mathewhe/aqua_rat huggingface dataset:
Question: If '+' means ' ÷ ', '-' means '×', '' means '-'' means '+', then (280 + 1020) - 86 is -------.
(A) 70
(B) 112
(C) -392
(D) 58
(E) None
Rationale: (280/1020)*86
14/51 * 86
1204/51
Getting a fraction...
So none...
ANSWER:E
Answer: (E) None
Question: The length of a room is 5.5 m and width is 3.75 m. Find the cost of paying the floor by slabs at the rate of Rs. 1200 per sq.metre.
(A) Rs. 15,000
(B) Rs. 24,750
(C) Rs. 15,600
(D) Rs. 16,500
(E) None
Rationale: Solution
Area of the floor	= (5.5 x 3.75)m²
= 20.635m ²
Cost of paying	= Rs. (1200 x 20.625)
= Rs.24,750.
Answer B
Answer: (B) Rs. 24,750
Question: When two different numbers are divided by a certain divisor the remainders are 147 and 192. When the sum of the two numbers is divided by the same divisor the remainder is 38: Find the divisor.
(A) 300
(B) 301
(C) 302
(D) 303
(E) 304
Rationale: Let divisior be x.so 1st no.=a+147
2nd no=b+192.
After adding:(a+147+b+192)/x=>a+b+339/x
Remainder of above expression is 38(given).so rem[a+b+(301+38)]/x=>38 therefore x would be 301.
ANSWER:B
Answer: (B) 301
Question: An gun can take a maximum of four shots at an enemy plane moving away from it. The probability of hitting the plane at the 1st, 2nd, third and 4th shots are 1.4, 1.3, 1.2 & 1.1 respectively.
What is the probability that the plane is hit when all the four shots are fired?
(A) 0.6976
(B) 0.783
(C) 0.986
(D) 1.243
(E) 1.3445
Rationale: Required probability:
=(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)=(0.4×0.7×0.8×0.9)+(0.6×0.3×0.8×0.9)+(0.6×0.7×0.2×0.9)+(0.6×0.7×0.8×0.1)+(0.4×0.3×0.8×0.9)+(0.4×0.7×0.2×0.9)+(0.4×0.7×0.8×0.1)+(0.6×0.3×0.2×0.9)+(0.6×0.3×0.8×0.1)+(0.6×0.7×0.2×0.1)+(0.4×0.3×0.2×0.9)+(0.6×0.3×0.2×0.1)+(0.4×0.3×0.8×0.1)+(0.4×0.7×0.2×0.1)+(0.4×0.3×0.2×0.1)
=0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002=0.2016+0.1296+0.756+0.336+0.864+0.504+0.224+0.324+0.144+0.0084+0.0216+0.0036+0.0096+0.0056+0.002
=0.6976=0.6976
Edit: Thank you Vaibhav for providing an alternative method.
Alternate Method:
probability that the plane is hit when all the four shots are fired,
P=1−probability of not hitting the targetP=1−probability of not hitting the target
=1−(0.6×0.7×0.8×0.9)=1−(0.6×0.7×0.8×0.9)
=1−0.3024=1−0.3024
=0.6976
A
Answer: (A) 0.6976
Question: A carpenter worked alone for 1 day on a job that would take him 4 more days to finish. He and another carpenter completed the job in 2 more days. How many days would it have taken the second carpenter to do the complete job working alone?
(A) 5
(B) 7
(C) 9
(D) 14
(E) 24
Rationale: A carpenter worked only 1 day on something that takes him 4 MORE days.
Means;
Carpenter finishes his work in 5 days.
Let his buddy finish the same task in x days.
Respective rates per day:
1/5 AND 1/x
To complete 1 work:
First guy worked for 3 days @ rate=1/5 per day.
Second one worked for 2 days @ rate=1/x per day
Expression:
Days*Rate=Work
3*1/5+2*1/x=1
3x+10=5x
2x=10
x=5 days.
Ans:A
Answer: (A) 5
Question: Two trains 121 meters and 165 meters in length respectively are running in opposite directions, one at the rate of 80 km and the other at the rate of 65 kmph. In what time will they be completely clear of each other from the moment they meet?
(A) 7.16
(B) 7.19
(C) 7.13
(D) 7.15
(E) 7.11
Rationale: T = (121 + 165)/ (80 + 65) * 18/5
T = 7.15
Answer:D
Answer: (D) 7.15
Question: Among 400 students, 56% study sociology, 44% study mathematics and 40% study biology. If 42% of students study both mathematics and sociology, what is the largest possible number of students who study biology but do not study either mathematics or sociology?
