mathewhe/aqua_rat huggingface dataset:
Question: If the price of a computer were reduced by 11 percent, which of the following could not be the final price of the computer? (Assume initial price to be integer in cents)
(A) $844.10
(B) $895.20
(C) $1,055.20
(D) $1,135.20
(E) $1,262.40
Rationale: Let X be the initial price of computer without discount
then price (final) after discount should be=X(1-11/100)------->X(8/9)=A(say)
means X=A*(9/8).....
so initial price to be integer(As per stem) final price must be multiple of 8
if we check options all were divisible by 8 except option (A)..which is Ans.
Ans A
Answer: (A) $844.10
Question: The ratio of the present ages of P and Q is 3:4. 5 years ago, the ratio of their ages was 5:7. Find the their present ages?
(A) 30, 40
(B) 30, 46
(C) 30, 49
(D) 30, 43
(E) 30, 43
Rationale: Their present ages be 3X and 4X.
5 years age, the ratio of their ages was 5:7, then (3X - 5):(4X - 5) = 5:7
X = 35 - 25 => X = 10.
Their present ages are: 30, 40..Answer:A
Answer: (A) 30, 40
Question: Two cars cover the same distance at the speed of 62 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car.
(A) 1873
(B) 1848
(C) 1984
(D) 1838
(E) 1939
Rationale: Explanation:
62(x + 1) = 64x
X = 31
62 * 32 = 1984 km
Answer: Option C
Answer: (C) 1984
Question: In a 100 m race, A can beat B by 25 m and B can beat C by 4 m. In the same race, A can beat C by:
(A) 21
(B) 22
(C) 28
(D) 25
(E) 30
Rationale: A:B = 100:75
B:C=100:96
A:C = 100/72 = 100:72
A beats(100-72) = 28 m
ANSWER C
Answer: (C) 28
Question: Tom found a box of 220 baseball cards. Being a thoughtful older brother, he wanted to save at least 50 percent of the cards for himself and split the remaining cards evenly among his 6 younger brothers. What is the lowest possible number of cards that Tom can save for himself that will also allow each of his 6 younger brothers to get an equal number of cards?
(A) 110
(B) 112
(C) 116
(D) 118
(E) 120
Rationale: This question can be easily solved by looking at the options.
Assuming number of cards to be x
We need to find the option for which (1/6)*(x/2) is an integer
Or x/12 is an integer.
Hence we need the lowest multiple of 12 from the given options.
Let us start from the lowest value:
Option A: 110. This is not a multiple of 12
Option E: 120 = 12*10. This is a multiple of 12. Hence the correct answer.
Correct Option: E
Answer: (E) 120
Question: One half of a two digit number exceeds its one third by 6. What is the sum of the digits of the number?
(A) 9
(B) 3
(C) 2
(D) 4
(E) 5
Rationale: x/2 â€“ x/3 = 6 => x =6
3 + 6 = 9
Answer A
Answer: (A) 9
Question: In what ratio must rice at $9.30/kg be mixed with rice at $10.80/kg so that the mixture is worth $10/kg?
(A) 1:3
(B) 9:4
(C) 8:7
(D) 11:9
(E) 11:7
Rationale: 9.30x + 10.80y= 10(x+y)
.80y= .70x
x/y= 8/7
C is the answer
Answer: (C) 8:7
Question: What is the difference between local value & face value of 9 in the numeral 65693?
(A) 84
(B) 89
(C) 81
(D) 90
(E) 10000
Rationale: (Local value of 9) - (Face value of 9)
= (90 - 9) =81
C
Answer: (C) 81
Question: Anand finishes a work in 7 days, Bittu finishes the same job in 8 days and Chandu in 6 days. They take turns to finish the work. Anand on the first day, Bittu on the second and Chandu on the third day and then Anand again and so on. On which day will the work get over?
