mathewhe/aqua_rat huggingface dataset:
Question: A trained covered x km at 30 kmph and another 2x km at 20 kmph. Find the average speed of the train in covering the entire 3x km.
(A) 22.5
(B) 99
(C) 24
(D) 66
(E) 887
Rationale: Total time taken = x/30 + 2x/20 hours
= 2x/15 hours
Average speed = 3x/(2x/15) = 22.5 kmph
Answer: A
Answer: (A) 22.5
Question: If x, y, and z are positive integers and 3x = 4y = 7z, then the least possible value of x - y + z is
(A) 33
(B) 40
(C) 49
(D) 19
(E) 61
Rationale: x - y + z = - 3x/4 + x + 3x/7
= (- 21 + 28 + 12 )x/28 = 19x/28
19 is not divisible by 28(it's a prime #), so for least value, x = 28
Answer - D
Answer: (D) 19
Question: Find the value of m 12519 x 9999 = m?
(A) 125177481
(B) 353654655
(C) 545463251
(D) 725117481
(E) 477899932
Rationale: 12519 x 9999 = 12519 x (10000 - 1)
= 12519 x 10000 - 12519 x 1
= 125190000 - 12519
= 125177481
A
Answer: (A) 125177481
Question: If 10 parallel lines in a plane is intersected by a family of another 8 parallel lines, how many parallelograms are there in the network thus formed?
(A) 80
(B) 63
(C) 120
(D) 160
(E) 1260
Rationale: parallelogram can formed by 2 horizontal and 2 vertical lines
for horizontal 10c2
for vertical 8c2
total parallelogram is 10 c2*8c2=45*28
=1260
ANSWER:E
Answer: (E) 1260
Question: Today is Thursday. The day after 55 days will be?
(A) Monday
(B) Tuesday
(C) Saturday
(D) Sunday
(E) wednesday
Rationale: Explanation:
55 days = 7 weeks 6 days = 6 odd days
Hence if today is Thursday, After 55 days, it will be = (Thursday + 6 odd days)
= Wednesday
Answer: Option E
Answer: (E) wednesday
Question: A father divides his estate among his three sons, in such a manner, that:
The first has $1000 less than half of the whole;
The second has 800 less than one third of the whole;
The third has 600 less than one fourth of the whole;
What is the value of the estate?
(A) 18800
(B) 28800
(C) 38800
(D) 48800
(E) None
Rationale: Solution
If the whole estate be represented by x, then the several shares will be x/2 - 1000, and x/3 - 800, and x/4 - 600.
And as these constitute the whole estate, they are together equal to x.
We have then this equation x/2 - 1000 + x/3 - 800 + x/4 - 600 = x.
Which reduced gives x = 28800
Proof 28800/2 - 1000 + 28800/3 - 800 + 28800/4 - 600 = 28800
Answer B
Answer: (B) 28800
Question: The speed of a boat in upstream is 60 kmph and the speed of the boat downstream is 80 kmph. Find the speed of the boat in still water and the speed of the stream?
(A) 10 kmph.
(B) 17 kmph.
(C) 18 kmph.
(D) 11 kmph.
(E) 12 kmph.
Rationale: Speed of the boat in still water = (60+80)/2 = 70 kmph. Speed of the stream = (80-60)/2
= 10 kmph.
Answer:A
Answer: (A) 10 kmph.
Question: The unit digit in the product (224 * 607 * 214 * 863) is:
(A) 2
(B) 5
(C) 6
(D) 8
(E) 10
Rationale: Explanation:
Unit digit in the given product = Unit Digit in (4*7*4*3) = 6
ANSWER: C
Answer: (C) 6
Question: 4 weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 16 weavers in 16 days?
(A) 16
(B) 32
(C) 64
(D) 96
(E) 128
Rationale: 1 weaver can weave 1 mat in 4 days.
16 weavers can weave 16 mats in 4 days.
16 weavers can weave 64 mats in 16 days.
The answer is C.
Answer: (C) 64
Question: An inspector rejects 10% of the meters as defective. How many will he examine to reject 12?
