divelab/Sys2Bench huggingface dataset:
Question: One root of the quadratic equation x2 - 12x + a = 0, is thrice the other. Find the value of a?
Options:
A)29
B)-27
C)28
D)7
E)None of these
Rationale: Let the roots of the quadratic equation be x and 3x.
Sum of roots = -(-12) = 12
a + 3a = 4a = 12 => a = 3
Product of the roots = 3a2 = 3(3)2 = 27.
ANSWER:E
Answer: E
Question: Find the angle between the hour hand and the minute hand of a clock when 3.25.
Options:
A)47 1/2°
B)45 1/2°
C)48 1/2°
D)46 1/2°
E)42 1/2°
Rationale: angle traced by the hour hand in 12 hours = 360°
Angle traced by it in three hours 25 min (ie) 41/12 hrs=(360*41/12*12)° =102 1/2°
angle traced by minute hand in 60 min. = 360°.
Angle traced by it in 25 min. = (360 X 25 )/60= 150°
Required angle = 1500 – 102 1/2°= 47 1/2°
Answer is A.
Answer: A
Question: A rectangular rug with side lengths of 2 feet and 6 feet is placed on a square floor that has an area of 65 square feet. If the surface of the rug does not extend beyond the area of the floor, what fraction of the area of the floor is not covered by the rug?
Options:
A)A.3/16
B)1/4
C)C.1/2
D)53/65
E)7/8
Rationale: Area of the rectangular rug = 2*6 = 12
Fraction not covered by the rug = (Total Area - Rug area) / Total Area
= (65 - 12)/65
= 53/65=D
Answer: D
Question: The cross-section of a cannel is a trapezium in shape. If the cannel is 10 m wide at the top and 6 m wide at the bottom and the area of cross-section is 640 sq m, the depth of cannel is?
Options:
A)34
B)97
C)37
D)80
E)22
Rationale: 1/2 * d (10 + 6) = 640
d = 80
Answer: D
Answer: D
Question: 2 hours after train A leaves Lucknow a train B leaves the same stationtraveling in the same direction at an average speed of 16 km/hr. After traveling 6 hrsthe train B overtakes the train A. What is the average speed of the train A?
Options:
A)12 km/hr
B)16.5 km/hr
C)17 km/hr
D)18 km/hr
E)None of these
Rationale: Explanation :
Total distance covered by B=16*6=96kmTotal time taken by A to cover same distance=2+6=8 hrsaverage speed of A=96/8=12 km/hr
Answer : A
Answer: A
Question: A trader sells 85 meters of cloth for Rs. 8500 at the profit of Rs. 15 per metre of cloth. What is the cost price of one metre of cloth?
Options:
A)Rs. 80
B)Rs. 85
C)Rs. 90
D)Rs. 95
E)None of these
Rationale: SP of 1m of cloth = 8500/85 = Rs. 105
CP of 1m of cloth = SP of 1m of cloth - profit on 1m of cloth
= Rs. 100 - Rs. 15 = Rs. 85.
ANSWER:B
Answer: B
Question: How much more would Rs.15000 fetch, after two years, if it is put at 20% p.a. compound interest payable half yearly than if is put at 20% p.a. compound interest payable yearly?
Options:
A)A)Rs.3,961.50
B)B)Rs.3,962.50
C)C)Rs.3,963.50
D)D)Rs.3,964.50
E)E)Rs.3,965.50
Rationale: 15000(11/10)4 - 15000(6/5)2 = 3,961.50
ANSWER:A
Answer: A
Question: Tough and Tricky questions: Word Problems.
A salesman's income consists of commission and base salary. His weekly income totals over the past 7 weeks have been $406, $413, $420, $436, $395, $410, $360. What must his average (arithmetic mean) income over the next two weeks be to increase his average weekly income to $500 over the 9-week period?
Options:
A)$570
B)$790
C)$630
D)$830
E)$715
Rationale: OFFICIAL SOLUTION:
(D) First, we need to add up the wages over the past 7 weeks: $406 + $413 + $420 + $436 + $395 + $410 + $360 = $2840.