(A) 3rd
(B) 6th
(C) 9th
(D) 7th
(E) 8th
Rationale: They completed 146/168 work in 6 days working one by one on eacg day.
On 7 th day , 22/168 work is left which will be completed by Anand on 7th day.
ANSWER:D
Answer: (D) 7th
Question: What is the sum of all the multiples of 12 between 30 and 200?
(A) 1648
(B) 1632
(C) 1626
(D) 1612
(E) 1800
Rationale: You first have to know all the multiples of 12 between 30 and 200. They are 12,24,36,48,60,72,84,96,108,120,132,144,156,168,180192. If you add all these numbers together, you get 1632.
Final Answer:
B
Answer: (B) 1632
Question: How many paying stones, each measuring 2 1/2 m * 2 m are required to pave a rectangular court yard 50 m long and 16 1/2 m board?
(A) 99
(B) 18
(C) 165
(D) 10
(E) 15
Rationale: 50 * 33/2 = 5/2 * 2 * x => x
= 165
Answer:C
Answer: (C) 165
Question: 4 buses runs between Chennai and Mysore. If a man goes from Chennai to Mysore by a bus and comes back to Mysore by another bus, then the total possible ways are
(A) 4
(B) 8
(C) 12
(D) 16
(E) None of these
Rationale: Since the man can go in 4 ways and can back in 3 ways. Therefore total number of ways are 4 x3 = 12ways.
Answer C
Answer: (C) 12
Question: If 3x - y = 6 and x+2y = 8, then what is the value of 4x + y?
(A) 1/7
(B) 14
(C) 15
(D) 52/7
(E) 60/7
Rationale: 3x-y=6 ...equation 1
x+2y=8 ...equation 2
adding both the equations
4x+y=14
correct answer option B
Answer: (B) 14
Question: A group of 55 adults and 70 children go for trekking. If there is meal for either 70 adults or 90 children and if 21 adults have their meal, find the total number of children that can be catered with the remaining food.
(A) 33
(B) 54
(C) 63
(D) 17
(E) 01
Rationale: Explanation:
As there is meal for 70 adults and 21 have their meal, the meal left can be catered to 49 adults.
Now, 70 adults = 90 children
7 adults = 9 children
Therefore, 49 adults = 63 children
Hence, the meal can be catered to 63 children.
ANSWER: C
Answer: (C) 63
Question: If the number of 37,29n, where n represents the ones digit, is a multiple of 3, then the value of n could be which of the following?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Then for any number to be a multiple of 3,The sum of its digits should be the multiple of 3.
i.e 3+7+2+9+n = multiple of three
or, 21 + n = multiple of 3.
If n=3, 21 + n =24,which is a multiple of 3.
Hence answer is C.
Answer: (C) 3
Question: What will the ratio of simple interest earned by certain amount at the same rate of interest for 6 years and that for 9 years.
(A) 1:2
(B) 2:1
(C) 2:2
(D) 2:3
(E) None of these
Rationale: Explanation:
Let the principal be P and rate be R
then
ratio = [(P∗R∗6/100) /(P∗R∗9/100)]
=6PR /9PR=2:3
Option D
Answer: (D) 2:3
Question: Each book on a certain shelf is labeled by a single category. For every 2 history books, there are 7 fantasy books and for every 3 fantasy books, there are 8 reference books. If the proportion of history to reference books is doubled, while the proportion of fantasy to reference books is maintained, which of the following could be the number of history books if there are fewer than 60 fantasy books on the shelf after the changes?
(A) 12
(B) 21
(C) 27
(D) 35
(E) 36
Rationale: For every 2 history books, there are 7 fantasy books:
Originally H:F = 2:7 = 6:21.
For every 3 fantasy books, there are 8 reference books:
F:R = 3:8 = 21:56
H:F:R = 6:21:56
After the changes, H:F:R = 12:21:56
There are fewer than 60 fantasy books, so there are 21 or 42 fantasy books.
