mathewhe/aqua_rat huggingface dataset:
Question: In how many ways CM and Minister be elected from a team of 12 members?
(A) 128
(B) 130
(C) 132
(D) 139
(E) 142
Rationale: To do this, if captain is elected first, then we have 12 ways of doing this.
For election of vice-captain, we have only 11 ways left, coz 1 way is already consumed. (Situations like this is called dependent situation. One selection depends upon other selection.)
So, the ans is 12*11 = 132 ways.
C
Answer: (C) 132
Question: When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree was 2/5 taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year?
(A) 3/10
(B) 2/5
(C) 1/2
(D) 4
(E) 6/5
Rationale: Say, the tree grows by x feet every year.
Then, 4 + 6x = (1+2/5)(4+4x)
or, x = 4
Answer D
Answer: (D) 4
Question: A man whose speed is 3.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
(A) 2.0kmph
(B) 2.3kmph
(C) 2.85kmph
(D) 3.0kmph
(E) 3.3kmph
Rationale: M = 3.5
S = 1.5
DS = 5
US = 2
AS = (2 * 5 * 2) /7 = 2.85
Answer:C
Answer: (C) 2.85kmph
Question: If A:B = 1/4: 1/6 B:C = 1/4:1/6 then A:B:C?
(A) 12:14:16
(B) 36:24:18
(C) 12:24:36
(D) 36:24:16
(E) 12:36:42
Rationale: A:B = 1/4:1/6 = 6:4
B:C = 1/4:1/6 = 6:4
--------------------
A:B:C = 36:24:16
Answer: D
Answer: (D) 36:24:16
Question: The simple interest on 200 for 7 months at 5 paise per rupee per month is
(A) 70
(B) 7
(C) 35
(D) 30.5
(E) None of these
Rationale: ∵ Rate = 5 paise per rupee = 5%
∴ S.I. = 200×5×7/100=70
Answer A
Answer: (A) 70
Question: A motorist knows four different routes from Bristol to Birmingham. From Birmingham to Sheffield he knows three different routes and from Sheffield to Carlisle he knows two different routes. How many routes does he know from Bristol to Carlisle ?
(A) 4
(B) 8
(C) 12
(D) 24
(E) 26
Rationale: Explanation:
Total number of routes from Bristol to Carlisle = (4 x 3 x 2) = 24.
Answer: D
Answer: (D) 24
Question: Local trains leave from a station at an interval of 14 minutes at a speed of 36 km/h. A man moving in the same direction along the road meets the trains at an interval of 18 minutes. Find the speed of the man.
(A) 8 km/h
(B) 7 km/h
(C) 6 km/h
(D) 5.8 km/h
(E) None of these
Rationale: Let speed of man = S km/h. Then,
36 × 14⁄60 = 18⁄60[36 - S] ⇒ 36 – S = 28 ⇒ S = 8 km/h.
Answer A
Answer: (A) 8 km/h
Question: For rs 600 Mr. Karan can buy a max of 24 cups of tea and for rs 1500 he can buy a maximum of 15 cups of coffee. He has 2200 in his pocket and purchase 8 cups of tea what is the max no of cups of coffee he can purchase with the remaining money?
(A) 20
(B) 30
(C) 40
(D) 50
(E) 60
Rationale: Explanation:
Let X = Rate of 1 cup of tea.
And Y = Rate of 1cup of coffee.
And Z = Max no of cups of coffee he can purchase with the remaining money.
From question we have,
X = 600/24 = 25.
and Y = 1500/15 = 100.
So acc. to the question,
=> 8X + ZY = 2200
=> 8(25) + 100Z = 2200
=> 200 + 100z = 2200
=> Z = 20.
ANSWER IS A
Answer: (A) 20
Question: In one hour,a boat goes 21 km along the stream and 9 km against the stream.The speed of the boat in still water (in km/hr) is :
(A) 3
(B) 5
(C) 10
(D) 9
(E) 15
Rationale: Solution
Speed in still water =1/2(21+9)kmph.= 15 kmph. Answer E
Answer: (E) 15
Question: A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 300 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?
