mathewhe/aqua_rat huggingface dataset:
Question: If the sum of the interior angles of a regular polygon measures up to 1080 degrees, then how many sides does the polygon have?
(A) 10
(B) 16
(C) 8
(D) 11
(E) 14
Rationale: one of the interior angle = 180 - 360/n
sum of the interior angles is = n (180 - 360/n)
given
n(180 - 360/n)=1080
180n - 360 = 1080
180n = 1440
n = 1440/180 = 8
ANSWER:C
Answer: (C) 8
Question: In an isoscele right angled triangle, the perimeter is 20 metre. Find its area.
(A) 9,320 m2
(B) 8,750 m2
(C) 7,980 m2
(D) 6,890 m2
(E) None of these
Rationale: In an isoscele right angled triangle,
Area = 23.3 × perimeter2
= 23.3 × 20(2) = 9320 m2
Answer A
Answer: (A) 9,320 m2
Question: In the expression 51840/x^4, for which of the following values of x will the expression NOT be an integer?
(A) 1/2
(B) 1
(C) 2
(D) 3
(E) 5
Rationale: We can straightaway eliminate A & B, since the expression will always yields an integer for those values
Out of C, D, and E. Let us consider option E. 51840 has only one trailing zero and tens digit is not 5, so It has just one 5 in it. But for the expression to be an integer numerator should have 5^4.
ANSWER:E
Answer: (E) 5
Question: HCF and LCM two numbers are 12 and 396 respectively. If one of the numbers is 36, then the other number is?
(A) 36
(B) 66
(C) 132
(D) 264
(E) 364
Rationale: 12 * 396 = 36 * x
x = 132
ANSWER:C
Answer: (C) 132
Question: Find the number of ways in which 4 letters may be selected from the word "Examination"?
(A) 66
(B) 70
(C) 136
(D) 330
(E) 4264
Rationale: EXAMINATION has 11 letters, and in which 'A', 'I' and 'N', all occur twice. 11C4, would have been fine if all letters were distinct.
So, we have E, X, M, T, O, (AA), (II), (NN). 8 distinct letters.
1. 4 letters selected, which are all distinct: 8C4 = 70
2. 2 letters alike, and 2 distinct (eg: AAEX) = 3C1 x 7C2 = 63
3. 2 letters alike, and 2 letters alike (eg: AAII) = 3C2 = 3
So answer is, 70 + 63 + 3 = 136.
ANSWER:C
Answer: (C) 136
Question: By selling a book for 250, 20% profit was earned. What is the cost price of the book?
(A) A)215
(B) B)208
(C) C)230
(D) D)235
(E) E)240
Rationale: SP = 120% of CP; :. CP = 250 × 100/120 = 208
Option 'B'
Answer: (B) B)208
Question: Calculate the ratio between x and y if 90% of x equal to 60% of y?
(A) 1 : 2
(B) 3 : 5
(C) 3 : 2
(D) 3 : 4
(E) 5 : 2
Rationale: Explanation:
90 x = 60 y
x: y = 90: 60 = 3 : 2
Answer:C
Answer: (C) 3 : 2
Question: There are 8 students. 4 of them are men and 4 of them are women. If 4 students are selected from the 8 students. What is the probability R that the number of men is equal to that of women?
(A) R=18/35
(B) 16/35
(C) 14/35
(D) 13/35
(E) 12/35
Rationale: METHOD-1:
Favorable outcomes (i.e. No. of Men= No. of Women =2) = 4C2 * 4C2 = 6*6 = 36
Total ways of selecting 4 out of 8 Students = 8C4 = 8! / (4! * 4!) = 70
Probability = 36/70 = 18/35
A
METHOD-2:Also see the mistake done by the person who posted this question
Probability of First selected person being Man = 4/8
Probability of Second selected person being Man = 3/7
Probability of First selected person being Woman = 4/6
Probability of Second selected person being Woman = 3/5
i.e. Probability = (4/8)*(3/7)*(4/6)*(3/5) *[4!/(2!*2!)]= 18/35
The important part for the readers is to understand the reason of multiplying[4!/(2!*2!)]here
When we take the probability of each case like we have have taken in this method then it always include ARRANGEMENTS as well and so we have to take every arrangement of the events as well
The arrangement of these 4 events can be done in 4! ways but since the second man can't be selected before 1st so we have to exclude their arrangement by dividing by 2! and similarly since the second Woman can't be selected before 1st so we have to exclude their arrangement by dividing by 2!