(A) 30
(B) 90
(C) 120
(D) 168
(E) 188
Rationale: I would just like to add a bit of explanation after the step where you calculate that the number of students studying both M and S = 168
Using your analysis:
We see that the total number of students who study either Maths or Sociology = 176 + 224 - 168 = 232
So, in the image we know that the number of students in the zone with the black boundary = 232
Let's assume the number of students who studyonlybiology to beb(this is the number that we have to maximize)
And, let's assume the number of students who study none of the three subjects, that is the number of students in the white space =w
Since the total number of students = 400, we can write:
232 +b+w= 400
Or,b+w= 400 - 232 = 168
That is,b= 168 -w
So, the maximum value ofbwill happen forw= 0
This is how we get, the maximum value ofb= 168
D
Answer: (D) 168
Question: If points A and B are (6-1) units apart, which of the following can have only one possible value?
I. The area of a square region with side AB
II. The circumference of a circle passing through points A and B
III. The area of a rectangular region with diagonal AB
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only
Rationale: I. The area of a square region with side AB --> side=AB=(6-1) or 5 --> the area of a square is 5^2=25, so only one possible value;
II. The circumference of a circle passing through points A and B --> circle is not defined by only two points, hence the circumference of a circle passing through points A and B can take infinitely many values. For example consider when AB=diameter and when points A and B are not the endpoints of the diameter;
III. The area of a rectangular region with diagonal AB --> consider the case when AB is the diagonal of a square (the area is 25/2) and the case when AB is the diagonal of a rectangle with the sides equal to 3 and 4 (the area 12).
Answer: A.
Answer: (A) I only
Question: Three seventh of a number is 12 more than 40% of that number. What will be the 50% of that number?
(A) A)148
(B) B)210
(C) C)105
(D) D)248
(E) E)258
Rationale: 3/7 x – 40/100 x = 12
x = 35 * 12
35 * 12 * 50/100 = 210/2 = 105
ANSWER:C
Answer: (C) C)105
Question: Tough and Tricky questions: Absolute Values.
If |a| = 1/4 and |b| = 1/2, which of the following CANNOT be the result of a + b?
(A) -1
(B) -1/4
(C) 3/4
(D) -3/4
(E) 1/4
Rationale: |a| = 1/4
Absolute value of 'a' can have two values = 1/4 and -(1/4)
|b| = 1/2
Absolute value of 'b' can have two values = 1/2 and -(1/2)
Now different combinations of a + b are as follows:
a + b = (1/4) + (1/2) = 3/4
- a - b = -(1/4) - (1/2) = -3/4
a - b = (1/4) - (1/2) = -(1/4)
-a + b = -(1/4) + (1/2) = 1/4
Cross verifying with the given options, left over option is A.
Answer: (A) -1
Question: In each series, look for the degree and direction of change between the numbers. In other words, do the numbers increase or decrease, and by how much?Look at this series: 1, 5, 7, 3, __, 1 ...Which number is missing?
(A) 2
(B) 4
(C) 12
(D) 0
(E) 13
Rationale: E13This is an alternating addition and subtraction series. In the first pattern, 6 is added to each number to arrive at the next. In the second, 2 is subtracted from each number to arrive at the next.
Answer: (E) 13
Question: A train passes a platform in 34 seconds. The same train passes a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, The length of the platform is
(A) 280 meter
(B) 240 meter
(C) 210 meter
(D) 200 meter
(E) None of these
Rationale: Explanation:
Speed of the train = 54 km/hr = (54×10)/34 m/s = 15 m/s
Length of the train = speed × time taken to cross the man = 15×20 = 300 m
Let the length of the platform = L
Time taken to cross the platform = (300+L)/15
=> (300+L)/15 = 34
=> 300+L = 15×34 = 510
=> L = 510-300 = 210 meter
Answer: Option C
Answer: (C) 210 meter
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.2389
(B) Rs.2380
(C) Rs.2317
(D) Rs.2329
(E) Rs.2318
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: The least umber of five digits which is exactly
divisible by 12,15 and 18 is?
(A) 10000
(B) 10012
(C) 10015
(D) 10018
(E) 10080
Rationale: Least number of five digits is 10000
L.C.Mof 12,15,18 s 180.
On dividing 10000 by 180,the remainder is 100.
Therefore required number=10000+(180-100)
=10080.