(A) A)100
(B) B)120
(C) C)250
(D) D)200
(E) E)160
Rationale: Then, 10% of x= 12
(10/100)x = 12
x = (12*100*)/10= 120
Answer is B
Answer: (B) B)120
Question: The Snow Lovers Ski Team is comprised of 4 men and 8 women. If a team of 5 skiers is to be randomly selected to pack the skis into the bus, what is the probability that the team will have exactly 3 women?
(A) 14/33
(B) 7/33
(C) 2/7
(D) 13/73
(E) 12/27
Rationale: Combination Probability Formula: nCr = n!/[r!(n-r)!]
Total possible, select 5 people from 12 people = 12C5 = 12!/[5!(12 - 5)!] = 792.
To have 3 women there must be 2 men, select 2 men from 4 = 4C2 = 6.
And, select 3 women from 8 = 8C3 = 56.
3 women and 2 men = (6)(56) = 336
Probability = (number outcomes favorable)/(total number outcomes) = 336/792 = 14/33
Answer: A
Answer: (A) 14/33
Question: The inverse ratio of 3: 2: 1 is?
(A) 2:9:5
(B) 2:3:0
(C) 2:3:5
(D) 2:3:6
(E) 2:3:1
Rationale: 1/3: 1/2: 1/1 = 2:3:6
Answer:D
Answer: (D) 2:3:6
Question: Compute the value of a + b + c + d.
(A) 40
(B) 50
(C) 60
(D) 70
(E) 80
Rationale: Let s = a + b + c + d. Subtracting s from each side of the equations gives us
ab - a - b = 13-s
bc - b - c = 27- s
cd - c -d = 30 - s
da - d - a = 17 - s
Adding one to each side of the equations and applying Simon's Favorite Factoring Trick gives
us
(a - 1)(b - 1) = 14 - s
(b - 1)(c - 1) = 28 -s
(c - 1)(d - 1) = 31 - s
(d - 1)(a - 1) = 18 - s
Multiplying the first and third equations and the second and fourth equations allows us to write
the following equality:
(a - 1)(b - 1)(c - 1)(d - 1) = (14 - s)(31 - s) = (28 - s)(18 - s)
Expanding and solving for s gives us s = 70 .
correct answer D
Answer: (D) 70
Question: The angles of a triangle are in the ratio 1:6:8. Find the measurement of the largest of three angles of triangle.
(A) 96°
(B) 100°
(C) 120°
(D) 140°
(E) 160°
Rationale: If the ratio of the three angles is 1:6:8, then the measures of these angles can be written as x, 6x and 8x. Also the sum of the three interior angles of a triangle is equal to 180°. Hence
x + 6x + 8x = 180
Solve for x
15x = 180
x = 12
The measures of the three angles are
x = 12°
6x = 6 × 12 = 36°
8x = 8 × 12 = 96°
A
Answer: (A) 96°
Question: Which of the following equations represents a line that is perpendicular to y=1/2*x+3?
(A) y−2x=8
(B) 2x+4y=10
(C) 3y+6x=12
(D) 4y−8x=16
(E) 5x−10y=20
Rationale: For two lines to be perpendicular, the product of slopes should be equal to -1.
Slope of line 1 = 1/2
Slope of the line perpendicular to line 1 must be -2. Option C can be rewritten as y = -2x + 4 --> Slope = -2
Answer: E
Answer: (E) 5x−10y=20
Question: In how many different ways can the letters of the word 'LEADING' be arranged such that the vowels should always come together?
(A) 120
(B) 190
(C) 250
(D) 370
(E) 720
Rationale: The word 'LEADING' has 7 letters. It has the vowels 'E','A','I' in it and these 3 vowels should always come together. Hence these 3 vowels can be grouped and considered as a single letter. that is, LDNG(EAI).
Hence we can assume total letters as 5 and all these letters are different. Number of ways to arrange these letters
=5!=5×4×3×2×1=120
In the 3 vowels (EAI), all the vowels are different. Number of ways to arrange these vowels among themselves
=3!=3×2×1=6=3!=3×2×1=6
Hence, required number of ways=120×6=720
Answer: E
Answer: (E) 720
Question: In how many ways can live boys and three girls sit in a row such that all boys sit together?