The number of history books could be 12 or 24.
The answer is A.
Answer: (A) 12
Question: I bought two books; for Rs.480. I sold one at a loss of 15% and other at a gain of 19% and then I found each book was sold at the same price. Find the cost of the book sold at a loss?
(A) 267
(B) 280
(C) 279
(D) 177
(E) 288
Rationale: x*(85/100) = (480 - x)119/100
x = 280
Answer:B
Answer: (B) 280
Question: A wheel has a diameter of x inches and a second wheel has a diameter of y inches. The first wheel covers a distance of d feet in 300 revolutions. How many revolutions does the second wheel make in covering d feet?
(A) 300xy
(B) 300x/y
(C) 300x - y
(D) 200y/x
(E) 600x/y
Rationale: First Wheel with diameter x inches ----> So the circumference = x*pi --------- (1)
Second Wheel with diameter y inches ----> So the circumference = y*pi --------- (2)
Revolutions = distance/circumference
So, from equation (1)
300 = d/(x*pi)
d = 300 * x * pi ---------- (3)
From equation (2)
Revolutions = d/(y*pi) = (300 * x * pi) / (y*pi) = 300x/y
Answer (B)
Answer: (B) 300x/y
Question: Find the average of all prime numbers between 10 and 40
(A) 15.6
(B) 22.5
(C) 18.6
(D) 32.2
(E) 26.9
Rationale: Prime numbers between 10 and 40 are 11, 13, 17, 19, 23, 29, 31, 37
Required average = (11+ 13+ 17+ 19+ 23+ 29+ 31+ 37)/8 = 180/8 = 22.5
Answer is B
Answer: (B) 22.5
Question: If Log2 x - 5 Log x + 6 = 0, then what would the value / values of x be?
(A) 5.3296
(B) 6.3296
(C) 7.3296
(D) 8.3296
(E) 9.3296
Rationale: log(2x)-5log(x)+6=0 (given)
log(2x)-log(x^5)=-6
log(2x/x^5)=-6 [since log(a)-log(b)=log(a/b)]
apply anti log
2/(x^4)=e^-6
2/(x^4)=2.4788*10^-3
x^4=806.85
x=5.3296
ANSWER:A
Answer: (A) 5.3296
Question: How many positive integers less than 10,000 are such that the product of their digits is 30?
(A) 12
(B) 24
(C) 36
(D) 38
(E) 50
Rationale: 30 = 1 * 30, 2 * 15, 3* 10, 5 *6
We have the option of using single digits 1,2,3,5 and 6
No : of four digit numbers such that the product is 30
The possible combinations are using digits (1,2,3,5) & (1,1, 5, 6) such that the product 30.
No: of different combinations possible using (1,2,3,5) = 4! = 24
No: of different combinations possible using (5,6,1,1) = 4!/2! = 12 ('1' is repeated twice)
Total 4 digit numbers so that the product is 30 is 24+12 = 36
No: of three digit numbers such that the product is 30
The possible combinations are using digits (2,3, 5) & (1,5,6)
No: of different combinations possible using (2,3,5) = 3! = 6
No: of different combinations possible using (1,5,6) = 3! = 6
Total 3 digit numbers so that the product is 30 is 6+6 = 12
No: of 2 digit numbers such that the product is 30 is 2 (56 and 65)
Total numbers under 10000 such that the product is 30 is 36+12+2 = 50
E
Answer: (E) 50
Question: Dawson has to secure 30% marks to clear his exam of class 8th.
He got 30 marks and failed by 36 marks.
What is the maximum marks ?
(A) 180
(B) 190
(C) 200
(D) 210
(E) 220
Rationale: E
220
To pass the exam ravish needs 30 + 36 = 66 marks.
=> (66/30) *100 = 220
Answer: (E) 220
Question: Rs.800 amounts to Rs.920 in 3 years at simple interest. If the interest is increased by 3%, it would amount to how much?
