mathewhe/aqua_rat huggingface dataset:
Question: Carl drove from his home to the beach at an average speed of 80 kilometers per hour and returned home by the same route at an average speed of 70 kilometers per hour. If the trip home took 1/2 hour longer than the trip to the beach, how many kilometers u did Carl drive each way?
(A)  350
(B)  345
(C)  320
(D)  280
(E)  240
Rationale: Let us backsolve here.
The answer option has to be divisible by 7 to give us 1/2.
Let us try u=280 km. Time taken will be 3.5 hours and 4 hours.
Hence D is the answer.
Answer: (D)  280
Question: Income and expenditure of a person are in the ratio 7 : 6. If the income of the person is Rs. 21000, then find his savings?
(A) Rs.3600
(B) Rs.3603
(C) Rs.3639
(D) Rs.3000
(E) Rs.3602
Rationale: Let the income and the expenditure of the person be Rs. 7x and Rs. 6x respectively.
Income, 7x = 21000 => x = 3000
Savings = Income - expenditure = 7x - 6x = x
So, savings = Rs.3000
Answer:D
Answer: (D) Rs.3000
Question: How many terminating zeroes E does 200! have?
(A)  40
(B)  48
(C)  49
(D)  55
(E)  64
Rationale: You have 40 multiples of 5, 8 of 25 and 1 of 125. This will give 49 zeros.C
Answer: (C)  49
Question: At a certain conference, 150 students spoke one or more of the following languages: Spanish, English, and French. If 57 students spoke Spanish, 90 spoke English, 65 spoke French, and 32 spoke only 2 languages, how many students spoke three different languages?
(A) 7
(B) 9
(C) 12
(D) 15
(E) 18
Rationale: 150=57+90+65-32-2x
x=15
D. 15
Answer: (D) 15
Question: Each week, Harry is paid X dollars per hour for the first 30 hours and 1.5X dollars for each additional hour worked that week. Each week, James is paid X dollars per hour for the first 40 hours and 2X dollars for each additional hour worked that week. Last week James worked a total of 50 hours. If Harry and James were paid the same amount last week, how many hours did Harry work last week?
(A) 35
(B) 36
(C) 37
(D) 38
(E) 50
Rationale: Amount earned by James = 40*x + 10*2x =60x
Therefore, Amount earned by James = 60x
But we know the amount Harry earned assuming working y hours (y>30) is 30*x + (y-30)*1.5x
[[We know y>30 because in 30h the most Harry could earn is 30x, but he has earned 60x]]
So x*(1.5y -45 +30) = 60x
Or x*(1.5y - 15) = 60x
So 1.5y - 15 = 60
So 1.5y = 75
So y = 50
Answer is E
Answer: (E) 50
Question: A scientist used a unique two-color code to identify each of the test subjects involved in a certain study. If the scientist found that choosing from among six colors produced enough color codes to identify all but 5 of the test subjects, how many test subjects were in the study? (Assume that the order of the colors in the codes does not matter.)
(A) 7
(B) 10
(C) 15
(D) 17
(E) 20
Rationale: If 6 colors have to be divided into groups of 2, the number of unique groupings 6C2 = 6! / (2!)(4!) = 15.
Number of combinations was sufficient to account for all but 5 of the subjects
Number of subjects = 15 + 5 = 20.
ANSWER:E
Answer: (E) 20
Question: If the average (arithmetic mean) of three consecutive integers is k + 1, then the product of the greatest and least integer is
(A) k2 - 9
(B) k^2 + 2k
(C) k2 + 4k - 5
(D) k2 + 6k + 9
(E) k2 + 4k - 12
Rationale: n = smallest number
n+2 = largest number
(n + n + 2)/2 = k+1
=> (2n+2)/2 = k+ 1
=> n + 1 = k + 1
=> n = k
So Product of n and n+2 = (k)(k+2)
=k^2 + 2k
Answer - B
Answer: (B) k^2 + 2k
Question: A train speeds past a pole in 15 sec and a platform 140 m long in 25 sec, its length is?
(A) 210
(B) 150
(C) 160
(D) 170
(E) 180
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 140)/25 = x/15 => x = 210 m.