(A) 1972
(B) 9022
(C) 2880
(D) 1097
(E) 2781
Rationale: Treat all boys as one unit. Now there are four students and they can be arranged in 4! ways. Again five boys can be arranged among themselves in 5! ways.
Required number of arrangements
= 4! * 5! = 24 * 120
= 2880.
Answer:C
Answer: (C) 2880
Question: How many minutes does the bus stop per hour, if the speed of the bus including stoppages is 25 kmph and excluding stoppages is 30 kmph?
(A) 5
(B) 9
(C) 10
(D) 12
(E) 15
Rationale: Explanation:
T = 5/30 * 60 = 10
Answer: Option C
Answer: (C) 10
Question: What is the value of 4^5+4^8?
(A)  4^12
(B)  4^35
(C)  17(4^5)
(D)  8^12
(E)  65(4^5)
Rationale: 4^5+4^8
=4^5(1+4^3)
=4^5 * 65
Answer E
Answer: (E)  65(4^5)
Question: Evaluate 45 / .05
(A) 700
(B) 900
(C) 705
(D) None of these
(E) 506
Rationale: Explanation:
45/.05 = 4500/5 = 900
Option B
Answer: (B) 900
Question: A, B and C completed a piece of work, A worked for 6 days, B for 9 days and C for 4 days. Their daily wages were in the ratio of 3:4:5. Find the daily wages of C, if their total earning was Rs.1480?
(A) 3387
(B) 277
(C) 100
(D) 288
(E) 266
Rationale: 3x 4x 5x
6 9 4
18x + 36x + 20x = 1480
74x = 1480 => x = 20
5x = 100 Rs.
Answer:C
Answer: (C) 100
Question: A corporation paid $5 million in federal taxes on its first $50 million of gross profits and then $30 million in federal taxes on the next $150 million in gross profits. By approximately what percent did the ratio of federal taxes to gross profits increase from the first $50 million in profits to the next $150 million in profits?
(A)  6%
(B)  14%
(C)  20%
(D)  140%
(E)  43%
Rationale: Difference in Ratios = (30/150) - (5/50) = (5/50)
% Change = (Change (5/50) / Original ratio (7/50)) *100 = 140%
Answer - D
Answer: (D)  140%
Question: How many three letter words are formed using the letters of the word TIME?
(A) 22
(B) 76
(C) 88
(D) 24
(E) 88
Rationale: The number of letters in the given word is four.
The number of three letter words that can be formed using these four letters is
= 4 * 3 * 2 = 24.
Answer: D
Answer: (D) 24
Question: Which is less than 3?
(A) 3
(B) 0.3
(C) 33
(D) 3/1
(E) 13
Rationale: 0.3 less than 3.
Answer: B
Answer: (B) 0.3
Question: A tank is 25 m long, 12 m wide and 6 m deep. The cost of plastering its walls and bottom at 75 paise per sq. m, is:
(A) Rs. 456
(B) Rs. 458
(C) Rs. 558
(D) Rs. 568
(E) None of these
Rationale: Explanation:
Area to be plastered = [2(l + b) x h] + (l x b)
= {[2(25 + 12) x 6] + (25 x 12)} m2
= (444 + 300) m2
= 744 m2.
Cost of plastering = Rs. 744 x 75 / 100 = Rs. 558
Answer: C
Answer: (C) Rs. 558
Question: The number of new words that can be formed by rearranging the letters of the word 'ALIVE' is?
(A) 168
(B) 127
(C) 119
(D) 154
(E) 252
Rationale: Number of words which can be formed
= 5! - 1 = 120 - 1
= 119.
Answer:C
Answer: (C) 119
Question: If three painters can complete three rooms in three hours, how many painters would it take to do 27 rooms in 9 hours?
(A) 10
(B) 8
(C) 7
(D) 9
(E) 11
Rationale: Explanation:
Three painters can complete three rooms in three hours.So 27 rooms can be painted in 9 hrs by 9 painters
Answer: D) 9 painters
Answer: (D) 9
Question: Two trains 200 m and 300 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
(A) 18
(B) 10.9
(C) 10.4
(D) 10.8
(E) 10.1
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 200 + 300 = 500 m.