(A) 226
(B) 992 rs
(C) 665
(D) 771
(E) 211
Rationale: (800*3*3)/100 = 72
920 + 72 = 992
Answer: B
Answer: (B) 992 rs
Question: A person travels equal distances with speeds of 3 km/hr, 4 km/hr and 5 km/hr and takes a total time of 50 minutes. The total distance is?
(A) 1 km
(B) 2 km
(C) 3.19 km
(D) 4 km
(E) 5 km
Rationale: C
3 km
Let the total distance be 3x km.
Then, x/3 + x/4 + x/5 = 50/60
47x/60 = 50/60 => x = 1.06.
Total distance = 3 * 1.06 = 3.19 km.
Answer: (C) 3.19 km
Question: Working alone at its constant rate, machine A produces x boxes in 10 minutes and working alone at its constant rate, machine B produces 2x boxes in 5 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce 7x boxes?
(A) 3 minutes
(B) 4 minutes
(C) 5 minutes
(D) 14 minutes
(E) 12 minutes
Rationale: Rate = Work / Time
Given Rate of Machine A = X / 10 min
Machine B Produces 2x boxes in 5 min hence , Machine B produces 4x boxes in 10 min .
Rate of Machine B = 4x / 10
we need tofind the combined time that machines A and B, working simultaneouslytakeat their respective constant rates
let's first find the combined Rate of Machine A and B
Rate of Machine A = X / 10 min + Rate of Machine B = 4x / 10 = 5X/10
Now combine Time = combine work needs to be done / Combine Rate = 7x/5x * 10 = 14 Min
Ans: D
Answer: (D) 14 minutes
Question: A sales staff is composed of a sales manager and two sales people, all of whom earn commission as a percentage of sales. Each sales person earns 5% commission on sales. In a given week, the sales staff earned a total of $2,750 in commissions on $5,000 worth of sales. What commission rate did the sales manager earn during that week?
(A) 25%
(B) 30%
(C) 35%
(D) 40%
(E) 45%
Rationale: E for me.
Let managers comminsion rate be M.
m*5000+ 2*0.05*5000=2750
5000*m=2250
m=45/100=45%
Answer: (E) 45%
Question: If you write down all the numbers from 1 to 100, then how many times do you write 3 ?
(A) 33
(B) 38
(C) 20
(D) 88
(E) 28
Rationale: Explanation:
Clearly, From 1 to 100, there are ten numbers with 3 as the unit's digit - 3, 13, 23, 33, 43, 53, 63, 73, 83, 93 and ten numbers with 3 as the ten's digit - 30, 31, 32, 33, 34, 35, 36, 37, 38, 39.
So, required number = 10 + 10 = 20.
Answer: C) 20
Answer: (C) 20
Question: R is a set containing 8 different numbers. S is a set containing 7 different numbers, all of which are members of R. Which of the following statements CANNOT be true?
(A)  The range of R is less than the range of S.
(B)  The mean of R is greater than the mean of S.
(C)  The range of R is equal to the range of S.
(D)  The mean of R is less than the mean of S.
(E)  The mean of R is equal to the mean of S.
Rationale: The range of a set is the difference between the largest and smallest elements of a set.
So, the answer is straight A: the range of a subset cannot be more than the range of a whole set: how can the difference between the largest and smallest elements of a subset bemorethan the difference between the largest and smallest elements of a whole set.
As for D:
Consider set R to be {-3, -2, -1, 0, 1, 2, 3, 4} --> mean=0.5.
(D) The mean of R is less than the mean of S --> remove the smallest term -3, then the mean of S will be 1, so more than 0.5. ANSWER IS A
Answer: (A)  The range of R is less than the range of S.
Question: A certain list has an average of 6 and a standard deviation of B (B is positive). Which of the following pairs of data when added to the list, must result in a list of 102 data with standard deviation less than B?