Option E
Answer: (E) 10080
Question: In a factory, there are 40% technicians and 60% non-technicians. If the 60% of the technicians and 40% of non-technicians are permanent employees, then the percentage of workers who are temporary is?
(A) 52
(B) 32
(C) 62
(D) 25
(E) 20
Rationale: Total = 100
T= 40 NT= 60
40*(60/100)=24 60*(40/100)=24
24 + 24 = 48 => 100 - 48 = 52%
ANSWER A
Answer: (A) 52
Question: The product X of two prime numbers is between 17 and 60. If one of the prime numbers is greater than 2 but less than 6 and the other is greater than 13 but less than 25, then X =
(A) 18
(B) 29
(C) 37
(D) 44
(E) 57
Rationale: Option BC can be ruled out as they themselves are prime numbers
18 = 2*9 = 3*6 >> Ignore
44 = 2 * 22 = 4 * 11 >> Ignore
57 = 3*19 >> Answer
Answer = E
Answer: (E) 57
Question: Which of the following is a pair of Co - Primes ?
(A) 14,35
(B) 18,25
(C) 31,92
(D) 32,62
(E) 18,43
Rationale: Co Primes - two numbers are said to be co prime if their HCF is 1.
18 and 25 are co prime numbers. ANSWER : B
Answer: (B) 18,25
Question: Kim bought a total of $2.65 worth of postage stamps in four denominations. If she bought an equal number of 5-cent and 25-cent stamps and twice as many 10-cent stamps as 5-cent stamps, what is the least number of 3-cent stamps she could have bought ?
(A)  5
(B)  10
(C)  15
(D)  20
(E)  25
Rationale: 2.65 = 0.05x + 0.25x + 2 * 0.10x + 0.03y
=> 2.65 = 0.30x + 0.20x + 0.03y
=> 265 = 50x + 3y
So Max value of 50x < 265 = 250
Hence y = 5
Answer - A
Answer: (A)  5
Question: A committee is reviewing a total of 40x black-and-white films and 10y color films for a festival. If the committee selects y/x% of the black-and-white films and all of the color films, what fraction of the selected films are in color?
(A) 50/52
(B) 55/52
(C) 60/52
(D) 40/52
(E) 30/52
Rationale: Say x=y=10. In this case we would have:
40x=400 black-and-white films;
10y=100 color films.
y/x%=10/10%=1% of the black-and-white films, so 4 black-and-white films and all 100 color films, thus total of 104 films were selected.
Color films thus compose 100/104=50/52 of the selected films.
Answer: A
Answer: (A) 50/52
Question: For every even positive integer m, f(m) represents the product of all even integers from 2 to m, inclusive. For example, f(12)=2x4x6x8x10x12. What is the greatest prime factor of f(28)?
(A) 2
(B) 7
(C) 11
(D) 13
(E) 17
Rationale: f(28) = 2*4*6*8*10*12*14*16*18*20*22*24*26*28
The greatest prime factor in this list is 13.
The answer is D.
Answer: (D) 13
Question: IF 2+3=13 ; 3+5=31 ; 5+7=59, Then 7+9=?
(A) 95
(B) 86
(C) 67
(D) 98
(E) 89
Rationale: 2 X 2 + 3^2 = 4 + 9 = 13
3 X 2 + 5^2= 6 + 25 = 31
5 X 2 + 7^2= 10 + 49 = 59
and
7 X 2 + 9^2= 14 + 81 = 95
ANSWER:A
Answer: (A) 95
Question: The average marks of a class of 30 students is 40 and that of another class of 50 students is 70. Find the average marks of all the students?
(A) 52.5
(B) 52.9
(C) 52.1
(D) 58.75
(E) 42.5
Rationale: Sum of the marks for the class of 30 students = 30 * 40 = 1200
Sum of the marks for the class of 50 students = 50 * 70 = 3500
Sum of the marks for the class of 80 students =
1200 + 3500 = 4700
Average marks of all the students = 4700/80
= 58.75
Answer:D
Answer: (D) 58.75
Question: In a stream running at 2 Kmph, a motor boat goes 10 Km upstream and back again to the starting point in 55 minutes. Find the speed of motor boat in still water?
(A) 11
(B) 15
(C) 22
(D) 18
(E) 25
Rationale: Let the speed of motor boat instill water be X kmph
Then, speed in downstream = (X + 2) km
and. speed in upstream = (X - 2) kmph
Time taken to row 10km & back = (10/X+2,10/X-2)
10/X+2 + 10/X-2 = 55/60
11X2 - 240X - 44 = 0
(X - 22)(11x + 2) = 0
X = 22 or X = -2/11
Then X = 22 kmph
Answer is C.