Required time = 500 * 9/250 = 18 secs
Answer: A
Answer: (A) 18
Question: A car dealership has 40 cars on the lot, 20% of which are silver. If the dealership receives a new shipment of 80 cars, 35% of which are not silver, what percentage of total number of cars are silver?
(A) 30%
(B) 35%
(C) 40%
(D) 45%
(E) 50%
Rationale: The number of silver cars is 0.2*40 + 0.35*80 = 36
The percentage of cars which are silver is 36/120 = 30%
The answer is A.
Answer: (A) 30%
Question: The area of a circular field is 13.86 hectares. Find the cost of fencing it at the rate of Rs. 4.70 per metre.
(A) 2399
(B) 6204
(C) 2999
(D) 5808
(E) 2888
Rationale: Explanation:
Area = (13.86 x 10000) sq.m = 138600 sq.m
Circumference =
Cost of fencing = Rs. (1320 x 4.70) = Rs. 6204.
Answer: B) 6204
Answer: (B) 6204
Question: A certain NYC taxi driver has decided to start charging a rate of 10 cents per person per mile. How much, in dollars, would it cost 3 people to travel x miles if he decides to give them a 50% discount?
(A) 15x/100
(B) 3x/100
(C) 3/200
(D) 3x/300
(E) x/200
Rationale: 1 person for x miles = 10 x cents
3 person for x miles = 3x10 x = 30x cents
After discount 50% = 30x/2 = 15x cents
In dollars = 15x/100
Answer : A
Answer: (A) 15x/100
Question: Tanks A and B are each in the shape of a right circular cylinder. The interior of tank A has a height of 9 meters and a circumference of 8 meters, and the interior of tank B has a height of 8 meters and a circumference of 10 meters. The capacity of tank A is what percent of the capacity of tank B?
(A) 72%
(B) 80%
(C) 100%
(D) 120%
(E) 125%
Rationale: For A, r=8/2pi. Its capacity = (4pi)^2 * 9= 144pi
For B, r=10/pi. Its capacity = (5pi)^2 *8 = 200pi
A/B = 144pi/200pi = 0.72
A
Answer: (A) 72%
Question: A four digit safe code does not contain the digits 1 and 4 at all. What is the probability that it has at least one even digit?
(A) ¼
(B) ½
(C) ¾
(D) 15/16
(E) 1/16
Rationale: 1) probability approach:
Probability of at least one even digit = Probability of one even digit + Probability of two even digits + Probability of three even digits + Probability of four even digits
I have four even digits: 0,2,6,8 and four odd digits: 3,5,7,9
So the probability of even digit is 1/21/2, as well of odd digit.
P1 = 1/21/2
P2 = 1/22=1/41/22=1/4
P3 = 1/23=1/81/23=1/8
P4 = 1/24=1/161/24=1/16
P = P1+P2+P3+P4 = 15/1615/16
2) combinatorial approach:
This approach is missing.
3) reversal probability approach:
Probability of at least one even digit = 1 - Probability of four odd digits
P = 1−1/24=15/16
ANSWER:D
Answer: (D) 15/16
Question: Tom and John traveled in the same direction along the equal route at their constant speed rates of 15 km per hour and 10 km per hour, respectively. After 15 minutes Tom passed John, Tom reaches a certain Gas station, how many R minutes it takes John to reach the station?
(A) 5 min
(B) 6 min
(C) 7 and 1/2 min
(D) 8 min
(E) 10 min
Rationale: Since the question states “after 15 minutes”, we can say Tom traveled 15/4km for 15 minutes as he can travel 15km per hour. Hence, using the same logic, we can say John traveled 10/4km as he travels 10km per hour. So, John has to travel (15/4)-(10/4)km=5/4km more. Since John’s speed is 10km/hour, which means 1km/6minutes. As he has to travel 5/4km more, it is going to take him 6(5/4) minutes. Hence,R= 6(5/4)=15/2 minutes. The correct answer is C.
Answer: (C) 7 and 1/2 min
Question: Sandy walks around a circular field at the rate of one round per hour while Molly runs around it at the rate of five rounds per hour. If they start in the same direction from the same point, how many minutes will it take until they meet again?