(A) (-6;0)
(B) (0;0)
(C) (0;6)
(D) (0;12)
(E) (6;6)
Rationale: Standard deviation shows how much variation there is from the mean. A low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.
So when we add numbers, which are far from the mean we are stretching the set making SD bigger and when we add numbers which are close to the mean we are shrinking the set making SD smaller.
According to the above adding two numbers which are closest to the mean will shrink the set most, thus decreasing SD by the greatest amount.
Closest to the mean are 6 and 6 (actually these numbers equal to the mean) thus adding them will definitely shrink the set, thus decreasing SD.
E)
Answer: (E) (6;6)
Question: In a jar there are 20 white balls, 25 green balls and 32 blue balls. How many balls must be taken out in order to make sure we have 22 balls of the same color?
(A) a)	23
(B) b)	46
(C) c)	57
(D) d)	63
(E) e)	67
Rationale: Here, we need to find minimum number of marbles to be taken out to get 22 marbles of same color.
For a instance, if we take 20 white marbles 1st and followed by 21 Green and then 21 Blue.
Total will be 20 + 21+ 21= 62 draws.
If we choose either Green or Blue next time. This will bring the total of either of these colored marble to 22.
So Minimum we need to take 62+1 = 63 Times to get 22 marbles of same color(either Green or Blue).
Answer : D.
Answer: (D) d)	63
Question: If the sides of a square are doubled in length, the area of the original square is now how many times as large as the area of the resultant square?
(A) 25%
(B) 50%
(C) 100%
(D) 200%
(E) 400%
Rationale: Let the original square have sides of length L and the new square have sides of length 2L.
The resulting areas are L^2 for the original square and 4L^2 for the new square (as the length of the side is square to get the area).
The original square's area is L^2/4L^2 or 25% of the new square's area. Choice A
Answer: (A) 25%
Question: The price of cooking oil has increased by 25% . The percentage of reduction that a family should effect in the use of cooking oil so as not to increase the expenditure on this account is :
(A) 15%
(B) 20%
(C) 25%
(D) 30%
(E) None
Rationale: Explanation:
Reduction in consumption:
=(25/125×100)%=20%
Correct Option: B
Answer: (B) 20%
Question: A man cheats while buying as well as while selling. While buying he takes 10% more than what he pays for and while selling he gives 20% less than what he claims to. Find the profit percent, if he sells at 11% below the cost price of the claimed weight.
(A) 19.81%
(B) 22.38%
(C) 37.5%
(D) 25%
(E) 37.5%
Rationale: There is a one step calculation method too. It requires more thought but is faster.
The man takes 10% more than what he pays for. So if he claims to take 100 pounds, he pays $100 but he actually takes 110 pounds for which he will take from the customer $110. Hence, in effect, there is a 10% mark up.
While selling, he sells 20% less. This means, he claims to sell 100 pounds and gets $100 but actually sells only 80 pounds and should have got only $80 for it. So this is again a mark up of $20 on $80 which is 25%.
But he also sells at 11% less
(1 + m1%)(1 + m2%)(1 - d%) = (1 + p%)
11/10 * 5/4 * 89/100 = (1 + p%)
profit % = 22.38%
B
Answer: (B) 22.38%
Question: The perimeter of a semi circle is 144 cm then the radius is?
(A) 29
(B) 28
(C) 277
(D) 24
(E) 21
Rationale: 36/7 r = 144 => r = 28
Answer:B
Answer: (B) 28
Question: Tough and Tricky questions: Mixture Problems.
A drink holding 6 ounces of an alcoholic drink that is 1 part rum to 2 parts coke is added to a jug holding 35 ounces of an alcoholic drink that is 1 part rum to 3 parts coke. What is the ratio of rum to coke in the resulting mixture?
