid Z-15 had an identical speed as that of X-13, but because Z-15 was observed for a longer period, it traveled five times the distance X-13 traveled during X-13's inspection. Asteroid X-13 traveled how many kilometers during its observation?
Options:
A)500
B)1,600/3
C)1,000
D)1,500
E)2,000
Rationale: X13: (t, d, s)
Y14: (t, 3d, s+8000mi/hour)
Z15: (t+2 seconds, s, 5d)
d=?
Distance = Speed*Time
x13: d = s*t
x14: 3d = (s+8000)*t ===> 3d = ts+8000t
z15: 5d = s*(t+2t) ===> 5d = st+2st ===> 5d - 2st = st
3d = 5d - 2st + 8000t
-2d = -2st + 8000t
2d = 2st - 8000t
d = st -4000t
x13: d = s*t
st - 4000t = s*t
s - 4000 = s
-2000 = s
I got to this point and couldn't go any further. This seems like a problem where I can set up individual d=r*t formulas and solve but it appears that's not the case. For future reference how would I know not to waste my time setting up this problem in the aforementioned way? Thanks!!!
The distance of Z15 is equal to five times the distance of X13 (we established that x13 is the baseline and thus, it's measurements are d, s, t)
S(T+2) = 5(S*T)What clues would I have to know to set up the equation in this fashion? Is it because I am better off setting two identical distances together?
ST+2S = 5ST
T+2 = 5T
2=4T
t= 1/2
We are looking for distance (d=s*t) so we need to solve for speed now that we have time.
Speed y14 - speed x13
Speed = d/t
3d/t - d/t = 8000 (remember, t is the same because both asteroids were observed for the same amount of time)
2d = 8000
2 = 4000
d=s*t
d=4000*(1/2)
d=2000
ANSWER: E
Answer: E
Question: Two trains are moving in the same direction at 72 kmph and 36 kmph. The faster train crosses a man in the slower train in 7 seconds. Find the length of the faster train?
Options:
A)70
B)20
C)30
D)75
E)15
Rationale: Relative speed = (72 - 36) * 5/18 = 2 * 5 = 10 mps.
Distance covered in 27 sec = 7 * 10 = 70 m.
The length of the faster train = 70 m.
Answer: A
Answer: A
Question: A lady grows Cauliflower in her garden that is in the shape of a square. Each Cauliflower takes 1 square foot of area in her garden. This year, she has increased her output by 401 Cauliflower when compared to last year. The shape of the area used for growing the Cauliflower has remained a square in both these years. How many Cauliflowers did she produce this year?
Options:
A)44001
B)44000
C)40400
D)40401
E)Cannot be determined
Rationale: Explanatory Answer
The shape of the area used for growing Cauliflower has remained a square in both the years.
Let the side of the square area used for growing Cauliflower this year be X ft.
Therefore, the area of the ground used for cultivation this year = X2 sq.ft.
Let the side of the square area used for growing Cauliflower last year be Y ft.
Therefore, the area of the ground used for cultivation last year = Y2 sq.ft.
As the number of Cauliflower grown has increased by 401, the area would have increased by 401 sq ft because each Cauliflower takes 1 sq ft space.
Hence, X2 - Y2 = 401
(X + Y)(X - Y) = 401.
401 is a prime number and hence it will have only two factors. i.e., 401 and 1.
Therefore, 401 can be expressed as product of 2 numbers in only way = 401* 1
i.e., (X + Y)(X - Y) = 401 * 1
So, (X + Y) should be 401 and (X - Y) should be 1.
Solving the two equations we get X = 201 and Y = 200.
Therefore, number of Cauliflower produced this year = X2 = 2012 = 40401
Alternative Approach : Use answer choices
The area in both the years are squares of two numbers.
That rules out choice A,B and C . as 44001,44000 and 40400 are not the square of any number.
Check Choice D: If this year's produce is 40401, last year's produce would have been 40401- 401= 40000
40000 is the square of 200.
So, 40401 is the answer.
Choice D.
Answer: D
Question: An workshop has 6 employees; there are 5 female employees and 1 male employee. In how many ways can a 3-person committee be created if the committee must include the male employee?