(A) 9
(B) 12
(C) 15
(D) 18
(E) 21
Rationale: Since Sandy and Molly move in the same direction along the circle, they will first meet each other when there is a difference of one round between the two.
The relative speed of Sandy and Molly is 5 - 1 = 4 rounds per hour.
The time required to complete one round at this speed is 1/4 hours = 15 minutes.
The answer is C.
Answer: (C) 15
Question: Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is ?
(A) 5/19
(B) 5/12
(C) 5/11
(D) 5/16
(E) 5/17
Rationale: Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9)
= 5/12
Answer: B
Answer: (B) 5/12
Question: A rower whose speed is 9 km/hr in still water rows to a certain point upstream and back to the starting point in a river which flows at 3 km/hr. What is the rower's average speed (in km/hr) for the total journey?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: time upstream = d / 6
time downstream = d / 12
total time = d/6 + d/12 = d/4
average speed = 2d / (d/4) = 8 km/hr
The answer is B.
Answer: (B) 8
Question: Each of the 11 letters A, H, I, M, O, T, U, V, W, X and Z appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many four letter computer passwords can be formed (no repetition allowed) with at least one symmetric letter
(A) 2,145
(B) 6,435
(C) 12,100
(D) 12,870
(E) 326,040
Rationale: Since we are given atleast one symmetric letter in the three letter word we can take the following cases
1. All four
2. One symmetry and other three non
3. Two symmetry and other two non
4. Three symmetry and one non
4. All the three letters can be arranged in 24 ways
( 11c4 + 11c1 * 15c3 + 11c2 * 15c2 + 11c3 *15c1 ) * 6
(330 +5005 + 5775+2475 ) * 24
326,040
IMO option E is the correct answer..
OA please...will correct if I missed anything.. E
Answer: (E) 326,040
Question: 5358 x 51 = ?
(A) 273258
(B) 273268
(C) 273348
(D) 273358
(E) None of them
Rationale: =5358 x 51 = 5358 x (50-1)
=5358 x 50 + 5358 x 1
=267900 + 5358 = 273258
Answer is A
Answer: (A) 273258
Question: A town's oldest inhabitant is x years older than the sum of the ages of the Lee triplets. If the oldest inhabitants is now J years old, how old will one of the triplets R be in 20 years?
J-X-40/3 is my answers.
J = X + L + L + L is the initial situation
After 20 years
J + 20 = X + L + L + L + 60 ...20 years for each triplet so 60 years totally.
J - X - 40/ 3 = L is my answer.
What wrong am i doing ? Since the age asked is after 20 years i also consider adding 20 years to J .
(A) (J - 50)/3
(B) 3(J + 20)/x
(C) (J + x - 50)/3
(D) (J - x + 60)/3
(E) (J + x - 20)/3
Rationale: here it goes:
Oldest inhabitant = sum of age of triplets + X
J = 3L + X so L = (J - X)/3
After 20 years = L + 20
R= (J - X)/3 + 20
= (J - X + 60)/3=D
Answer: (D) (J - x + 60)/3
Question: Which is the following is divisible by 11.
(A) 4305
(B) 4825
(C) 4805
(D) 4905
(E) 4906
Rationale: Explanation:
Sum of first 'n' natural numbers = n(n + 1)/2
Sum of first 9 natural numbers = 9(9 + 1)//2 = 9 x 5 = 45
Sum of first 99 natural numbers = 99(99 + 1)//2 = 99 x 50 = 4950
4950 - 45 = 4905
Answer: Option D
Answer: (D) 4905
Question: A can give B 120 meters start and C 200 meters start in a kilometer race. How much start can B give C in a kilometer race?
(A) 90.09 meters
(B) 111.12 meters
(C) 112.12 meters
(D) 113.12 meters
(E) None of these
Rationale: Explanation:
A runs 1000 meters while B runs 880 meters and C runs 800 meters.
Therefore, B runs 880 meters while C runs 800 meters.
So, the number of meters that C runs when B runs 1000 meters = (1000 x 800)/880 = 909.09 meters
Thus, B can give C (1000 - 909.09) = 90.09 meters start
Answer: A
Answer: (A) 90.09 meters
Question: What is the square root of 4,624?