To average $500 over 9 weeks, the salesman would need to earn: $500 × 9 = $4500.
Subtract $2840 from $4500 to determine how much he would need to earn, in total, over the next 2 weeks to average $500 for the 9 weeks: $4500 – $2840 = $1660.
Dividing $1660 by 2 will give us the amount he needs to earn on average over the next 2 weeks: $1660/2 = $830.
The correct answer is choice (D).
Answer: D
Question: A student was asked to find the arithmetic mean of the numbers 13,31,78,92,115,103,68,10,57,21,34 and a. He found the mean to be 60. What should be the remainder in the place of a?
Options:
A)98
B)105
C)120
D)165
E)132
Rationale: We have (13+31+78+92+115+103+68+10+57+21+34+a) / 12 = 60
622+a= 720
a = 98
Answer is A
Answer: A
Question: How many 5 letter combinations can be made from the letters of the word VERMONT if the first letter has to be a vowel and the last letter has to be a vowel, and each letter can be used only once?
Options:
A)21
B)42
C)120
D)600
E)720
Rationale: Vowel: E O
Consonants: V R M N T
First letter can be filled in 2 Ways ( As the question states that first letter has to be a vowel)
Fifth letter can be filled in 1 Ways ( As the question states that the last letter has to be a vowel)
Now since each letter can be used only once, and 2 letters out of 7 letters are already used in First and Fifth letter
Second letter can be filled in 5 Ways
Third letter can be filled in 4 Ways
Fourth letter can be filled in 3 Ways
So, Total number of ways = 2 Ways x 5 Ways x 4 ways x 3 ways x 1 ways = 120
Answer C
Answer: C
Question: Average of 80 numbers are 42. When 5 more numbers are included, the average of 85 numbers become 45. Find the average of 5 numbers.
Options:
A)82
B)89
C)93
D)98
E)69
Rationale: Solution: Total of 80 numbers = 80*42 = 3360;
Now, total of 85 numbers = 85*45 = 3825;
Hence, sum of 5 numbers = 3825-3360 = 465;
Average of five numbers = 465/5 = 93.
Solve while reading Method:
Average of 80 number was 42, when 5 more numbers are added average become 45, that means 3 is given to each number to make their average 45 and 5 numbers also keep 45 as to maintain the entire average.
So, the sum of five numbers = 240+225 = 465,
Hence, average of five numbers = 93.
Answer: Option C
Answer: C
Question: A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs.10.50 less, he would have gained 30%. Find the cost of the article.
Options:
A)30
B)40
C)50
D)60
E)70
Rationale: Let C.P=100
Gain=25%
S.P=125
Supposed C.P=80
Gain=30%
S.P=(130*80)/100=104
Diff=(125-104)=21
Diff 21 when C.P=100
then Diff 10.50 when C.P=(100*10.50)/21=50
ANSWER:C
Answer: C
Question: if abcd is four digit highest number that is divisible by 10.9.22 give remainder 4,9,10. find bc
Options:
A)75
B)89
C)95
D)98
E)97
Rationale: 9954.............>95
ANSWER:C
Answer: C
Question: Which of the following numbers completes
the sequence 3, 8, 14, 21, 29, 38, 48, 59, 71, 84, ___?
Options:
A)35
B)36
C)37
D)98
E)109
Rationale: The numbers increase at a somewhat steady rate, so you have to figure out how much
you have to add to each number to produce the next in the sequence: 3 + 5 = 8; 8 + 6 = 14;
14 + 7 = 21; 21 + 8 = 29, and so on. The rule for the sequence is to add successively larger
numbers to each number; therefore, the next number is 84 + 14 = 98.
correct answer D)98
Answer: D
Question: Birbal is a witty trader who trade of a mystical fruit grown far in north. He travels from one place to another with three sacks which can hold 30 fruits each. None of the sack can hold more than 30 fruits. On his way, he has to pass through thirty check points and at each check point, he has to give one fruit for each sack to the authorities.