A
Answer: (A) R=18/35
Question: Farm Tax is levied on the 60% of the cultivated Land. The tax department collected total $ 4000 through the farm Tax from the village of Mr. willam. Mr. willam paid only $ 500 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is :
(A) 15%
(B) 25%
(C) 12.5%
(D) 20.83%
(E) none
Rationale: Only trick n this question is to ignore 60% information as farm tax is levied uniformly in the village and that includes Mr William's land.
What percentage of tax Mr William paid ? This will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village. That leads to (500/4000)x100 =12.5%in percentage terms.
But the question asks ratio between his total land to total cultivated land. Hence the answer is 12.5%x (100/60) = 20.833% and the answer is not there in the options.
The correct answer is (D).
Answer: (D) 20.83%
Question: A train running at the speed of 60 km/hr crosses a pole in 8 seconds. Find the length of the train.
(A) 133.33
(B) 882
(C) 772
(D) 252
(E) 121
Rationale: Speed = 60*(5/18) m/sec = 50/3 m/sec
Length of Train (Distance) = Speed * Time
(50/3) * 8 = 133.33 meter.Answer: A
Answer: (A) 133.33
Question: If an article is sold at 18% profit instead of 9% profit, then the profit would be $54 more. What is the cost price?
(A) $500
(B) $600
(C) $700
(D) $800
(E) $900
Rationale: 9% * cost price = $54
1% * cost price = $54 / 9 = $6
The cost price is $600.
The answer is B.
Answer: (B) $600
Question: A sum of money is to be distributed among A, B, C, D in the proportion of 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?
(A) 1000
(B) 3000
(C) 2000
(D) 4000
(E) 5000
Rationale: Let the shares of A, B, C and D be Rs. 5x, Rs. 2x, Rs. 4x and Rs. 3x respectively.
Then, 4x - 3x = 1000
x = 1000.
B's share = Rs. 2x = Rs. (2 x 1000) = Rs. 2000.
Answer is C.
Answer: (C) 2000
Question: 2, 6, 12, 20, 30, 42, 56, ?
(A) 63
(B) 67
(C) 69
(D) 72
(E) 75
Rationale: The pattern is 1 × 2, 2 × 3, 3 × 4, 4 × 5, 6 × 7, 7 × 8,....
Answer : D.
Answer: (D) 72
Question: The following sets each have a mean of 10 and the standard deviations are given in variable form.
Set I = {10, 10, 10, 10, 10, 10}, standard deviation = P
Set II = {6, 6, 6, 14, 14, 14}, standard deviation = Q
Set III = {7, 8, 9, 11, 12, 13}, standard deviation = R
Rank these three standard deviations from least to greatest.
(A) P, Q, R
(B) P, R, Q
(C) Q, P, R
(D) Q, R, P
(E) R, Q, P
Rationale: SD is minimum when the terms are closer to the mean.
In set 1, we have all terms equal to mean. hence, its SD is 0.(The Lowest)
Comparing Set 2 and Set 3, Set 3 has terms more closer to mean than set 2. hence, Set 2 Sd is the highest.
So, Answer is B
Answer: (B) P, R, Q
Question: In a graduating class of 238 students, 144 took geometry and 119 took biology. What is the difference between the greatest possible number and the smallest possible number of students that could have taken both geometry and biology?
(A) 144
(B) 119
(C) 113
(D) 88
(E) 31
Rationale: Greatest Possible Number taken both should be 144 (As it is maximum for One)
Smallest Possible Number taken both should be given by
Total - Neither = A + B - Both
Both = A+B+Neither - Total (Neither must be 0 to minimize the both)
So 144 + 119 + 0 - 238 = 25
Greatest - Smallest is 144-25 = 119
So answer must be B. 119
Answer: (B) 119
Question: A sum was put a simple interest at a certain rate for 2 years. Had it been put at 4% higher rate, it would have fetched Rs. 60 more. The sum is:
(A) Rs.750
(B) Rs.700
(C) Rs.820
(D) Rs.940
(E) Rs.900
Rationale: Explanation :
Let the sub be Rs.x and the initial rate be R%.Then
x × (R+4) × 2/100−x×R×2/100=60
⇒x × 4×2/100=60
⇒x × 2 /100=15
⇒2x=1500
⇒x=750
Answer : Option A
Answer: (A) Rs.750
Question: A and B invests Rs.3000 and Rs.4000 respectively in a business. If A doubles his capital after 6 months. In what ratio should A and B divide that year's profit?