(A) A)18
(B) B)9
(C) C)68
(D) D)62
(E) E)81
Rationale: A square root of a number is a number times itself equals the original number.
Ex) The square root of 81 is 9 because 9 times itself(9) equals the original number(81).
68*68=4,624
4624 divided by x = 68
x=68
(C)68
Answer: (C) C)68
Question: A bag contains 8 red balls, 5 green balls and 6 white balls. A ball is drawn at
random from the box. What is the probability that the ball drawn is either red or green?
(A) 2/5
(B) 3/5
(C) 1/5
(D) 13/19
(E) 8/15
Rationale: Total number of balls = (8 + 5 + 6) = 19.
Therefore, n(S) = 19.
Let E1 = event of drawing a red ball.
and E2 = event of drawing a green ball.
Then, E1 n E2 = f.
P (E1 n E2) = P(E1) + P(E2) = (4/19 + 5/19) = 13/19
ANSWER:D
Answer: (D) 13/19
Question: By selling an Iron-box for Rs. 1000, a shop keeper gains 20%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. His gain percent during the sale is?
(A) 5%
(B) 6%
(C) 12%
(D) 11%
(E) 8%
Rationale: Explanation:
Marked price = Rs. 1000
C.P. = 100/120 * 1000 = Rs. 833.33
Sale price = 90% of Rs. 1000 = Rs. 900
Required gain % = 6.6/833.33 * 100 = 8%.
Answer: E
Answer: (E) 8%
Question: If ABC is an equilateral triangle and AB||CD, what fraction of the area of quadrilateral ABDC is shaded?
(A) 1/4
(B) 1/(2√3)
(C) 1/3
(D) 1/2
(E) 2/3
Rationale: Height of triangle = Height of quadrilateral ABDC = (sqrt 3/2)x3.
Area of triangle ABC =( sqrt 3/4)x3x3
Area of quadrilateral ABDC = ((3+6)/2)x((sqrt 3/2)x3)
Therefore, ratio of Area of triangle ABC to Area of quadrilateral ABDC = 1/3
Answer: (C) 1/3
Question: What percent is 50 gm of 1 kg?
(A) 0.5 %
(B) 1%
(C) 1.5%
(D) 2%
(E) 5%
Rationale: 1 kg = 1000 gm
50/1000 × 100 = 5000/1000
=5%
E)
Answer: (E) 5%
Question: Of the d students at a certain college, x are studying French and y are studying German. If w are studying both French and German, which of the following expresses the number of students at the college not studying either French or German ?
(A)  d + w- x- y
(B)  d - w- x- y
(C)  d- w - x + y
(D)  w + x + y- z
(E)  w - x - y - z
Rationale: {Total} = {French} + {German} - {Both} + {Neither}
d = x + y - w + {Neither}
{Neither} = d + w - x - y.
Answer: A.
Answer: (A)  d + w- x- y
Question: If the arithmetic mean of p and q is 10 and the arithmetic mean of q and r is 26, what is the value of r-p?
(A) 20
(B) 10
(C) 32
(D) 40
(E) 5
Rationale: Arithmetic mean expression for p and q:
(p+q)/2=10 ; p+q=20 ----eq1
Arithmetic mean expression for q and r:
(q+r)/2=20 ; q+r=52 ----eq2
Subtracting eq1 from eq2 we get: r-p=32
Hence, the correct answer is C
Answer: (C) 32
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 24 seconds. The ratio of their speeds is?
(A) 3/6
(B) 3/2
(C) 7/3
(D) 3/5
(E) 5/2
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train
= 27 x meters, and length of the second train
= 17 y meters. (27 x + 17 y) / (x + y) = 24 ==> 27 x + 17 y = 24 x + 24 y
==> 3 x = 7 y ==> x/y
= 7/3.
Answer:C
Answer: (C) 7/3
Question: In how many different ways can 4 physics, 3 math, and 4 chemistry books be arranged in a row so that all books of the same subject are together?
(A) 16,936
(B) 18,226
(C) 20,736
(D) 22,426
(E) 24,856
Rationale: Let's think of each subject as a group so there are 3 groups.
The number of ways to arrange these 3 groups is 3!
Within each subject the books can be re-arranged.