How many mystical fruits remain after he goes through all the thirty check points?
Options:
A)25 Fruits
B)20 Fruits
C)23 Fruits
D)21 Fruits
E)27 Fr5uits
Rationale: A
25 Fruits
Remember we told you that Birbal is a witty trader. So his sole motive is to get rid of the sacks as fast as he can.
For the first sack:
He must be able to fill fruits from one sack to other two sacks. Assume that he is able to do that after M check points. Now to find M,
(Space in first sack) M + (Space in second sack) M = (Remaining fruits in Third Sack) 30 – M
M = 10
Thus after 10 checkpoints, Birbal will be left with only 2 sacks containing 30 fruits each.
Now he must get rid of the second sack.
For that, he must fill the fruits from second sack to the first sack. Assume that he manages to do that after N checkpoints.
(Space in First Sack) N = (Remaining fruits in second sack) 30 – N
N = 15
Thus after he has crossed 25 checkpoints, he will be left be one sack with 30 fruits in it. He has to pass five more checkpoints where he will have to give five fruits and he will be left with twenty five fruits once he has crossed all thirty check points.
Answer: A
Question: If it is 6:27 in the evening on a certain day, what time in the morning was it exactly 2,876,397 minutes earlier? (Assume standard time in one location.)
Options:
A)6:30
B)6:25
C)6:17
D)6:12
E)6:08
Rationale: 6:27 minus 2,876,397 in any way must end with 0.
The only answer choice which ends with 0 is A.
The answer is A.
Answer: A
Question: If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance traveled by him is?
Options:
A)50 km
B)16 km
C)18 km
D)29 km
E)19 km
Rationale: Let the actual distance traveled be x km. Then,
x/10 = (x + 20)/14
4x - 200 =>x = 50 km.
Answer:a
Answer: A
Question: Which of the following is not a leap year?
Options:
A)700
B)800
C)900
D)1000
E)1200
Rationale: The century divisible by 400 is a leap year.
The year 700 is not a leap year.
Answer: Option A
Answer: A
Question: Two trains of equal length are running on parallel lines in the same directions at 46km/hr. and 36km/hr. The faster trains pass the slower train in 144 seconds. The length of each train is:
Options:
A)82m
B)150m
C)172m
D)200m
E)None of these
Rationale: Explanation:
The relative speed of train is 46-36 = 10 Km/hr = (10 X 5) / 18 = 25/9 m/s10×518=259m/s
In 144 secs the total distance traveled is 144x25/9 = 400 m.
Therefore the length of each train is = 400/2 = 200 m.
Answer D
Answer: D
Question: 21 ball numbered 1 to 21. A ballis drawn and then another ball is drawn without replacement.
Options:
A)8/41
B)9/31
C)9/42
D)7/31
E)9/41
Rationale: The probability that first toy shows the even number,
=1021=1021
Since, the toy is not replaced there are now 9 even numbered toys and total 20 toys left.
Hence, probability that second toy shows the even number,
=920=920
Required probability,
=(1021)×(920)=(1021)×(920)
=9/42
C
Answer: C
Question: An article is bought for Rs.675 and sold for Rs.900, find the gain percent?
Options:
A)33 1/8%
B)33 1/2%
C)33 1/3%
D)33 6/3%
E)32 1/3%
Rationale: 675 ---- 225
100 ---- ? => 33 1/3%
Answer:C
Answer: C
Question: Simplify: 5793405 x 9999
Options:
A)57925286595
B)57928256595
C)57989252865
D)57568226348
E)None of them
Rationale: 5793405 x 9999=5793405(10000-1)
=57934050000-5793405
=57928256595.
Answer is B
Answer: B
Question: A man buys a cycle for Rs. 1600 and sells it at a loss of 12%. What is the selling price of the cycle?
Options:
A)1410
B)1420
C)1430
D)1408
E)1540
Rationale: S.P. = 88% of Rs. 1600 = 88/100 x1600= Rs. 1408
answer : D
Answer: D
Question: Angela, Bernie, and Colleen can complete a job, all working together, in 3 hours. Angela and Bernie, working together at their respective rates, can complete the same job in 4 hours. How long would it take Colleen, working alone, to complete the entire job?