(A) 300
(B) 320
(C) 330
(D) 340
(E) 290
Rationale: Answer A
300 * T = 1 km => T = 1/360 km/h
V*(T+2/3600) = 1
V (1/360 + 2/3600) = 1 => V = 300 km/h
Answer: (A) 300
Question: A certain scholarship committee awarded scholarships in the amounts of $1250, $2500 and $4000. The Committee awarded twice as many $2500 scholarships as $4000 and it awarded three times as many $1250 scholarships as $2500 scholarships. If the total of $52500 was awarded in $1250 scholarships, how many $4000 scholarships were awarded?
(A) 7
(B) 6
(C) 9
(D) 10
(E) 15
Rationale: Since the starting point is given as the $4000 scholarship,
Assume $4000 scholarships to be x
By the given information, $2500 scholarships = 2x
and $1250 scholarships = 6x
Gievn: Total $1250 scholarships = $52500
6x*1250 = 52500
Solve for x = 7
Option A
Answer: (A) 7
Question: In a garden, there are yellow and green flowers which are straight and curved. If the probability of picking a green flower is 3/4 and picking a straight flower is 1/2, then what is the probability of picking a flower which is yellow and curved
(A) 1/8
(B) 1/6
(C) 1/4
(D) 3/4
(E) 7/8
Rationale: Good question.
So we have a garden where all the flowers have two properties: color (green or yellow) and shape (straight or curved).
We're told that 3/4 of the garden is green, so, since all the flowers must be either green or yellow, we know that 1/4 are yellow. We're also told there is an equal probability of straight or curved, 1/2.
We want to find out the probability of something being yellow and straight, Pr( Yellow and Straight ).
So if we recall, the probability of two unique events occurring simultaneously is the product of the two probabilities, Pr( A and B ) = P(A) * P(B). So we multiply the two probabilities, Pr(yellow)* Pr(curved) = 1/4 * 1/2 = 1/8, or A.
Answer: (A) 1/8
Question: The angles of a triangle are in the ratio 1:3:8. Find the measurement of the three angles of triangle.
(A) 100°
(B) 110°
(C) 120°
(D) 140°
(E) 160°
Rationale: If the ratio of the three angles is 1:3:8, then the measures of these angles can be written as x, 3x and 8x. Also the sum of the three interior angles of a triangle is equal to 180°. Hence
x + 3x + 8x = 180
Solve for x
12x = 180
x = 15
The measures of the three angles are
x = 15°
3x = 3 × 15 = 45°
8x = 8 × 15 = 120°
C
Answer: (C) 120°
Question: If the first day of a year (other than leap year) was Friday, then which was the last day of that year?
(A) Saturday
(B) Friday
(C) Tuesday
(D) Monday
(E) None of these
Rationale: Explanation :
Given that first day of a normal year was Friday
Odd days of the mentioned year = 1 (Since it is an ordinary year)
Hence First day of the next year = (Friday + 1 Odd day) = Saturday
? Last day of the mentioned year = Friday
Answer : Option B
Answer: (B) Friday
Question: A man in a train travelling at 28km/hr notices that a train going in the opposite direction passes him in 12 sec.If the length of this train is 210m find its speed .
(A) 35 km/hr
(B) 40 km/hr
(C) 50 km/hr
(D) 60 km/hr
(E) 70 km/hr
Rationale: relative speed of trains = 210/12 mtrs/sec = 210*18/(12*5)= 63 km/hr
speed of 2nd train = 63-28=35 km/hr
ANSWER:A
Answer: (A) 35 km/hr
Question: The mean of 50 observations was 36. It was found later that an observation 43 was wrongly taken as 23. The corrected new mean is
(A) 35.2
(B) 36.1
(C) 36.2
(D) 36.4
(E) None
Rationale: Solution
Correct sum= (36x50+43-23)
= 1820.
âˆ´ Correct mean= 1820 / 50
= 36.4.