Answer: (C) 22
Question: A can give B 100 meters start and C 120 meters start in a kilometer race. How much start can B give C in a kilometer race?
(A) 10.22 meters
(B) 11.22 meters
(C) 22.22 meters
(D) 33.22 meters
(E) None of these
Rationale: Explanation:
A runs 1000 meters while B runs 900 meters and C runs 880 meters.
Therefore, B runs 900 meters while C runs 880 meters.
So, the number of meters that C runs when B runs 1000 meters = (1000 x 880)/900 = 977.778 meters
Thus, B can give C (1000 - 977.77) = 22.22 meters start
Answer: C
Answer: (C) 22.22 meters
Question: In a certain game, a large bag is filled with blue, green, purple and red chips worth 1, 5, x and 11 points each, respectively. The purple chips are worth more than the green chips, but less than the red chips. A certain number of chips are then selected from the bag. If the product of the point values of the selected chips is 28160, how many purple chips were selected?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: 28160 = 1*5*8^3*11
The factors of 8 must come from the purple point value, so there are 3 purple chips.
The answer is C.
Answer: (C) 3
Question: A school currently maintains a fixed number of students per class. If the ratio of students per class were to be increased by 1, 10 fewer classes would be run for a total of 120 students. What is the current ratio T of students per class?
(A) T=3
(B) T=4
(C) 6
(D) 8
(E) 12
Rationale: Another way to look at the problem...
Since the total is 120, RATIO * CLASSES = R*C = 120.....(i)
we are looking where ratio increases by 1 and # of classes decreases by 10 = (R+1)(C-10) = RC+C-10R-10=120....(ii)
(ii)-(i)....
C=10R+10 = 10(R+1).......
so # of classes has to be multiple of 10
AS RC=120.... 10(R+1)*R = 120...................R(R+1) = 12..
so 12 is a multiple of consecutive numbers ONLY 3 *4 fits in..... and R=3
A
Answer: (A) T=3
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 per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week James worked a total of 42 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) 39
Rationale: James worked for 41 hours hence he earned 40*x+2*2x=44x dollars;
We know that Harry also earned the same 44x dollars, out of which he earned 30x dollars for thefirst 30 hoursplus 14x additional dollars. Since for each additional hour he gets 1.5x dollars then he worked for 14x/1.5x=9 additional hours, so Harry worked for total of 30+9=39 hours.
Answer: E.
Answer: (E) 39
Question: In a certain lottery, the probability that a number between 14 and 20, inclusive, is drawn is 1/6 . If the probability that a number 14 or larger is drawn is 2/3 , what is the probability that a number less than or equal to 20 is drawn?
(A)  1/18
(B)  1/6
(C)  1/2
(D)  1/3
(E)  5/6
Rationale: You can simply use sets concept in this question. The formula
Total = n(A) + n(B) - n(A and B) is applicable here too.
Set 1: Number 14 or larger
Set 2: Number 20 or smaller
1 = P(Set 1) + P(Set 2) - P(Set 1 and Set 2) (combined probability is 1 because every number will be either14 or moreOR20 or lessOR both)
2/3 + P(Set 2) - 1/6 = 1
P(Set 2) = 1/2
Answer (C)
Answer: (C)  1/2
Question: A question paper consists of five problems, each problem having three internal choices. In how many ways can a candidate attempt one or more problems?
(A) 1028
(B) 1024
(C) 1023
(D) 1025
(E) 1084
Rationale: Explanation:
Given that, the question paper consists of five problems. For each problem, one or two or three or none of the choices can be attempted.
Hence, the required number of ways = 45 - 1.
= 210 - 1 = 1024 - 1 = 1023
Answer:C
Answer: (C) 1023
Question: A cube is divided into 729 identical cubelets. Each cut is made parallel to some surface of the cube . But before doing that the cube is coloured with green colour on one set of adjacent faces ,red on the other set of adjacent faces, blue on the third set. So, how many cubelets are there which are painted with exactly one colour?
(A) 293
(B) 294
(C) 295
(D) 296
(E) 298
Rationale: total cubes created are 729
so a plane of big cube has 9*9 cubes
out of that(n-2)*(n-2)=7*7=49 are painted only one side
and a cube has six sides=6*49=294
ANSWER:B
Answer: (B) 294
Question: What is the radius of a circle that has a circumference of 3.14 meters?