So we need to multiply 3! by 4!*3!*4! which is 3!*4!*3!*4! = 20,736
The answer is C.
Answer: (C) 20,736
Question: The sum of the squares of the fifth and the eleventh term of an AP is 3 and the product of the second and fourteenth term is equal to P.Find the product of the first and the fifteenth term of the AP.
(A) (58P-39)/45
(B) (98P+39)/72
(C) (116P-39)/90
(D) (98P+39)/90
(E) None of these
Rationale: (T5)^2+(T11)^2=3
T2*T14=P
T1*T15=?
(a+4d)^2+(a+10d)^2=3
2a^2+28ad+116d^2=3.....(1)
(a+d)(a+13d)=P
a^2+14ad+13d^2=P
a^2+14ad = P- 13d^2
1.5-45d^2=P
2P=3-90d^2...........(2)
a^2+14ad=?
=P-13d^2
=P-13(3-2P)/90
=(116P-39)/90
ANSWER:C
Answer: (C) (116P-39)/90
Question: The fourth proportional to 14, 22 and 28 is?
(A) 21
(B) 66
(C) 88
(D) 99
(E) 44
Rationale: (22*28)/14 = 44
Answer: E
Answer: (E) 44
Question: Ramu bought an old car for Rs. 42000. He spent Rs. 13000 on repairs and sold it for Rs. 64900. What is his profit percent?
(A) 17%
(B) 68%
(C) 18%
(D) 15%
(E) 38%
Rationale: Total CP = Rs. 42000 + Rs. 13000
= Rs. 55000 and SP
= Rs. 64900
Profit(%) = (64900 - 55000)/55000 * 100
= 18%
Answer: C
Answer: (C) 18%
Question: For any positive x, y and z if x is n% of y and z is m% of y then what percentage Z must x be of z?
(A) (n/m)%
(B) (m × n)%
(C) (100 / [m × n]) %
(D) (100 × m/n)%
(E) (100 × n/m)%
Rationale: x is n% of y MEANS x= (n/100 )* y------------------------eq1
z is m% of y MEANS z= (m/100 )* y------------------------eq2
Find equation of xz
substitute value of y from 2nd equation into Ist equation
so x= (n/100)*(100z/m)
so x= (n/m)z
or x= (100n/m)z/100
so answer Z is 100n/m %.E
Answer: (E) (100 × n/m)%
Question: What profit percent is made by selling an article at a certain price, if by selling at 2/3rd of that price, there would be a loss of 20%?
(A) 55%
(B) 24%
(C) 20%
(D) 25%
(E) 11%
Rationale: Option C
Explanation:
SP2 = 2/3 SP1
CP = 100
SP2 = 80
2/3 SP1 = 80
SP1 = 120
100 --- 20 => 20%
Answer: (C) 20%
Question: Jason is 4 times older than Bob at present. 8 years ago Jason was 12 times older. How old are Jason?
(A) 10
(B) 11
(C) 12
(D) 13
(E) 14
Rationale: Jason age y=4(x)----(1), let us say Jason is x and bob is y
after 8 years Jason age is 8 12 time older than bob so y-8=12(x-8)---(2)
replace (2) equation y with with equation (1) value solve we get x=11 so y=44
ANSWER:B
Answer: (B) 11
Question: A man travels 150km by train at 50km/hr, 200km by ship at 20km/hr, 300km by aeroplane at 100km/hr and 100km by car at 50km/hr. What is the average speed for the entire distance?
(A) 35.3km/hr
(B) 41.67km/hr
(C) 48.9km/hr
(D) 52.6km/hr
(E) 27.6km/hr
Rationale: Total distance traveled = 150+200+300+100 = 750km
Total time taken = 150/50 + 200/20 + 300/100 + 100/50 = 18 hrs
Average speed = 750/18 = 41.67km/hr approximately ;
Answer is B
Answer: (B) 41.67km/hr
Question: Express of the following as a fraction: 0.008%
(A) 3/1250
(B) 9/1250
(C) 6/1250
(D) 1/1250
(E) None of them
Rationale: 0.008 = 8/100 = 1/1250.
Answer is D.
Answer: (D) 1/1250