Answer: Option A
Answer: (A) 210
Question: If x^y denotes x raised to the power y, Find last two digits of (1141^3843) + (1961^4181)
(A) 22
(B) 37
(C) 29
(D) 82
(E) 02
Rationale: Remember 1 raised to any power will give 1 as unit digit.
To find the digit in the 10th place, we have to multiply, 10th digit in the base x unit digit in the power.
So the Last two digits of the given expression = 21 + 61 = 82
Answer:D
Answer: (D) 82
Question: Which number need to add to 1782452 to get a number exactly divisible by 92?
(A) 44
(B) 43
(C) 42
(D) 41
(E) 48
Rationale: 1782452 / 92 = 19374 and reminder = 44.
92-44 = 48
So, the next number divisible by 92 is 48 places in front of 1782452
Which means 48 + 1782452 =1782500
48 should be added to 1782452
E
Answer: (E) 48
Question: When Jack picks olives for two hours at three times his regular speed, he picks 10 pounds of olives more than Mac working for five hours at 80% of his regular speed. Therefore, if Mac picks olives for one hour at double his regular speeds, and Jack picks olives for four hours at 70% of his regular speed, then
(A) Jack picks double the amount of olives Mac picks
(B) Mac picks 10 pounds more than Jack
(C) Jack picks 10 pounds more than Mac
(D) Mac picks 5 more pounds than Jack
(E) Jack picks 5 more pounds than Mac
Rationale: Let's say Jack's regular speed is J olives/hr and Mac's regular speed is M olives/hr
Given:
2*3J = 10 + 5*(4/5)M
3J = 5 + 2M
Question:if Mac picks olives for one hour at double his regular speeds, and Jack picks olives for four hours at 75% of his regular speed
Mac picks 2M and Jack picks 4*(3/4)J = 3J
They are asking you for the relation between 3J and 2M. You already know 3J = 5 + 2M
So Jack picks10 pounds more olives than Mac.
C
Answer: (C) Jack picks 10 pounds more than Mac
Question: Find the least number must be subtracted from 165826 so that remaining no.is divisible by 4?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: On dividing 165826 by 4 we get the remainder 2, so 2 should be subtracted
B
Answer: (B) 2
Question: Of the families in City X in 2000, 30 percent owned a personal computer. The number of families in City X owning a computer in 2004 was 20 percent greater than it was in 1994, and the total number of families in City X was 10 percent greater in 2004 than it was in 2000. what percent of the families in City X owned a personal computer in 1998?
(A) 55.42%
(B) 52.25%
(C) 56.23%
(D) 30.70%
(E) 32.72%
Rationale: Say a 100 families existed in 2000 then the number of families owning a computer in 2000 - 30
Number of families owning computer in 2000 = 30 * 120/100 = 36
Number of families in 2004 = 110
The percentage = 36/110 * 100 = 32.72%.
Option: E
Answer: (E) 32.72%
Question: 3-3*8+2=
(A) A)2
(B) B)-13
(C) C)-19
(D) D)-17
(E) of the above
Rationale: 3-3*6+2 = 5-24 = -19...
so the answer is -19... C
Answer: (C) C)-19
Question: At 30 minutes past 6 o'clock, what is the angle between the two hands?
(A) 15
(B) 30
(C) 45
(D) 60
(E) 75
Rationale: The hour hand moves 360 degrees in 12 hours.
The hour hand moves 30 degrees in 1 hour and 15 degrees in 30 minutes.
The minute hand moves 360 degrees in 60 minutes and 180 degrees in 30 minutes.
At 30 minutes past 6, the hour hand has moved 195 degrees.
At 30 minutes past 6, the hour hand has moved 180 degrees.
The angle between the two hands is 15 degrees.
The answer is A.
Answer: (A) 15
Question: The number of students in a classroom are a multiple of both 5 and 15.what is the possible total number of students?