Options:
A)8 hours
B)10 hours
C)12 hours
D)16 hours
E)20 hours
Rationale: A+B+C complete the job in 3 hours.
A+B complete the job in 4 hours.
A+B and C complete the job in 3 hours -->1/(A+B) + 1/C = 1/3-->1/4+1/C=1/3 ----> C=12 hours. ANS C
Answer: C
Question: A shopkeeper sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount was offered?
Options:
A)24.5
B)28.5
C)30
D)Data inadequate
E)None of these
Rationale: Explanation:
Let C.P. be Rs. 100.
Then, S.P. = Rs. 123.50
Let marked price be Rs. x. Then, 95/100 x = 123.50
x = 12350/95 = Rs. 130
Now, S.P. = Rs. 130, C.P. = Rs. 100
Profit % = 30%.
ANSWER IS C
Answer: C
Question: The average number of shirts with Salman, Ambani and Dalmiya is 40, if all of them reached a shopping mall in Delhi and purchased 8 shirts each of them then average number of shirt each of them now has
Options:
A)66
B)63
C)48
D)can't be determined
E)None of these
Rationale: Answer
Required average
= Old average + New average
= 40 + 8 = 48
Correct Option: C
Answer: C
Question: Two pipes A and B can fill a cistern in 20 and 30 minutes respectively, and a third pipe C can empty it in 50 minutes. How long will it take to fill the cistern if all the three are opened at the same time?
Options:
A)17 1/4 min
B)28 1/7 min
C)17 1/7 min
D)17 1/8 min
E)15 15/19 min
Rationale: 1/20 + 1/30 - 1/50 = 19/300
300/19 = 15 15/19
Answer:E
Answer: E
Question: If I walk at 3 kmph, I miss the train by 2 min, if however, I walk at 4 kmph. I reach the station 2 min before the arrival of the train. How far do I walk to reach the station?
Options:
A)1/7 km
B)3/5 km
C)5/5 km
D)4/4 km
E)4/5 km
Rationale: E
4/5 km
x/3 – x/4 = 4/60
x = 4/5 km
Answer: E
Question: A positive whole number has factors of 2 and 4. The number MUST be divisible by: I. 16 II. 8 III. 4
Options:
A)I & II
B)II & III
C)III
D)I
E)II
Rationale: 4 , 8 is not divisible by 16.But 16 is divisible by 2,4,8
So answer is I
Answer : D
Answer: D
Question: What is the probability of a/b will be an integer when a=2x3y and b=2l3m and all of x, y, I, m are positive integers?
Options:
A)1/6
B)2/3
C)1/2
D)1/4
E)3/4
Rationale: There r 4 numbers to be filled i.e, x,y,l,m
out of which only one condition satisfies to get a/b as integer
ANSWER:D
Answer: D
Question: A Fruit Seller buys lemons at 2 for a rupee and sells them at 5 for three rupee. His profit percentage is
Options:
A)30%
B)50%
C)60%
D)20%
E)None
Rationale: C.P of 2 Lemons= Re 1
So, C.P of 5 Lemons= 5*1/2=5/2
S.P of 5 Lemons= Rs 3
Therefore, Profit Percentage={(3-5/2)5/2}100 =20%
Answer: Option D
Answer: D
Question: 8 3/4 + 7 2/17 - 9 1/15=?
Options:
A)7 719/1020
B)9 817/1020
C)9 719/1020
D)6 817/1020
E)None of them
Rationale: Given sum=8+3/4+7+2/17-(9+1/15)
=(8+7-9)+(3/4+2/17-1/15)
=6+(765+120-68/1020
=6 817/1020
Answer is D
Answer: D
Question: A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist travelling in the same direction along the same path at a constant rate of 32 miles per hour. the cyclist stopswaits for the hiker 5 min after passing her while the hiker continues to walk at her constant rate. how many minutes must the cyclist wait until the hiker catches up
Options:
A)6 2/3
B)15
C)20
D)25
E)35
Rationale: Here is how I did it:
The cyclist travels 32 miles in 60 mins, so in 5 mins he will travel [(32*5)/60] miles, which equals 8/3 miles in 5 mins.