Answer D
Answer: (D) 36.4
Question: Sum of the local value and the face value of 4 in the numeral 153489216 is
(A) 40004
(B) 4004
(C) 4000004
(D) 400004
(E) 44
Rationale: (Local value of 4) + (Face value of 4) = (400000 + 4) = 400004
D
Answer: (D) 400004
Question: Two numbers N and 16 have LCM = 48 and GCF = 8. Find N.
(A) 12
(B) 32
(C) 24
(D) 46
(E) 57
Rationale: The product of two integers is equal to the product of their LCM and GCF. Hence.
16 * N = 48 * 8
N = 48 * 8 / 16 = 24
correct answer C
Answer: (C) 24
Question: Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit?
(A) Rs.2329
(B) Rs.2380
(C) Rs.2329
(D) Rs.2320
(E) Rs.2328
Rationale: Kamal : Sameer = (9000 * 12) : (8000 * 7)
= 108:56 = 27:14
Sameer's share = 6970 * 14/41 = Rs.2380.
Answer: B
Answer: (B) Rs.2380
Question: P(x, y) is the intersection point between the circle (x^2 + y^2 = 4) and the line (y = x +2). Which of the following can be the point P?
(A) (1, 2).
(B) (2, 0)
(C) (0, -2)
(D) (-2, 0)
(E) (2, 2)
Rationale: circle x^2+y^2=4 cuts line y=x+2.
so intercept will be x^2+(x+2)^2=4
x(x+1)=0,
x=0 or x=-1.
in the options only c has x=0.
ANSWER:C
Answer: (C) (0, -2)
Question: If one positive integer is greater than another positive integer by 3, and the difference of their cubes is 279, what is their sum?
(A) 5
(B) 7
(C) 9
(D) 11
(E) 13
Rationale: 1^3 = 1
2^3 = 8
3^3 = 27
4^3 = 64
5^3 = 125
6^3 = 216
7^3 = 343
The two numbers are 4 and 7.
The answer is D.
Answer: (D) 11
Question: If x is to be chosen at random from the set {1, 2, 3, 4} and y is to be chosen at random from the set {5, 6, 7, 8}, what is the probability that xy will be even?
(A)  1/6
(B)  1/3
(C)  1/2
(D)  2/3
(E)  5/6
Rationale: Probably the best way to solve would be to use 1 - P(opposite event) = 1 - P(odd) = 1 - P(odd)*P(odd) = 1 - 2/4*2/3 = 8/12 = 1/2.
Answer: C.
Answer: (C)  1/2
Question: How many different 4 digit numbers can be formed from the number 1234 by re-arranging its digits so that the odd digits occupy even position
(A) 2
(B) 8
(C) 4
(D) 7
(E) 3
Rationale: There are 2 odd numbers which have to be placed at 2 even places =2!=2 ways
There are 2 even numbers which have to be placed at 2 odd places. So 2! = 2 ways
so total number of ways of arranging all these numbers are 2 * 2 = 4 ways
Answer:C
Answer: (C) 4
Question: 2 men and 2 women are lined up in a row. What is the number of cases where they stand with each other in turn? (The number of cases in which men (or women) do not stand next to each other)
(A) 4
(B) 15
(C) 18
(D) 21
(E) 24
Rationale: The list should be WMWMW. Hence, from women 2! And men 2!, we get (2!)(2!)=4. Therefore, the correct answer is A.
Answer: (A) 4
Question: How many integers from 0 to 50 inclusive have a remainder of 3 when divided by 5?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: The numbers should be of the form 5c+3.
The minimum is 3 when c=0.
The maximum is 48 when c=9.
There are 10 such numbers.
The answer is E.
Answer: (E) 10
Question: In an increasing sequence of 8 consecutive even integers, the sum of the first 4 integers is 284. What is the sum of all the integers in the sequence?