(A) 9:5
(B) 9:8
(C) 9:6
(D) 9:1
(E) 9:2
Rationale: (3*6 + 6*6): (4*12)
54:48 => 9:8
Answer: B
Answer: (B) 9:8
Question: The regular price per can of a certain brand of soda is $0.15. If the regular price per can is discounted 10 percent when the soda is purchased in 24-can cases, what is the price of 75 cans of this brand of soda purchased in 24-can cases?
(A) $16.32
(B) $18.00
(C) $10.125
(D) $24.48
(E) $28.80
Rationale: The discounted price of one can of soda is (0.9)($0.15), or $0.135
Therefore, the price of 75 cans of soda at the discounted price would be (75)($0.135) = 10.125
Answer: C.
Answer: (C) $10.125
Question: Line E has the equation 3x + y = 7. Which of the following lines is perpendicular to Line E?
(A)  y = 3x + 4
(B)  y = –3x – 6
(C)  y = (1/3)x – 1
(D)  y = (–1/3)x + 2
(E)  y = (–7/3)x – 5
Rationale: I first rewrote the equation in the standard y=mx+b form. Therefore, Line E as presented, 3x + y = 7, can be rewritten as follows: y=-3x+7.
Thought process next is what line would be perpendicular to Line E? Any line with a reciprocal of the slope but in the opposite direction. The reciprocal of any fraction/integer is 1 over that number/integer. Therefore the reciprocal of -3 is -1/3 - need to drop the negative sign because the line would kinda run parallel and we want perpendicular. Scan the answers choices and notice C as the only one.
Answer: (C)  y = (1/3)x – 1
Question: If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 50, what is the compound interest on the same sum at the rate and for the same time?
(A) Rs.51.25
(B) Rs.51.26
(C) Rs.51.22
(D) Rs.51.98
(E) Rs.51.11
Rationale: Sum = (50 * 100) / (2 * 5)
= Rs. 500
Amount = [500 * (1 + 5/100)2]
= Rs. 551.25
C.I. = (551.25 - 500)
= Rs. 51.25.
Answer: A
Answer: (A) Rs.51.25
Question: A train travels 125 km in 2.5 hours and 270 km in 3 hours.find the average speed of train.
(A) 80 kmph
(B) 60 kmph
(C) 72 kmph
(D) 90 kmph
(E) None of these
Rationale: As we know that Speed = Distance / Time
for average speed = Total Distance / Total Time Taken
Thus, Total Distance = 125 + 270 = 395 km
Thus, Total Speed = 5.5 hrs
or,Average Speed = 5=395/5.5
or, 72kmph.
ANSWER:C
Answer: (C) 72 kmph
Question: A car travelling with 2/3 km of its actual speed covers 12km in 2hr 14 min 28 sec find the actual speed of the car?
(A) 8.9kmph
(B) 2.96kmph
(C) 1.09kmph
(D) 45.9kmph
(E) 4.8kmph
Rationale: time taken =2hr 14 min 28 sec=823/50hrs
let the actual speed be x kmph
then 2/3 x*823/50=12
x==1.09kmph
Answer (C)
Answer: (C) 1.09kmph
Question: If m = 3^n, what is the greatest value of n for which m is a factor of 19!
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: Solution-
Consider multiples of 25!=> 3,6,9,12,15,18
Count no. of 3 in each multiple.