Options:
A)10
B)12
C)15
D)24
E)30
Rationale: An workshop has 6 employees;for male 1C1 = 1 ........ A
foe female = 5C2 = 10.........B
total = 10*1
= 10 - answer=A
Answer: A
Question: haresh went to buy fruits.she bought 1 apple , 3 bananas , 5 oranges and paid 21 rupees.another person bought 7 apple ,5 bananas , 3 oranges and paid 51 rupees.if i want to buy 1 apple, 1 banana , 1 orange then how much i have to pay?
Options:
A)8
B)9
C)10
D)11
E)7
Rationale: There can be multiple possible rates of apple, banana and orange to satisfy given conditions, But cost of 1 apple, 1 banana , 1 orange will be Rs 9.
1x+3y+5z = 21........(1)
7x+5y+3z = 51........(2)
Adding (1) and (2), we get
8x+8y+8z = 72
8*(x+y+z)=72
x+y+z=9
ANSWER:B
Answer: B
Question: The speed of a boat in still water is 8km/hour. If it can travel 1 km upstream in 1 hourr, what time it would take to travel the same distance downstream?
Options:
A)2 minutes
B)4 minutes
C)6 minutes
D)7 minutes
E)8 minutes
Rationale: Speed of the boat in still water = 8 km/hr
Speed upstream =11 = 1 km/hr
Speed of the stream = 8-1 = 7 km/hr
Speed downstream = (8+7) = 15 km/hr
Time taken to travel 1 km downstream =115 hr = 1×6015= 4 minutes
B
Answer: B
Question: A dog is tied to a tree by a long nylon cord. If the dog runs from the due North side of the tree to the due South side of the tree with the cord extended to its full length at all items, and the dog ran approximately 30 feet, what was the approximate length of the nylon cord, in feet?
Options:
A)30
B)25
C)15
D)10
E)5
Rationale: Because the cord was extended to its full length at all items, the dog ran along a semi-circular path, from north to south.
The circumference of a full circle is 2*pi*r, but since we only care about the length of half the circle, the semi-circle path is pi*r.
pi*r = 30. Round pi = 3, then r = 10.
Chord is about 10 feet long
ANSWER:D
Answer: D
Question: X can finish a work in 21 days. Y can finish the same work in 15 days. Y worked for 5 days and left the job. how many days does X alone need to finish the remaining work?
Options:
A)12
B)13
C)16
D)14
E)18
Rationale: Work done by X in 1 day = 1/21
Work done by Y in 1 day = 1/15
Work done by Y in 5 days = 5/15 = 1/3
Remaining work = 1 – 1/3 = 2/3
Number of days in which X can finish the remaining work = (2/3) / (1/21) = 14
D
Answer: D
Question: During the first two weeks of January, the total rainfall in Springdale was 30 inches. If the rainfall during the second week was 1.5 times the rainfall during the first week, what was the rainfall during the second week of January?
Options:
A)5 inches
B)6 inches
C)9 inches
D)10 inches
E)18 inches
Rationale: Total rainfall in 2 weeks = 18 inches.
Assume the rainfall in second week = 1.x
Rainfall in first week = x
Total rainfall = 2.5x = 18 inches
x = 12 and 1.5x = 18
Rainfall during second week = 18 inches
Option E
Answer: E
Question: The least number which when divided by 4, 6, 7 and 8 leaves a remainder 6, but when divided by 9 leaves no remainder, is
Options:
A)340
B)342
C)523
D)363
E)None of these
Rationale: Explanation:
L.C.M of 4, 6, 7, 8 = 168
therefore Required Number is of the form 168k+6.
Least value of k for which (168k+6) is divisible by 9 is k = 2
therefore Required Number = (168 x 2+6)=342. Answer: B
Answer: B
Question: Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.
Options:
A) $ 165
B) $ 145
C) $ 175
D) $ 180
E) $ 170
Rationale: Let the 1st paycheck be x (integer).
Mrs. Rodger got a weekly raise of $ 145.
So after completing the 1st week she will get $ (x+145).
Similarly after completing the 2nd week she will get $ (x + 145) + $ 145.
= $ (x + 145 + 145)
= $ (x + 290)
So in this way end of every week her salary will increase by (B)$ 145.