(A) 552
(B) 568
(C) 574
(D) 586
(E) 600
Rationale: let the first term of the sequence be x
since it is consecutive even integers the terms be we x, x+2,x+4...x+14 (up to 8 terms)
now,
sum of first 4 terms =284
or,
4x+12=284
x=272/4=68
Thus the answer can now be calculated by either summing up 68+70+72+... 8th term
or
s=n/2(2a+(n-1)d
=8/2(2*68+(7*2))
=4(136+14)=600
E
Answer: (E) 600
Question: The value of a bike depreciates at the rate of 25% every year. It was purchased 2 years ago. If its present value is Rs.4500 , its purchase price was
(A) 8000
(B) 7500
(C) 7000
(D) 6500
(E) 6000
Rationale: Explanation:
= Rs.8000
Answer: A
Answer: (A) 8000
Question: Two trains travel in opposite directions at 36 kmph and 45 kmph and a man sitting in slower train passes the faster train in 4 seconds. The length of the faster train is
(A) 80 m
(B) 100 m
(C) 90 m
(D) 180 m
(E) None
Rationale: Solution
Relative Speed	= (36 + 45) km/hr
= (81 x 5/18) m/sec
= (45/2) m/sec
Length of the train	= (45 / 2 x 4) m
= 90 m.
Answer C
Answer: (C) 90 m
Question: John and Peter are among the ten players a volleyball coach can choose from to field a six-player team. If all six players are chosen at random, what is the probability of choosing a team that includes John and Peter?
(A) 1/2
(B) 1/3
(C) 1/4
(D) 2/5
(E) 3/10
Rationale: The total possible ways of selecting a 6-member team is 10C6 = 210
The possible ways which include John and Peter is 8C4 = 70
The probability of choosing both John and Peter is 70/210 = 1/3
The answer is B.
Answer: (B) 1/3
Question: A gets 3 times as much money as B gets, B gets only Rs.25 more then what C gets. The three gets Rs.675 in all. Find the share of B?
(A) 186
(B) 167
(C) 168
(D) 140
(E) 177
Rationale: A+B+C = 675
A = 3B
3B+B+B-25 = 675
5B = 700
B = 140
Answer: D
Answer: (D) 140
Question: Let's play a game. I have all the ten digits of numbers available. I use all the digits just once to create a number of ten digits. Can you find out what number I have in mind using the following clues?
One digit is divisible by 1.
Two digits are divisible by 2.
Three digits are divisible by 3.
Four digits are divisible by 4.
Five digits are divisible by 5.
Six digits are divisible by 6.
Seven digits are divisible by 7.
Eight digits are divisible by 8.
Nine digits are divisible by 9.
Ten digits are divisible by 10.
(A) 3816547290
(B) 3816557290
(C) 3816547280
(D) 3813547290
(E) 3816147290
Rationale: A
3816547290
Answer: (A) 3816547290
Question: In a birthday party, every person shakes hand with every other person. If there was a total of 28 handshakes in the party, how many persons were present in the party?
(A) 5
(B) 8
(C) 1
(D) 9
(E) 7
Rationale: Suppose there are nn persons present in a party and every person shakes hand with every other person. Then, total number of handshakes
= nC2=n(n−1)/2
n(n−1)=28×2n(n−1)=56
n=8
Ans: B
Answer: (B) 8
Question: A fence consists of m lengths of fence that are each n feet long. A fence post separates each length of fence by its width of x feet. What is the total length H of the fence including the fence posts on each end?
(A) mn
(B) m(n + x)
(C) H=m(n + x) + x
(D) m(n + x) + 2x
(E) 2mn
Rationale: Notice that since a fence post separates each length of fence, then there will be m+1 posts, for example if there are m=2 fences, then there will be 3 posts: PFPFP. Thus the total length H of the posts is (m+1)x.
The total length of the fence is mn, therefore the total length of the fence including the fence posts on each end is (m+1)x+mn=mx+x+mn=m(n+x)+x.
Answer: C.
Answer: (C) H=m(n + x) + x
Question: A and B start a business, with A investing the total capital of Rs.50000, on the condition that B pays A interest @ 10% per annum on his half of the capital. A is a working partner and receives Rs.1500 per month from the total profit and any profit remaining is equally shared by both of them. At the end of the year, it was found that the income of A is twice that of B. Find the total profit for the year?