(A) 90
(B) 70
(C) 50
(D) 63
(E) 95
Rationale: the number of students in a classroom are a multiple of both 5 and 15,so it must be divisible by 5 and 15
63--ruled out [not divisible by 5 & 15]
70,50&95 are all divisible by 5 but not by 15--wrong
90 is divisible by both 5 and 15 [ 90/5=18 and 90/15=6]
answer : (A)
Answer: (A) 90
Question: Out of first 20 natural numbers, one number is selected at random. The probability that it is either an even number or a prime number is -.
(A) 17/20
(B) 1/5
(C) 19/25
(D) 1/7
(E) 2/9
Rationale: n(S) = 20
n(Even no) = 10 = n(E)
n(Prime no) = 8 = n(P)
P(Eá´œP) = 10/20 + 8/20 - 1/20 = 17/20
ANSWER A
Answer: (A) 17/20
Question: There is 60% increase in an amount in 6years at SI. What will be the CI of Rs. 11,000 after 3 years at the same rate?
(A) 3641
(B) 2572
(C) 4542
(D) 2343
(E) 3972
Rationale: Let P = Rs. 100. Then, S.I. Rs. 60 and T = 6 years.
R = 100 x 60 = 10% p.a.
100 x 6
Now, P = Rs. 11000. T = 3 years and R = 10% p.a.
C.I.
= Rs. 11000 x 1 +	10 3	- 1
100
= Rs. 11000 x	331
1000
= 3641.
A
Answer: (A) 3641
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 3 cups of tea. Last week Mo drank a total of 20 cups of tea and hot chocolate together. If during that week Mo drank 10 more tea cups than hot chocolate cups, then how many rainy days were there last week?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: T= the number of cups of tea
C= the number of cups of hot chocolate
T+C = 20 T-C=10 -> T= 15. C=5.
Mo drinks 3 cups of tea a day then number of days that are not rainy = 15/3 = 5
So number of rainy days = 7-5 = 2
A is the answer.
Answer: (A) 2
Question: Find the average of first 7 multiples of 5?
(A) 10
(B) 15
(C) 12.5
(D) 13
(E) 20
Rationale: average = (5+10+15+20+25+30+35)/7 = 20
Answer is E
Answer: (E) 20
Question: Bob invested one half of his savings in a bond that paid simple interest for 2 years and received $500 as interest. He invested the remaining in a bond that paid compound interest (compounded annually) for the same 2 years at the same rate of interest and received $605 as interest. What was the annual rate of interest?
(A)  5%
(B)  10%
(C)  12%
(D)  15%
(E)  42%
Rationale: First divide $500/2years to get 250$/yr non-compounding interest.
Next, subtract from the total compound after 2 years to see the interest gained in the second year. This can be done because the same amount has been invested in both accounts and the interest gained for the first year will be the same. So, $605-$250= $355.
To find the difference in interest gained, $355-$250= $105 increase in interest after the first year through compounding.
From this information we can set up the equation $250 * X% = $105.=42% giving us answer choice E.
Answer: (E)  42%
Question: Shobha's Mathematics Test had 75 problems i.e. 10 arithmetic, 30 algebra and 35 geometry problems. Although she answered 70% of the arithmetic, 40% of the algebra and 60% 0f the geometry problems correctly, she did not pass the test because she got less than 60% of the problems right. How many more questions she would have needed to answer correctly to earn a 60% passing grade?
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: Solution
Number of questions attempted correctly
= (70% of 10 + 40% of 30 + 60% of 35)
= (7 + 12 + 21)
= 40.
Questions to be answered correctly for 60% grade = 60% of 75 = 45.
Required no of questions = (45 - 40) = 5.
Answer A
Answer: (A) 5
Question: A train moves past a post and a platform 264 metre long in 8 seconds and 20 seconds respectively. What is the speed of the train
(A) 79.2 km/hr
(B) 69 km/hr
(C) 74 km/hr
(D) 61 km/hr
(E) 50 km/hr
Rationale: let length and speed x
train crosses the post in 8 sec
x=8v=train crosses the platform in 20 sec => x+264=20v
v=264/12 = 22m/s
22* 18/5 = km/hr = 79.2 km/hr
ANSWER A
Answer: (A) 79.2 km/hr
Question: Six machines at a certain factory operate at the same constant rate. If five of these machines, operating simultaneously, take 36 hours to fill a certain production order, how many fewer hours does it take all six machines, operating simultaneously, to fill the same production order?