(A) 2:5
(B) 5:15
(C) 3:5
(D) 4:7
(E) 14:5
Rationale: Answer = B) 5:15
........................ Rum ..................... Coke ................. Total
First Drink ........... 2 ............................ 4 ..................... 6 (Ratio 1:2)
Second Drink ....... 8 ............................. 24 ................... 32 (Ratio 1:3)
Total .................. 10 ............................. 28 .................... 38
Ratio = 10:30 = 5:15
B
Answer: (B) 5:15
Question: How many pages the book have, if total 306 digits are used to form the page numbers?
(A) 135 pages
(B) 136 pages
(C) 137 pages
(D) 138 pages
(E) 139 pages
Rationale: First 9 pages .. 9 digits
next 90 pages .. 180 digits
next 39 pages ... 117 digits
----------------------
Total ...138 pages ...300 digits
ANSWER:D
Answer: (D) 138 pages
Question: Sound is said to travel in air at about 1100 feet per second. A man hears the axe striking the tree, 11/5 seconds after he sees it strike the tree. How far is the man from the wood chopper?
(A) 2197 feet
(B) 2420 ft
(C) 2500 feet
(D) 2629 feet
(E) None of these
Rationale: Distance =(1100*11/5)feet=2420 feet.
Correct Option: B
Answer: (B) 2420 ft
Question: A fires 5 shots to B's 3 but A kills only once in 3 shots while B kills once in 2 shots. When B has missed 36 times, A has killed:
(A) 60 birds
(B) 72 birds
(C) 30 birds
(D) 80 birds
(E) 40 birds
Rationale: Let the total number of shots be x. Then,
Shots fired by A =(5/8)x
Shots fired by B =(3/8)x
Killing shots by A =(1/3)of	(5/8)x=(5/24)x
Shots missed by B =(1/2) of (3/8)x	=(3/16)x
3x/16= 36 or x =(36 x 16)/3= 192.
Birds killed by A =(5x/24)	=(5/24*192)= 40.
Answer is E
Answer: (E) 40 birds
Question: A train 125 m long passes a man, running at 5 km/hr in the same direction in which the train is going, in 15 seconds. The speed of the train is?
(A) 35
(B) 50
(C) 88
(D) 66
(E) 22
Rationale: Speed of the train relative to man
= (125/15) m/sec = (25/3) m/sec. [(25/3) * (18/5)] km/hr
= 30 km/hr. Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr. x - 5
= 30 ==> x
= 35 km/hr.
Answer:A
Answer: (A) 35
Question: On a store counter are exactly two boxes containing only purple marbles and yellow marbles. Box A has 30 purple marbles and 20 yellow marbles; box B has 15 purple marbles and 35 yellow marbles. If Melanie randomly selects one of the boxes and then randomly selects one marble from the box, what is the probability that the marble selected will be purple?
(A)  3/20
(B)  3/10
(C)  9/20
(D)  3/5
(E)  9/10
Rationale: We are given that box A has 30 purple marbles and 20 yellow marbles and that box B has 15 purple marbles and 35 yellow marbles. We need to determine the probability, when selecting one marble from the box, of selecting a purple marble. Since we have two boxes, A and B, there are multiple scenarios to account for when selecting the marbles. We must account for the probability of first selecting either box and then secondly for selecting a purple marble. Let’s start with Box A.
P(selecting box A) = ½
P(selecting a purple marble in box A) = 30/50 = ⅗
Thus, the probability of selecting a purple marble from box A is ½ x ⅗ = 3/10
Next we can determine the probability of selecting a purple marble from box B.
P(selecting box B) = ½
P(selecting a purple marble in box B) = 15/50 = 3/10
Thus, the probability of selecting a purple marble from box B is ½ x 3/10 = 3/20
Now we can determine the probability of selecting a purple marble from box A or box B:
3/10 + 3/20 = 6/20 + 3/20 = 9/20.
Answer: C
Answer: (C)  9/20
Question: $ represents addition and * represents subtraction,what is the value of the following expression?