(A) 59099
(B) 59009
(C) 590055
(D) 59000
(E) 59001
Rationale: Interest received by A from B = 10% of half of Rs.50000 = 10% * 25000 = 2500.
Amount received by A per annum for being a working partner = 1500 * 12 = Rs.18000.
Let 'P' be the part of the remaining profit that A receives as his share. Total income of A = (2500 + 18000 + P)
Total income of B = only his share from the remaining profit = 'P', as A and B share the remaining profit equally.
Income of A = Twice the income of B
(2500 + 18000 + P) = 2(P)
P = 20500
Total profit = 2P + 18000
= 2*20500 + 18000 = 59000.Answer: D
Answer: (D) 59000
Question: If the first day of a year (other than leap year) was Sunday, then which was the last day of that year?
(A) Saturday
(B) Sunday
(C) Tuesday
(D) Monday
(E) None of these
Rationale: Explanation :
Given that first day of a normal year was Sunday
Odd days of the mentioned year = 1 (Since it is an ordinary year)
Hence First day of the next year = (Sunday+ 1 Odd day) = Monday
Therefore, last day of the mentioned year = Sunday. Answer : Option B
Answer: (B) Sunday
Question: How many halves are there in three-fourth?
(A) 8.1
(B) 12
(C) 32
(D) 7.3
(E) 1.5
Rationale: divide 3/4 by 1/2
=3/4÷1/2
=3/4*2/1
=6/4
=1.5.
Answer is E.
Answer: (E) 1.5
Question: 0.002 x 0.008 = ?
(A) 1.6e-05
(B) 0.001
(C) 0.01
(D) 0.1
(E) NONE OF THESE
Rationale: Explanation:
2 x 8 = 16.
Sum of decimal places = 6
0.002 x 0.008 = 0.000016
Answer- A
Answer: (A) 1.6e-05
Question: in how many possible ways you can write 3240 as product of 3 positive integers a, b, c .
(A) 450
(B) 420
(C) 350
(D) 320
(E) 300
Rationale: 3240 => 2^3 * 3^4 * 5^1
a => 2^x1 * 3^y1 * 5^z1
b => 2^x2 * 3^y2 * 5^z2
c => 2^x3 * 3^y3 * 5^z3
a * b * c = 3240
x1 + x2 + x3 = 3 => 5C2
y1 + y2 + y3 = 4 => 6C2
z1 + z2 + z3 = 1 => 3C2
5C2 * 6C2 * 3C2 = 10 * 15 * 3 = 450
ANSWER:A
Answer: (A) 450
Question: How long does a train 165 meters long running at the rate of 54 kmph take to cross a bridge 660 meters in length?
(A) 28
(B) 27
(C) 55
(D) 18
(E) 12
Rationale: T = (660 + 165)/54 * 18/5
T = 55
Answer: C
Answer: (C) 55
Question: A man swims downstream 90 km and upstream 55 km taking 5 hours each time; what is the speed of the current?
(A) 3.8
(B) 3.5
(C) 3.3
(D) 3.2
(E) 1.6
Rationale: 90 --- 5 DS = 18
? ---- 1
55 ---- 5 US = 11
? ---- 1 S = ?
S = (18 - 11)/2 = 3.5
Answer: B
Answer: (B) 3.5
Question: A dog takes 2 leaps for every 3 leaps of a hare. If one leap of the dog is equal to 3 leaps of the hare, the ratio of the speed of the dog to that of the hare is :
(A) 1:5
(B) 2:5
(C) 3:5
(D) 4:5
(E) 6:5
Rationale: Explanation:
Dog : Hare = (2*3) leaps of hare : 3 leaps of hare = 6 : 5.
Answer: E) 6:5
Answer: (E) 6:5
Question: If 21 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect?
(A) 150
(B) 170
(C) 190
(D) 210
(E) 230
Rationale: If two lines are not parallel, then they will intersect in exactly one point. Lines can be extended infinitely on both ends so somewhere they will intersect with each other if they are not parallel. We are also given that no three lines are concurrent. This means that no three lines intersect at the same point. So every pair of two lines we select will have a unique point of intersection which they will not share with any third line.