(A) 6
(B) 8
(C) 10
(D) 12
(E) 15
Rationale: The total work is 5*36 = 180 machine hours
The time required for six machines is 180/6 = 30 hours, thus 6 fewer hours.
The answer is A.
Answer: (A) 6
Question: A thief steals at a car at 2.30 p.m. and drives it at 50 km/hr. The theft is discovered at 3 p.m. and the owner sets off in another car at 75 km/hr. When will he overtake the thief?
(A) 6 p.m
(B) 9 p.m
(C) 4 p.m
(D) 2 p.m
(E) 1 p.m
Rationale: :
Suppose the thief is overtaken x hrs after 2.30 p.m.
Then, distance covered by the owner in (x - 1/2) hrs.
50x = 75(x - 1/2) => x =3/2 hrs.
So, the thief is overtaken at 4 p.m.'
Answer: C
Answer: (C) 4 p.m
Question: 120 students represent x percent of the boys at a school. If the boys at the school make up 30% of the total school population of x students, what is x?
(A) 120
(B) 150
(C) 180
(D) 200
(E) 250
Rationale: Let B be the number of boys in the school.
120 = xB/100
B = 0.3x
12000=0.3x^2
x^2 = 40000
x = 200
The answer is D.
Answer: (D) 200
Question: 20 beavers, working together in a constant pace, can build a dam in 3 hours. How many hours will it take 12 beavers that work at the same pace, to build the same dam?
(A) 2.
(B) 4.
(C) 5.
(D) 6
(E) 8.
Rationale: Total Work = 20*3= 60 Beaver hours
12 Beaver * x =60 Beaver hours
x=60/12=5
ANSWER:D
Answer: (D) 6
Question: In a class of boys and girls Vikas's rank is 9th and Tanvi's rank is 17th . Vikas's rank among the boys in that class is 4th from the top and 18th from the bottom and Tanvi's rank among the girls is 8th from top and 21st from bottom. In the order of rank, how many girls are there between Tanvi and Vikas?
(A) 29
(B) 8
(C) 2
(D) 4
(E) 6
Rationale: Explanation:
Vikas's rank in the class is 9. So there are 8 people before him. His rank among boys is 4. So 3 boys are before him. So there are 8 – 3 = 5 girls before him.
Tanvi's rank among the girls is 8. So there are 7 girls before her. So number of girls between Vikas and Tanvi is 7 – 5 = 2
Answer: C
Answer: (C) 2
Question: If x3−6x2+11x−6=0x3−6x2+11x−6=0 and x3+3x2−6x−8=0x3+3x2−6x−8=0 have one common root between them. What is the value of that root?
(A) 3
(B) 2
(C) 6
(D) 9
(E) 1
Rationale: There are two equations,
x3−6x2+11x−6=0x3−6x2+11x−6=0 - - - (i)
x3+3x2−6x−8=0x3+3x2−6x−8=0 - - - (ii)
So both (i) and (ii) have one root in common and we know that at the root the value of both the equations is 0. Suppose that common root is x then,
x3−6x2+11x−6x3−6x2+11x−6 = x3+3x2−6x−8x3+3x2−6x−8 ⇒⇒ 9x2−17x−2=09x2−17x−2=0
⇒⇒ (x - 2)(9x + 1) = 0 or x = 2 or -1/9. As by applying the Descartes rule in (i) we can see it cannot have any negative root so x = 2.
Why are we getting two values x = 2 and x = -1/9?
x = 2 and x = -1/9 are the pint of intersections of these two equations out of which x = 2 is the point of intersection at x axis therefore this point (x = 2) is the common root as well.
Answer:B
Answer: (B) 2
Question: If in a book a total of 3209 digits are used for numbering, then find out the total number of pages in the book.