3=3x1->1
6=3x2->1
9=3x3->2
12=3x4->1
15=3x5->1
18=3x3x2->2
---- count 3's =8 so answer is 8
Answer : A
Answer: (A) 8
Question: Sn=1^8+2^8+3^8+----------n^8
find the unit digit of S29
(A) 6
(B) 5
(C) 7
(D) 8
(E) 9
Rationale: unit digit of-
1^8=1
2^8=6
3^8=1
4^8=6
5^8=5
6^8=6
7^8=1
8^8=6
9^8=1
so 1+6+1+6+5+6+1+6+1=33 so from here we get 3 as unit digit for 1^8+2^8+.....+9^8
now for 11 to 19 same way unit digit is 3
then from 21 to 29 unit digit is 3
so 3+3+3=9
so unit digit is 9
ANSWER:E
Answer: (E) 9
Question: Two alloys A and B are composed of two basic elements. The ratios of the compositions of the two basic elements in the two alloys are 5 : 3 and 1 : 1, respectively. A new alloy X is formed by mixing the two alloys A and B in the ratio 4 : 3. What is the ratio of the composition of the two basic elements in alloy X ?
(A) 1 : 1
(B) 2 : 3
(C) 5 : 2
(D) 4 : 3
(E) 7 : 9
Rationale: Mixture A has a total of 5 + 3 = 8 parts. If in the final mixture this represents 4 parts, then the total number of parts in mixture B should be (8/4)*3 = 6.
So, we should take of mixture B a quantity with 3 and 3 parts, respectively.
This will give us in the final mixture (5 + 3) : (3 + 3), which means 4:3
Answer D.
Answer: (D) 4 : 3
Question: Ramesh purchased a refrigerator for Rs. 17500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 10% if no discount was offered?
(A) 34778
(B) 26888
(C) 24475
(D) 17600
(E) 12778
Rationale: Price at which the TV set is bought = Rs. 17,500
Discount offered = 20%
Marked Price = 17500 * 100/80 = Rs. 21875
The total amount spent on transport and installation = 125 + 250 = Rs. 375\Total price of TV set = 21875 + 375 = Rs. 22250
The price at which the TV should be sold to get a profit of 10% if no discount was offered = 22250 * 110/100
= Rs. 24475
Answer: C
Answer: (C) 24475
Question: A certain college party is attended by both male and female students. The ratio of male to female students is 3 to 5. If 6 of the male students were to leave the party, the ratio would change to 1 to 2. How many total students are at the party?
(A) 64
(B) 72
(C) 80
(D) 88
(E) 96
Rationale: The ratio is 3:5 = 6:10, so there are 6k males and 10k females.
If 6 males left, the ratio would be 1:2 = 5:10, so there would be 5k males and 10k females.
6k-5k = 6
k = 6
6k + 10k = 36 + 60 = 96
The answer is E.
Answer: (E) 96
Question: Two dice are rolled. What is the probability the sum will be greater than 9?
(A) 1/9.
(B) 1/12.
(C) 5/36.
(D) 1/6.
(E) 1/5.
Rationale: Combinations possible: (6,6) , (5,6) , (6,5) , (5,5) = 4
Total combinations possible: 6*6=36
Answer = 4/36 = 1/9 Option A.
Answer: (A) 1/9.
Question: A man divides $8600 Among 4 Sons, 4 Daughters and 2 Nephews. If each daughter receives four times as much as each nephews and each son receives five times as much as each nephews, how much does each daughter receive?
(A) A)$200
(B) B)$1000
(C) C)$800
(D) D)$1011.76
(E) E)$400
Rationale: Let the share of each nephews be $X.
Then, share of each daughter=$4X, share of each son= $5X.
So, 4*4X+4*4X+2*X=8600
16X+16X+2X=8600
34X=8600, X=252.94.
Daughter receives four times of nephew so 4 * 252.94 = 1011.76.
So Each Daughter receives $800. answer is option D) $1011.76.
Answer: (D) D)$1011.76
Question: If x, y, and z are negative integers and 3x - 3y = -3z, then which of the following statements must be true?
I.	x = y
II.	x > y
III. x = z
(A) I and II
(B) I only
(C) II only
(D) III only
(E) None
Rationale: 3x-3y=-3z
x-y=-z
Since z<0; -z>0
x-y>0
x>y
II correct.
We can't say much about z though;
x=-5; y=-100; z=-95
I and II incorrect.
Ans:C
Answer: (C) II only
Question: The area of a rectangle is 15 square centimeters and the perimeter is 16 square centimeters. What are the dimensions of the rectangle?