The number of ways to select 2 lines from 21 lines is 21C2 = 210
The answer is D.
Answer: (D) 210
Question: What is the greatest prime factor of 7!6! + 6!5! ?
(A) 17
(B) 23
(C) 37
(D) 43
(E) 53
Rationale: 7!6! + 6!5! = 6!5!(7*6+1) = 6!*5!*43
The answer is D.
Answer: (D) 43
Question: A list of measurements in increasing order is 2, 5, 6, 8, 15 and x. If the median of these measurements is 3/4 times their arithmetic mean, what is the value of x?
(A) 16
(B) 18
(C) 20
(D) 22
(E) 24
Rationale: The median is (6+8)/2 = 7
The mean is (2+5+6+8+15+x)/6 = (36+x)/6
(36+x) /6 * 3/4 = 7
x = 56-36 = 20
The answer is C.
Answer: (C) 20
Question: Can you find the last number in the below sequence
3 , 7 , 10 , 11 , 12 , 17 ?
(A) 44
(B) 55
(C) 60
(D) 40
(E) 20
Rationale: E
20(Twenty) : when you write them , these are only numbers having vowel 'E'
Answer: (E) 20
Question: A and B complete a work in 5 days. A alone can do it in 10 days. If both together can do the work in how many days?
(A) 3.33 days
(B) 3.99 days
(C) 2.99 days
(D) 2.98 days
(E) 2.44 days
Rationale: 1/5 + 1/10 = 3/10
10/3 = 3.33 days
Answer: A
Answer: (A) 3.33 days
Question: If n is a prime number greater than 5, what is the remainder when n^2 is divided by 12 ?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 5
Rationale: There are several algebraic ways to solve this question, but the easiest way is as follows:since we cannot have two correct answers just pick a prime greater than 5, square it and see what would be the remainder upon division of it by 12.
n=7 --> n^2=49--> remainder upon division 49 by 12 is 1.
Answer: B.
Answer: (B) 1
Question: A train 2000 m long can cross an electric pole in 25 sec and then find the speed of the train?
(A) 322
(B) 324
(C) 326
(D) 328
(E) 330
Rationale: Length = Speed * time
Speed = L/T
S = 2000/25
S = 80 M/Sec
Speed= 80*18/5 (To convert M/Sec in to Kmph multiply by 18/5)
Speed = 324 Kmph
Answer: B
Answer: (B) 324
Question: The average (arithmetic mean) of five numbers is 5. If 2 is subtracted from each of four of the numbers, what is the new average?
(A) 3.4
(B) 4.5
(C) 6.2
(D) 5.7
(E) 6.9
Rationale: Let the numbers be a , b, c , d , e ,f
So, Total of these 5 numbers must be 25
Or, a + b + c + d + e = 25
So, 12 must be subtracted from the total sum
i.e a + b + c + d + e - 8
Or, 25 - 8 = 17
Hence average of the 5 numbers now is 17/5 =>3.4
So, Answer will be A
Answer: (A) 3.4
Question: There are 13 boys and 10 girls in a class. If three students are selected at random, in how many ways that 1 girl or 2 boys are selected ?
(A) 88
(B) 90
(C) 92
(D) 96
(E) 98
Rationale: n(s) = sample space = 23C3 = 1771
E = event that 1 girl and 2 boys are selected
n(E) = we have to select 2 boys from 13 or 1 girl from 10
= 13C2 + 10C1
= 88
Ans - A
Answer: (A) 88
Question: When the no.7y86038 is exactly divisible by 11, then the smallest whole no.in place of y?
(A) 1
(B) 3
(C) 5
(D) 7
(E) 9
Rationale: The given number =7y86038
Sum of the odd places =8+0+8+7=23
Sum of the even places = 3+6+y
(Sum of the odd places)- (Sum of even places) = Number (exactly divisible by 11)
23-(9+y) = divisible by 11
14 � y = divisible by 11.
Y must be 3, to make given number divisible by 11.