(A) 23777
(B) 69667
(C) 26976
(D) 2697
(E) 1079
Rationale: Explanation:
Number of digits used in 1 digit numbers = 1*9 = 9
Number of digits used in 2 digit numbers = 2*90 = 180
Number of digits used in 3 digit numbers = 3*900 = 2700
Number of digits used in 1 digit numbers = 3209 – (9+180+2700) = 320
Hence, number of pages with 4 digit number = 320/4 = 80
Total number of pages = 1079
ANSWER: E
Answer: (E) 1079
Question: Present ages of X and Y are in the ratio 5:6 respectively. Seven years hence this ratio will become 6:7 respectively. What is X's present age in years?
(A) 35years
(B) 20years
(C) 25years
(D) 30years
(E) 28years
Rationale: Let the present ages of X and Y is 5x and 6x
5x+7 / 6x+7 = 6/7
x = 7
X's present age = 5*7 = 35 years
Answer is A
Answer: (A) 35years
Question: A man buy a book in Rs50 & sale it Rs80. What is the rate of profit ???
(A) 10%
(B) 60%
(C) 30%
(D) 25%
(E) 28%
Rationale: cp=50
sp=80
profit=80-50=30
%=30/50*100=60%
ANSWER:B
Answer: (B) 60%
Question: A sum of money is to be distributed among A, B, C, D in the proportion of 5:2:4:3. If C gets Rs. 2500 more than D, what is B's share?
(A) A)8239
(B) B)2900
(C) C)4500
(D) D)2393
(E) E)5000
Rationale: Let the shares of A, B, C and D be 5x, 2x, 4x and 3x Rs. respectively.
Then, 4x - 3x = 2500 => x = 2500.
B's share = Rs. 2x = 2 * 2500 = Rs. 5000.
Answer: E
Answer: (E) E)5000
Question: Fresh dates contain 90% water while dry dates contain 28% water . How many kg of dry dates can be obtained from 36kg of fresh dates ?
(A) 5Kg
(B) 10Kg
(C) 12 Kg
(D) 16Kg
(E) 18Kg
Rationale: 36 kilograms of fresh dates contain 0.1*36=3.6 kilograms of non-water.
Dry dates obtained from these fresh dates will contain the same amount of non-water and we are told that this amount should be 72% of the dry dates, thus x*0.72=3.6 --> x=5 kilograms.
Answer: A.
Answer: (A) 5Kg
Question: A can do a piece of work in 4 hours . A and C together can do it in just 2 hours, while B and C
together need 3 hours to finish the same work. In how many hours B can complete the work ?
(A) 10 hours
(B) 12 hours
(C) 16 hours
(D) 18 hours
(E) None of these
Rationale: ExplanaƟon:
Work done by A in 1 hour = 1/4
Work done by B and C in 1 hour = 1/3
Work done by A and C in 1 hour = 1/2
Work done by A,B and C in 1 hour = (1/4)+(1/3) = 7/12
Work done by B in 1 hour = (7/12)�(1/2) = 1/12
=> B alone can complete the work in 12 hour
Answer: B
Answer: (B) 12 hours
Question: What annual payment dischargea debit of Rs.12900, due in 4yrs.At 5% rate?
(A) 2300
(B) 2400
(C) 3000
(D) 3500
(E) 3600
Rationale: A.P.=(200X12900)/[4(200+5X3)]=3000 Ans
Alternative
100+105+110+115=12900
430=12900
100=12900/(430)X100=3000
C
Answer: (C) 3000
Question: In the xy-coordinate system, what is the slope of the line that goes through the point (7, 3) and is equidistant from the two points P = (5, 5) and Q = (13, 7)?
(A) 0.5
(B) 0.75
(C) 1.0
(D) 1.25
(E) 1.5
Rationale: First, get the middle coordinate between (5,5) and (13,7)...
x = 5 + (13-5)/2 = 9
y = 5 + (7-5)/2 = 6
Second, get the slope of (9,6) and (7,3). m = 6-3 / 9-7 = 3/2 = 1.5
Answer: E
Answer: (E) 1.5
Question: The radius of a wheel is 22.6 cm. What is the distance covered by the wheel in making 750 resolutions?