Answer: B
Question: A fair price shopkeeper takes 10% profit on his goods. He lost 20% goods during theft. His loss percent is:
Options:
A)8
B)10
C)11
D)12
E)13
Rationale: Explanation:
Suppose he has 100 items. Let C.P. of each item be Re. 1.
Total cost = Rs. 100. Number of items left after theft = 80.
S.P. of each item = Rs. 1.10
Total sale = 1.10 * 80 = Rs. 88
Hence, loss % = 12/100 * 100 = 12%
Answer is D
Answer: D
Question: An amount of money is to be divided between P, Q and R in the ratio of 3:7:12. If the difference between the shares of P and Q is Rs.2400, what will be the difference between Q and R's share?
Options:
A)3009
B)3000
C)3002
D)3001
E)3005
Rationale: 4 --- 2000
5 --- ? => 3000
Answer: B
Answer: B
Question: If the sides of a triangle are 91 cm, 84 cm and 35 cm, what is its area?
Options:
A)120 cm2
B)1470 cm2
C)216 cm2
D)197 cm2
E)275 cm2
Rationale: The triangle with sides 91 cm, 84 cm and 35 cm is right angled, where the hypotenuse is 91 cm.
Area of the triangle
= 1/2 * 84 * 35
= 1470 cm2
Answer: B
Answer: B
Question: Little John had $10.50. He spent $2.25 on sweets and gave to his two friends $2.20 each. How much money was left?
Options:
A)$1.85
B)$ 3.85
C)$4.85
D)$6.85
E)$5.85
Rationale: John spent and gave to his two friends a total of
2.25 + 2.20 + 2.20 = $6.65
Money left
10.50 - 6.65 = $3.85
correct answer is B) $ 3.85
Answer: B
Question: (√112+√567)/√175=?
Options:
A)2√2
B)13/5
C)3√2
D)3√3
E)√2
Rationale: (√112+√567)/√175=(4√7+9√7)/5√7
=13/5
Hence, the correct answer is B.
Answer: B
Question: When a metallic ball bearing is placed inside a cylindrical container, of radius 2 cm, the height of the water, inside the container, increases by 0.6 cm. The radius, to the nearest tenth of a centimeter, of the ball bearing is
Options:
A)1 cm
B)1.2 cm
C)2 cm
D)0.6 cm
E)None
Rationale: Solution
When the ball was put in water, the volume of water increased by.
pi*22*0.6 = 2.4 pi cubic cm
The above volume is equal to the volume of the ball with radius r to find. Hence
(4/3)*pi*r3 = 2.4 pi
Solve the above for r
r = 1.2 cm
Answer B
Answer: B
Question: What is the least number that should be added to 1054, so the sum of the number is divisible by 23?
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: (1054 / 23) gives a remainder 19 so we need to add 4.
The answer is D.
Answer: D
Question: The vertices of a rectangle in the standard (x,y) coordinate place are (0,0), (0,4), (9,0) and (9,4). If a line through (1,1) partitions the interior of this rectangle into 2 regions that have equal areas, what is the slope of this line?
Options:
A)1/5
B)2/7
C)3/8
D)2/9
E)1/4
Rationale: We should know that a rectangle can be divided into two equal areas by a straight line only when the straight line passes through the center of the rectangle.
The center of the rectangle is the point (4.5,2).
The slope of line passing through points (1,1) and (4.5,2) = (2-1)/(4.5-1) = 1/3.5 = 2/7
The answer is B.
Answer: B
Question: A batsman makes a scores of 98 runs in his 19th inning and thus increases his average by 4. What is his average after 19th inning ?
Options:
A)22
B)24
C)28
D)26
E)None of the above
Rationale: Let the average score of 19 innings be x.
Then, 18x+98/19=x+4
The average score after 20th innings
= x + 4 = 22 + 4 = 26
Answer D
Answer: D
Question: 0.1+0.1^2+0.1^3 =
Options:
A) 0.1
B) 0.111
C) 0.1221
D) 0.2341
E) 0.3
Rationale: You have a mistake in your question. Choice B should be (.111) and not (.11).
The equation in the solution can be simplified to (.1 + .01 + .001).
Adding those together you get:
.100
.010
.001
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.111 - Which is answer choice (B)
Answer: B