Now the hiker travels 4 miles in 60 mins. To travel 8/3 miles, he will take [(60*8/3)/4] = 40 mins.
Hence 40-5 = 35 mins
E
Answer: E
Question: 10^(600) Ã· 10^(580) = ?
Options:
A)10^10
B)10^20
C)10^22
D)10^23
E)10^24
Rationale: 10^(600) Ã· 10^(580) = 10^ (600-580) = 10^20
Answer : B
Answer: B
Question: What decimal fraction is 30 ml of a litre ?
Options:
A).3
B).0003
C).003
D)0.03
E)None of these
Rationale: Answer
Required fraction = 30/1000
= 3/100
= .03
Correct Option: D
Answer: D
Question: Simplify: 896 x 896 - 204 x 204
Options:
A)761200
B)761400
C)761800
D)761500
E)None of them
Rationale: (896)^2 - (204)^2 = (896 + 204) (896 - 204) = 1100 x 692 = 761200.
Answer is A.
Answer: A
Question: The sum of digits of a two digit number is 10,The difference between the digits is 6. Find the number
Options:
A)85
B)94
C)82
D)72
E)None
Rationale: Description :
=> x+y=10, x-y=6
Adding these 2x =16
=> x=8, y=2.
Thus the number is 82
Answer C
Answer: C
Question: In a certain supermarket, a triangular display of cans is arranged in 10 rows, numbered 1 through 10 from top to bottom. Each successively numbered row contains 3 more cans than the row immediately above it. If there are fewer than 150 cans in the entire display, how many cans are in the fifth row?
Options:
A)10
B)11
C)13
D)14
E)16
Rationale: Let x be the number of cans in row 1.
The total number of cans is x + (x+3) + ... + (x+27) =
10x + 3(1+2+...+9) =
10x + 3(9)(10)/2 =
10x + 135
Since the total is less than 150, x must equal 1.
The number of cans in the 5th row is 1 + 3(4) = 13
The answer is C.
Answer: C
Question: Consider a right triangle EBC 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 EBC
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 EBC r = (x + z - y)/2 where y is the hypotenuse and x and y are other two sides.
Answer: C
Answer: C
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 6m/h. what is the speedof the person while he was going to his office?
Options:
A)4km/h
B)9km/h
C)10km/h
D)11km/h
E)13km/h
Rationale: u = k , v= 3k
{2uv}{u+v}/2uv
\frac{2\times k\times 3k}{(k+3k)}=6
1.5k = 6
k=4km/h
A
Answer: A
Question: Two trains, A and B, started simultaneously from opposite ends of a 75-mile route and traveled toward each other on parallel tracks. Train A, traveling at a constant rate, completed the 75-mile trip in 3 hours; Train B, traveling at a constant rate, completed the 75-mile trip in 2 hours. How many miles had train A traveled when it met train B?
Options:
A) 20
B) 22.5
C) 30
D) 37.5
E) 45
Rationale: As the ratio of the rates of A and B is 2 to 3 then the distance covered at the time of the meeting (so after traveling the same time interval) would also be in that ratio, which means that X would cover 2/(2+3)=2/5 of 75 miles: 75*2/5=30 miles.
Answer: C.
Answer: C
Question: A certain auto manufacturer sold 5% fewer vehicles in 2007 than in 2006. If the manufacturer sold 2.1 million vehicles in 2006, how many vehicles, to the nearest 10,000, did the manufacturer sell in 2007?
Options:
A)63,000
B)2,000,000
C)2,030,000
D)2,040,000
E)2,300,000
Rationale: Let's assume in 2006 the manufacturer sold X.