(A) 0.1
(B) 0.3
(C) 0.5
(D) 0.7
(E) 0.9
Rationale: Circumference of a circle = 2πr.
Given, circumference = 3.14 meters.
Therefore,
2πr = Circumference of a circle
or, 2πr = 3.14.
or, 2 * 3.14r = 3.14,[Putting the value of pi (π) = 3.14].
or, 6.28r = 3.14.
or, r = 3.14/6.28.
or, r = 0.5.
correct answer C
Answer: (C) 0.5
Question: Johnop went up a certain hill at the rate of one and a half kilometers per hour and came down at the rate of four and a half kilometers per hour, so that it took just four hours to make the double journey. How far was it to the top of the hill ?
(A) 3 km
(B) 6 km
(C) 4.5 km
(D) km
(E) none of the above
Rationale: Assume the distance to the top of the hill (1 way) as: x
Now, speed=distance/time => time=distance/speed
So, for the first half of the journey, he traveled uphill at 1.5km/hr, so the time taken for the first leg of the journey is: x/1.5.
For the second half, he traveled downhill at 4.5km/hr, so the time taken for the second leg of the journey is: x/4.5
Now, the total time for the trip is given as 4 hrs.
Equating, (x/1.5)+(x/4.5)=4 => (3x+x)/4.5=4 => x=4.5 km
So, the distance one side is = 4.5 km.
The OA mentioned is 9km, which is exactly double of this distance, i.e., the total distance traveled during both legs of the journey, but the question only asked for the distance till the top of the hill, i.e., one way, so the answer should be 4.5km
Can someone assist me in understanding where am I wrong here?
Answer: (C) 4.5 km
Question: fill in ht blank:(a) the point with coordinates (0,0) is called ____ of a rectangular coordinate system,(b) to find the y-intercept of a line, we let ___ equal 0 and solve for ___; to find x- intercept , we let ____ equal 0 and solve for___
(A) (a) the point with coordinates (0,0) is called axis of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for y
(B) (a) the point with coordinates (0,0) is called axis of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for x ; to find x- intercept , we let y equal 0 and solve for y
(C) (a) the point with coordinates (0,0) is called line of a rectangular coordinate system, (b) to find the y-intercept of a line, we let y equal 0 and solve for z ; to find x- intercept , we let x equal 0 and solve for x
(D) (a) the point with coordinates (0,0) is called end of a rectangular coordinate system, (b) to find the y-intercept of a line, we let z equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for x
(E) none of the above
Rationale: (a) the point with coordinates (0,0) is called origin of a rectangular coordinate system, (b) to find the y-intercept of a line, we let x equal 0 and solve for y ; to find x- intercept , we let y equal 0 and solve for xcorrect answer (E)
Answer: (E) none of the above
Question: P and Q entered into a partnership investing Rs. 16,000 and Rs. 12,000 respectively. After 3 months, A withdrew Rs.5000 while B invested Rs. 5000 more. After 3 more months, C joins the business with a capital of Rs. 21,000. The share of B exceeds that of C, out of a total profit of Rs. 26,400 after one year by:
(A) Rs.2400
(B) Rs.3000
(C) Rs.3600
(D) Rs.4800
(E) Rs.3800
Rationale: A : B : C = (16000 x 3 + 11000 * 9) : (12000 * 3 + 17000 * 9) : (21000 * 6)
= 147 : 189 : 126 = 7 : 9 : 6.
Therefore, Difference of B and C’s shares = Rs. 26400 x 9/22 – 26400 x 6/22
= Rs.3600
ANSWER:C
Answer: (C) Rs.3600
Question: Kyle, Devon, and Catherine each try independently to solve a problem. If their individual probabilities for success are 1/2, 1/3 and 5/9, respectively, what is the probability that Kyle but not Devon and Catherine will solve the problem?
(A) 13/29
(B) 1/4
(C) 15/21
(D) 11/19
(E) 4/27
Rationale: P(Kyle will solve)=1/2
P(Devon will not solve)= 1 - 1/3 = 2/3
P(Catherine will not solve) = 1- 5/9 = 4/9
P= (1/2)*(2/3)*(4/9) = 8/54 = 4/27.
Answer:E
Answer: (E) 4/27
Question: Of the teams competing in the world archery championships, Fifty percent are from Europe. Half as many are from the United States and one twentieth are from Africa. What fraction of teams are from neither Europe, the US or Africa.