15 * 5 $ 15 $ 10 $ 30 * 25 * 35 * 25 $ 20 * 25 * 20
(A) -15
(B) -35
(C) -55
(D) -45
(E) -65
Rationale: 15-5+15+10+30-25-35-25+20-25-20
=10+15+10+30-25-35-25+20-25-20
=25+10+30-25-35-25+20-25-20
=35+30-25-35-25+20-25-20
=65-25-35-25+20-25-20
=40-35-25+20-25-20
=5-25+20-25-20
=-20+20-25-20
=0-25-20
=-45
ANSWER:D
Answer: (D) -45
Question: In a tournament prize of 1st, 2nd, and 3rd is given in same interval.If total amount of prize Rs 4800 and prize of 1st is Rs 2000, find the interval??
(A) 600
(B) 450
(C) 350
(D) 550
(E) 400
Rationale: Let the interval is x.
prize of 2nd and 3rd is 2000-x and 2000-2x
2000+2000-x+2000-2x = 4800
x = 400
Answer :E
Answer: (E) 400
Question: A player holds 13 cards of four suits, of which seven are black and six are red. There are twice as many diamonds as spades and twice as many hearts as diamonds. How many clubs does he hold
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: Explanation:
Clearly, the black cards are either clubs or spades while the red cards are either diamonds or hearts.
Let the number of spades be x. Then, number of clubs = (7 - x).
Number of diamonds = 2 x number of spades = 2x;
Number of hearts = 2 x number of diamonds = 4x.
Total number of cards = x + 2x + 4x + 7 - x = 6x + 7.
Therefore 6x + 7 = 13 6x = 6 x - 1.
Hence, number of clubs = (7 - x) = 6.
Answer: C
Answer: (C) 6
Question: The length of the bridge, which a train 160 meters long and travelling at 45 km/hr can cross in 30 seconds, is:
(A) 239
(B) 277
(C) 215
(D) 88
(E) 232
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (160 + X)/30
= 25/2 ==> 2(160 + X) = 750 ==> X = 215 m.
Answer: C
Answer: (C) 215
Question: If x = 9/3 and y = 4/3, what is the value of the expression -2x – y^2?
(A) -28/51
(B) -70/9
(C) 45/87
(D) 13/21
(E) 14/40
Rationale: x = 9/3 and y = 4/3
==> -2(9/3) - (4/3)^2 = -18/3 - 16/4 = -70/9
Ans: B
Answer: (B) -70/9
Question: A rower can row upstream at 22 kph and downstream at 34 kph. What is the speed of the rower in still water?
(A) 28
(B) 29
(C) 30
(D) 31
(E) 32
Rationale: Let V be the rower's speed in still water.
Let S be the speed of the current in the stream
V-S = 22
V+S = 34
When we add the two equations, we get: 2V = 56
Then V = 28 kph.
The answer is A.
Answer: (A) 28
Question: A truck driver drove for 2 days. On the second day, he drove 3 hours longer and at an average speed of 15 miles per hour faster than he drove on the first day. If he drove a total of 1,000 miles and spent 21 hours driving during the 2 days, what was his average speed on the first day, in miles per hour?
(A) 25
(B) 30
(C) 35
(D) 39
(E) 45
Rationale: Day 1
2t+3=21
t=9
Day 2
t+3
9+3=12
9r+12(r+15)=1000
r=39
Answer:D
Answer: (D) 39
Question: If two of the four expressions x+y, x+5y, x-y, and 5x-y are chosen at random, what is the probability R that their product will be of the form of x^2-(by)^2, where b is an integer?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 1/5
(E) R=1/6
Rationale: Only (X+y)(x-y) pair will give the form x^2-(by)^2
The probability of selecting these two pairs are 1/4 * 1/3 = 1/12, assuming x+y is picked first, then x-y, but x-y can be picked first followed by x+y. So the probability R= 1/12 * 2 = 1/6
Ans E
Answer: (E) R=1/6