(A) 754 m
(B) 704 m
(C) 1055.04 m
(D) 1058.04 m
(E) 204 m
Rationale: In one resolution, the distance covered by the wheel is its own circumference. Distance covered in 750 resolutions.
= 750 * 2 * 22/7 * 22.6 = 105504 cm
= 1055.04 m
Answer:C
Answer: (C) 1055.04 m
Question: A bullet train passes a station platform in 36 seconds and a man standing on the platform in 22 seconds. If the speed of the bullet train is 54 km/hr, what is the length of the platform?
(A) 240 m
(B) 220 m
(C) 260 m
(D) 224 m
(E) 210 m
Rationale: A
210 M
Speed = 54 x 5/18 = 15 m/s
Length of the bullet train = (15 x 22)m = 330 m.
Let the length of the platform be x metres.
Then, (x + 330)/36 = 15
--> x + 330 = 540
x = 210m. E
Answer: (E) 210 m
Question: How many times are the hands of a clock at right angle in a week?
(A) 803
(B) 830
(C) 380
(D) 308
(E) 318
Rationale: In 1 day, they are at right angles 44 times.
In a week, they are at right angles 308 times. Answer: Option D
Answer: (D) 308
Question: A train 240 m long passed a pole in 24 sec. How long will it take to pass a platform 650 m long?
(A) 88 sec
(B) 89 sec
(C) 17 sec
(D) 288 sec
(E) 277 sec
Rationale: Speed = 240/24 = 10 m/sec.
Required time = (240 + 650)/10 = 89 sec
Answer:B
Answer: (B) 89 sec
Question: If five students are made to sit in a row, then 6 don't have seats. If 12 students are made to sit in a row, then three rows are empty. How many students have to sit a row such that each row has equal number of students and all students are seated?
(A) 0
(B) 1
(C) 4
(D) 5
(E) 6
Rationale: Let there be a rows.
Then 5a + 6 = 12(a-3) [equating the number of students]
=> a= 6
and total number of students = 36
Therefore 6 students much sit in each row such that each row has an equal number of students and all students are seated.
Option (E)
Answer: (E) 6
Question: Machine Z and machine B are each used to manufacture 660 sprockets. It takes machine Z 10 hours longer to produce 660 sprockets than machine B. Machine B produces 10 percent more sprockets per hour than machine Z. How many sprockets per hour does machine Z produces?
(A) 6
(B) 6.6
(C) 60
(D) 100
(E) 110
Rationale: I think the correct answer is A.
Machine Z produces at a speed of Z sp/hour and B at a speed of B sp/hour.
so, 660/Z=(660/B)+10 and B=1,1 Z--->1,1*660=660+11Z---A=6, so answer A is correct
Answer: (A) 6
Question: If an object travels at four feet per second, how many feet does it travel in one hour?
(A) 30
(B) 300
(C) 720
(D) 14400
(E) 18000
Rationale: Speed = 4 feet per second.
1 Hour= 60X60 Seconds = 3600 Seconds.
Total no of feet traveled in 1 hour = 3600X4 = 1800X10 = 14400
Answer D
Answer: (D) 14400
Question: A table is bought for Rs.400/- and sold at Rs.250/- find gain or loss percentage
(A) 5%loss
(B) 10%gain
(C) 20%gain
(D) 37.5%loss
(E) 20% loss
Rationale: Formula = (Selling price ~ Cost price)/Cost price * 100
= (250 - 400)/400 = 37.5% loss
D
Answer: (D) 37.5%loss
Question: The probability that a brand A widget is defective is x, the probability that a brand B widget is defective is 0.06, and the probability that a brand C widget is defective is 0.08. There are 40 brand A widgets, 35 brand B widgets, 25 brand C widgets, and nothing else in a container. If a widget is selected at random from the container, the probability that the widget selected is defective is 0.051. What is the value of x?