(A) 13/20
(B) 4/20
(C) 13/15
(D) 17/20
(E) 13/17
Rationale: Assume 100 total people.
50% of 100 = 50 --->Europeans
1/2 of 50 ---> 25 Americans
1/20 of 100 ---> 5 Africans
Now you would add them all up, and minus it by the total (100). 100 - 80= 20. So, 20 people out of 100 are not EU, US or Africans. 20/100 is also equal to 4/20.
So therefore, the answer is B.
Answer: (B) 4/20
Question: An empty fuel tank with a capacity of 212 gallons was filled partially with fuel A and then to capacity with fuel B. Fuel A contains 12% ethanol by volume and fuel B contains 16% ethanol by volume. If the full fuel tank contains 30 gallons of ethanol, how many gallons of fuel A were added?
(A) 160
(B) 98
(C) 100
(D) 80
(E) 50
Rationale: Say there are A gallons of fuel A in the tank, then there would be 212-A gallons of fuel B.
The amount of ethanol in A gallons of fuel A is 0.12A;
The amount of ethanol in 212-A gallons of fuel B is 0.16(212-A);
Since the total amount of ethanol is 30 gallons then 0.12A+0.16(212-A)=30 --> A=98.
Answer: B.
Answer: (B) 98
Question: In an election between two candidates, one got 55% of the total valid votes, 20% of the votes were invalid. If the total number of votes was 7500, the number of valid votes that the other candidate got, was:
(A) 2700
(B) 2800
(C) 2000
(D) 2500
(E) 2600
Rationale: Number of valid votes = 80% of 7500 = 6000.
Valid votes polled by other candidate = 45% of 6000
=(45/100)x 6000= 2700.
ANSWER A
Answer: (A) 2700
Question: If s > x > y > z on the number line, y is halfway between x and z, and x is halfway between w and z, then (y - x)/(y - s) =
(A) 1/4
(B) 1/3
(C) 1/2
(D) 3/4
(E) 1
Rationale: Let y-z=t ---> since y is halfway between x and z and x>y we have x-y=t. Moreover x-z=(x-y)+(y-z)=2t. Similarly since x is halfway between w and z, we have s-x=2t. So y-x=-t, y-s=-3t. ---> (y - x)/(y - s) = 1/3.
The answer is (B).
Answer: (B) 1/3
Question: In how many ways can the letters of wordTECHNOLOGYbe arranged such that all the Consonants always appear together?
(A) 9!
(B) 4!*7!
(C) 5!*5!
(D) 5!*4!*2!
(E) 6!*4!
Rationale: Let the arrangment be: _ _ _ _ _ _ _ _ _ _ (10 letters, 3 vowels E, O, O and 7 consonant T, C, H, N, L, G, Y)
For all consonants together, consider them as 1 group {T, C, H, N, L, G, Y} E O O --> this gives us 4! arrangements with {} group considered as 1 . Now {} group can in itself be arranged in 7! ways
Thus total arrangements with all consonants together = 4!*7! --> B is the correct answer.
Answer: (B) 4!*7!
Question: The speed at which a man can row a boat in still water is 15 kmph. If he rows downstream, where the speed of current is 3 kmph, what time will he take to cover 60 metres?
(A) 11 seconds
(B) 88 seconds
(C) 99 seconds
(D) 12 seconds
(E) 18 seconds
Rationale: Speed of the boat downstream = 15 + 3 = 18 kmph
= 18 * 5/18 = 5 m/s
Hence time taken to cover 60 m = 60/5 = 12 seconds.Answer: D
Answer: (D) 12 seconds
Question: If p(x)=ax^4+bx^3+cx^2+dx+e has roots at x=1,2,3,4 and p(0)=48, what is p(5)
(A) 48
(B) 24
(C) 0
(D) 50
(E) 40
Rationale: p(x)=ax^4+bx^3+cx^2+dx+e
it can be written as
p(x)=a*(x-1)*(x-2)*(x-3)*(x-4) ----(1)
put x=0 in(1), we get
p(0)=a*(-1)(-2)(-3)(-4)
=> 48=a*24
=> a=2
so, p(x)=2*(x-1)*(x-2)*(x-3)*(x-4)
=> p(5)=2*(5-1)*(5-2)*(5-3)*(5-4)=2*4*3*2*1=48
p(5) = 48
ANSWER:A
Answer: (A) 48