In 2007 he sold X-5/100(X)
If sales in 2006,X= 2.1 million find X-5/100(X)
(2.1 x 10^6)-5/100(2.1 x 10^6)
2100000-105000=1,995,000-----> 2,000,000(approx)
ANSWER:B
Answer: B
Question: The ratio of the present ages of Giri and Hari is 5:8. 12 years hence, the ratio of their ages will be 11:14. Find the difference in their present ages?
Options:
A)7
B)6
C)9
D)2
E)5
Rationale: Let the present ages of Giri and Hari be 5x and 8x years respectively.
(5x + 12)/(8x + 12) = 11/14
70x + 168 = 88x + 132 => x = 2
Difference in their ages will be the same at all times.
This difference = Difference of their present ages
=> 8x - 5x = 3x => 6 years
Answer: B
Answer: B
Question: How many times are the hands of a clock at right angle in a day?
Options:
A)22
B)44
C)48
D)50
E)52
Rationale: IN 12 HR RIGHT ANGLES = 22
IN 24 HRS RIGHT ANGLES = 44 times
ANSWER B
Answer: B
Question: Gold is 10 times as heavy as water and copper is 6 times as heavy as water. In what ratio should these be mixed to get an alloy 8 times as heavy as water?
Options:
A)3:2
B)1:1
C)3:1
D)5:2
E)4:3
Rationale: G = 10W
C = 6W
Let 1gm of gold mixed with x gm of copper to get 1+x gm of the alloy
1gm gold + x gm copper = x+1 gm of alloy
10W+6Wx = x+1 * 8W
10+6x = 8(x+1)
x = 1/1
Ratio of gold with copper = 1:1 = 1:1
Answer is B
Answer: B
Question: Which of the following data sets has the smallest standard deviation?
Options:
A) {1, 2, 3, 4, 5}
B) {2, 3, 3, 3, 4}
C) {2, 2, 2, 4, 5}
D) {0, 2, 3, 4, 6}
E) {-1, 1, 3, 5, 7}
Rationale: since we are asked to compare 'standard deviation', we should look out for similarity between all the sets..
The SIMILARITY is - the SUM of all sets is equal =15..
and hence average = 15/5 = 3...
Now we have 5 different sets which have AVG as 3, so we will look for the spread of the other elements of set around the AVERAGE..
clearly E has a range of 7-(-1) or 8, and has the highest standard deviation..
Next is D, which has a range of 6-0 or 6..
and {2, 3, 3, 3, 4} has smallest standard of deviation.
ans B
Answer: B
Question: A store owner estimates that the average price of type A products will increase by 20% next year and that the price of type B products will increase by 11% next year. This year, the total amount paid for type A products was $3500 and the total price paid for type B products was $8600. According to the store owner's estimate, and assuming the number of products purchased next year remains the same as that of this year, how much will be spent for both products next year?
Options:
A)$13,746
B)$15,325
C)$16,000
D)$16,225
E)$17,155
Rationale: cost of type A products next year = 1.20 * 3500 = 4200
cost of type B products next year = 1.11 * 8300 = 9546
total 4200 +9546 = 13746
ANSWER:A
Answer: A
Question: Two pipes A and B can separately fill a tank in 2 minutes and 15 minutes respectively. Both the pipes are opened together but 4 minutes after the start the pipe A is turned off. How much time will it take to fill the tank?
Options:
A)15
B)10
C)12
D)17
E)14
Rationale: 4/12 + x/15 = 1
x = 10
Answer:B
Answer: B
Question: How many of the following numbers are divisible by 132?
264, 396, 462, 792, 968, 2178, 5184, 6336,528,1320,660
Options:
A)4
B)5
C)6
D)7
E)8
Rationale: Explanation:
A number is divisible by 132, if it is divisible by each one of 11, 3 and 4.
Clearly, 968 is not divisible by 3. None of 462 and 2178 is divisible by 4.
Also, 5184 is not divisible by 11.
Each one of remaining 7 is divisible by each one of 11, 3 and 4 and therefore, by 132.