(A) 0.02
(B) 0.01
(C) 0.025
(D) 0.03
(E) 0.04
Rationale: Given probability of defective items in each brand,
So, the number of items defective in brand A=x*40, in brand B=0.06*35 and brand C=0.08*25
Total number of widgets=40+35+25=100
the probability that the widget selected is defective is 0.051=(x*40+0.06*35+0.08*25)/100
=> 40x+2.1+2=5.1
=>40x=1
>x=1/40=0.025
Ans C
Answer: (C) 0.025
Question: There are 3 numbers A, B and C. If A:B = 3/4, B:C = 4/5, C:D = 5/6, then A:C will be?
(A) 1 : 2
(B) 3 : 5
(C) 5 : 7
(D) 6 : 11
(E) 5 : 3
Rationale: Sol. A : B = 3 : 4, B : C = 4 : 5, C : D = 5 : 6
∴A∶B∶C∶D= 3 : 4 : 5 : 6.
Thus, A : C = 3 : 5
B
Answer: (B) 3 : 5
Question: A rectangular field has area equal to 150 sq m and perimeter 50 m. Its length and breadth must be?
(A) 33
(B) 28
(C) 77
(D) 10
(E) 99
Rationale: lb = 150
2(l + b) = 50 => l + b = 25
l – b = 5
l = 15 b = 10
Answer: D
Answer: (D) 10
Question: The perimeter of a triangle is 28 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
(A) 87 cm2
(B) 28 cm2
(C) 98 cm2
(D) 26 cm2
(E) 35 cm2
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle
= 2.5 * 28/2
= 35 cm2
Answer:E
Answer: (E) 35 cm2
Question: A certain company reported that the revenue on sales increased 50 % from 2000 to 2003, and increased 80 % from 2000 to 2005. What was the approximate percent increase in revenue for this store from 2003 to 2005?
(A)  20 %
(B)  40 %
(C)  35 %
(D)  32 %
(E)  29 %
Rationale: Assume the revenue in 2000 to be 100. Then in 2003 it would be 150 and and in 2005 180, so from 2003 to 2005 it increased by (180-150)/150=30/150=~20%.
Answer: A
Answer: (A)  20 %
Question: A, B and C started a shop by investing Rs. 4,000, Rs. 12,000 and Rs. 8,000 respectively. At the end of the year, the profits were distributed among them. If Câ€™s share of profit be Rs. 1,000, then the total profit was :
(A) 3,000
(B) 60,000
(C) 80,000
(D) 120,000
(E) None
Rationale: Sol.
A : B : C = 4000 : 12000 : 8000 = 1: 3 : 2. so, Câ€™s share : Total Profit = 2 : 6
Let the total profit be Rs. x. Then, 2/6 = 1000/x or x
= 1000 * 6/ 2 = 3000.
Answer A
Answer: (A) 3,000
Question: If 3x+y=40, 2x-y=20, for integers of x and y, 2y^2=?
(A) 2
(B) 4
(C) 0
(D) 10
(E) 32
Rationale: 3x+y = 40
2x-y = 20
5x = 60
x = 12
y = 4
2y^2 = 2*16=32
Answer is E
Answer: (E) 32
Question: Vijay bought 160 shirts at the rate of Rs. 225 per shirt. The transport expenditure was Rs. 1400. He paid an octroi at the rate of Rs. 1.75 per shirt and labour charges were Rs. 320. What should be the selling price of one shirt, if he wants a profit of 20%?
(A) 288
(B) 267
(C) 108
(D) 285
(E) 171
Rationale: Total CP per shirt = 225 + 1400/160 + 1.75 + 320/160 = Rs. 237.5
SP = CP[(100 + profit%)/100]
= 237.5 * [(100 + 20)/100] = Rs. 285.
Answer: D
Answer: (D) 285
Question: If x and y are numbers such that (x+3)(y-3)=0, what is the smallest possible value of x^2 + y^2
(A) 0
(B) 3
(C) 6
(D) 9
(E) 12
Rationale: From (x+3)(y-3)=0 it follows that either x=-3 or y=3. Thus either x^2=9 or y^2=9.
Now, if x^2=9, then the least value of y^2 is 0, so the least value of x^2 + y^2 = 9 + 0 = 9.
Similarly if y^2=9, then the least value of x^2 is 0, so the least value of x^2 + y^2 = 0 + 9 = 9.
Answer: D.
Answer: (D) 9