B
Answer: (B) 3
Question: In the xy plane line m has the equation 4x + y = u. Line n passes through the origin and is perpendicular to line m. If point p has the coordinates (r, r+1) and is on both line n and m what is the value of r?
(A) -4/3
(B) 1/4
(C) -4
(D) 3/4
(E) 4/3
Rationale: The equation of line m is y=-4x+u. Now, since line n is perpendicular to line m, then its slope is negative reciprocal of the slope of line m, so the slope of n is 1/4. Next, as line n passes through the origin (0, 0) and has the slope of 1/4 then its equation is y=1/4*x.
Point (r, r+1) lies on line n means that (r+1)=1/4*r --> r=-4/3.
Answer: A.
Answer: (A) -4/3
Question: A car covers a certain distance at aspeed of 60 kmph in 4 hours. To cover the same distance in 2hr, it must travel at a speed of?
(A) 567 km/hr
(B) 678 km/hr
(C) 782 km/hr
(D) 120 km/hr
(E) 720 km/hr
Rationale: Distance = (60 x 4) = 240 km.
Speed = Distance/Time
Speed = 240/2 = 120 kmph
Answer : D
Answer: (D) 120 km/hr
Question: If integers a and b are distinct factors of 30, which of the following CANNOT be a factor of 30?
I. ab + b^2
II. (a + b)^2
III. a + b
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III
Rationale: Factors of 30 are: 1, 2, 3, 5, 6, 10, 15, and 30.
I. ab + b^2 --> if a=1 and b=2 then ab + b^2=6, which is a factor of 30. OK;
II. (a + b)^2 --> (a + b)^2 is a perfect square, no perfect square (but 1) is a factor of 30. DISCARD;
III. a + b --> if a=1 and b=2 then a + b=3, which is a factor of 30. OK.
Answer: B.
Answer: (B) II only
Question: In how many ways can the letters of the word ASTERIX be arranged in a row so that the vowels appear in alphabetic order?
(A) 800
(B) 820
(C) 880
(D) 960
(E) 840
Rationale: three letters can be arranged in 3! ways.
only one combination AEI is required.
7 letters can be arranged in 7! ways.
thus 7!/ 3! * 1 = 840.
Answer: (E) 840
Question: A man swims downstream 72 km and upstream 45 km taking 9 hours each time; what is the speed of the current?
(A) 1.9
(B) 1.5
(C) 1.4
(D) 1.1
(E) 1.6
Rationale: 72 --- 9 DS = 8
? ---- 1
45 ---- 9 US = 5
? ---- 1 S = ?
S = (8 - 5)/2 = 1.5
Answer: B
Answer: (B) 1.5
Question: Anand and Deepak started a business investing Rs. 1000 and Rs. 5000 respectively. Out of a total profit of Rs. 2000, Deepak's share is:
(A) 3776
(B) 1284.2
(C) 8400
(D) 1666.6
(E) 1671.8
Rationale: Ratio of their shares = 1000: 5000= 1:5
Deepak's share = 2000 * 5/6 = Rs. 1666.6.
Answer: D
Answer: (D) 1666.6
Question: power windows: 60%
anti-lock brakes: 25%
CD player: 75%
The table above shows the number of vehicles at Bill's car dealership that have certain features. No vehicle has all three features, but 10% have power windows and anti-lock brakes, 15% have anti-lock brakes and a CD player, and 22% have power windows and a CD player. What percent of the vehicles at Bill's car dealership have a CD player but no power windows or anti-lock brakes?
(A) 25
(B) 18
(C) 11
(D) 38
(E) 0
Rationale: Answer: D
Were looking for the number of cars with a CD player but no other features. We know that 40% of the cars have a CD player, 15% have a CD player and anti-lock brakes, while 22% have a CD player and power windows. Since no car has all three features, those account for all of the possibilities except for what were looking for.
If a car has a CD player, it must either have anti-lock brakes, power windows, or no other features. Since the total of cars with a CD player is 75%, we can set up the following equation:
75=15+22+x
x=38, choiceD.
Answer: (D) 38