Answer: D
Answer: D
Question: Two trains of equal are running on parallel lines in the same direction at 44 km/hr and 36 km/hr. The faster train passes the slower train in 36 sec. The length of each train is?
Options:
A)40
B)88
C)66
D)55
E)22
Rationale: Let the length of each train be x m.
Then, distance covered = 2x m.
Relative speed = 44 - 36 = 8 km/hr.
= 8 * 5/18 = 20/9 m/sec.
2x/36 = 20/9 => x = 40.
Answer:A
Answer: A
Question: What is the unit digit in (4137)754?
Options:
A)6
B)5
C)9
D)13
E)15
Rationale: Explanation:
Unit digit in (4137)754 = Unit digit in {[(4137)4]188 x (4137)2}
=Unit digit in { 292915317923361 x 17114769 }
= (1 x 9) = 9
C
Answer: C
Question: A husband wants to share of x% of his savings of total $10,0000 to his wife. After home expenses, the husband reduce this amount by (x − 9)%. In terms of x, how much $ amount will the wife get?
Options:
A)x*x – 9x
B)(x)(1009 – x)
C)(1000)(1009 – x)
D)(1000)(91– x)
E)(x-9)/1000
Rationale: Based on the answer choices and the question, this question begs the use of x=9 as a sample number.
Initial = 9%*100000 = 9000
Reduction = 9-9=0%, so no math required here to calculate the reduction; just make sure that you can calculate 9000 in your answer.
A. x*x – 9x = 0; No
B. (x)(1009 – x) = 9000; Winner!
C. (1000)(1009 – x) > 9000; No
D. (1000)(91 – x) > 9000; No
E. (x-9)/1000 = 0; No
B
Answer: B
Question: Find the missing figures :
?% of 70 = 2.125
Options:
A)3.04
B)6.05
C)8.7
D)7.7
E)4.05
Rationale: (i)	Let x% of 70= 2.125. Then , (x/100)*70 = 2.125
X = (2.125 * 100/70) = 3.04
Answer is A.
Answer: A
Question: What is the sum of natural numbers between 90 and 100
Options:
A)1045
B)4860
C)5000
D)5500
E)5550
Rationale: a = first number
l = last number
Sn = n/2[a + l]
between 90 and 100 numbers = 11 => 100 - 90 = 10 + 1 = 11
Sn = 11/2 Ã— 190 = 11 Ã— 95 = 1045
Answer : A
Answer: A
Question: The compound and the simple interests on a certain sum at the same rate of interest for two years are Rs.11730 and Rs.10200 respectively. Find the sum.
Options:
A)33498
B)17000
C)2665
D)28876
E)313
Rationale: The simple interest for the first year is 10200/2 is Rs.5100 and compound interest for first year also is Rs.5100. The compound interest for second year on Rs.5100 for one year
So rate of the interest = (100 * 1530)/ (5100 * 1) = 30% p.a.
So P = (100 * 10200)/ (30 * 2) = Rs.17000
Answer:B
Answer: B
Question: Find the expenditure on digging a well 14m deep and of 3m diameter at Rs.15 per cubic meter?
Options:
A)2998
B)2799
C)2890
D)1485
E)2780
Rationale: 22/7 * 14 * 3/2 * 3/2
= 99 m2
99 * 15
= 1485
Answer:D
Answer: D
Question: The banker's discount on Rs.1800 at 12% per annum is equal to the true discount on Rs.1872 for the same time at the same rate. Find the time?
Options:
A)3 months
B)4 months
C)5 months
D)6 months
E)7 months
Rationale: Solution
S.I on Rs.1800 = T.D on Rs.1872.
P.W on Rs.1872 is Rs.1800.
Rs.72 is S.I on Rs. 1800 at 12%.
Time	=(100x72 / 12x1800)
= 1/3 year
= 4 months.
Answer B
Answer: B
Question: Which of the following is a prime number?
Options:
A)2
B)4
C)25
D)9
E)27
Rationale: Clearly, 2 is a prime number. Ans : A
Answer: A