(A) 2&4
(B) 3&5
(C) 4&6
(D) 5&7
(E) 6&8
Rationale: Let x and y be the length and width of the rectangle. Using the formulas for the area and the perimeter, we can write two equations.
15 = x y and 16 = 2 x + 2 y
Solve the second equation for x
x = 8 - y
Substitute x in the equation 15 = x y by 8 - y to rewrite the equation as
15 = (8 - y) y
Solve for y to find
y = 3 and y = 5
Use x = 8 - y to find x
when y = 3 , x = 5 and when y = 5 , x = 3.
The dimensions of the rectangle are 3 and 5.
correct answer B
Answer: (B) 3&5
Question: 6) A marketing firm determined that , of 180 households surveyed, 80 used neither Brand A nor Brand B soap.60 used only Brand A soap and for every household that used both brands of soap, 3 used only brand B soap.how many of the 200 household surveyed used both brands of soap?
(A) a) 15
(B) b) 20
(C) c) 30
(D) d) 10
(E) e) 45
Rationale: 100 = At least one of Soap A or B
Both brands = x
Brand B = 3x
=> 60 + x + 3x = 100
=> 4x = 40
=> x = 10
Answer - D
Answer: (D) d) 10
Question: How many ways are there to split a group of 4 students into two groups of 2 students each? (The order of the groups does not matter)
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 4C2 = 6
If we consider these groups, each group will be counted twice.
The number of ways to choose 2 groups of 2 is 6/2 = 3
The answer is B.
Answer: (B) 3
Question: 40% of the people read newspaper X, 50% read newspaper Y and 10% read both the papers.What percentage of the people read neither newspaper ?
(A) 18%
(B) 20%
(C) 22%
(D) 16%
(E) 30%
Rationale: n(A)=40,n(B)=50,n(AnB)=10.
n(AuB)=n (A)+n (B)-n(AnB)=40+50-10=80.
Hence, percentage passed =(100-80)%=20%.
Answer is B
Answer: (B) 20%
Question: The speed of a boat in still water is 60kmph and the speed of the current is 25kmph. Find the speed downstream and upstream?
(A) 80,47 kmph
(B) 80,80 kmph
(C) 85,35 kmph
(D) 80,40 kmph
(E) 83,40 kmph
Rationale: Speed downstream = 60 + 25 = 85 kmph
Speed upstream = 60 - 25 = 35 kmph.Answer:C
Answer: (C) 85,35 kmph
Question: If the sum of the 4th term and the 12th term of an arithmetic progression is 12, what is the sum of the first 15 terms of the progression?
(A) 90
(B) 80
(C) 70
(D) 60
(E) 50
Rationale: 4th term + 12th term = 12
i.e., (a+3d)+(a+11d) = 12
Now, Sum of first 15 terms = (15/2) * [2a + (15-1)d]
= (15/2) * [2a + 14d]
= (15/2) * 12 --------------- From (1)
=90
Answer : A
Answer: (A) 90
Question: If r and p are two different prime numbers, which of the following is the smallest possible value of r + p?
(A) 1
(B) 3
(C) 5
(D) 8
(E) 10
Rationale: By definition only positive numbers can be primes.
Two smallest primes are 2 and 3 --> 2 + 3 = 5.
Answer: C
Answer: (C) 5
Question: In Goshawk-Eurasian nature reserve 30 percent of the birds are Hawks, and 40 percent of the non-Hawks are Paddyfield-Warblers. If there are 25 percent as many Kingfishers as Paddyfield-Warblers in the reserve, then what percent of the birds W in the nature reserve are not Hawks, Paddyfield-Warblers, or Kingfishers?
(A) 25%
(B) 35%
(C) 45%
(D) 70%
(E) 80%
Rationale: 1. We are given the following percentages: 30 (70), 40 (60), 25 (75). There are two threads from here. First starts at 30% and finishes there. Second one starts at 70, then 40, and then 25. We need a value that is divisible by 7, 2, and 5 at least once. lets pick a number now, say 700. So say if Non Hawks are 700 (this is 70% of the total, so total = 1000), then Paddy Warbs are 2/5 x 700 = 1400/5 = 280. Kingfishers, therefore, are 280/4 = 70. Lets add them up. 300 hawks + 280 Peddy Warbs + 70 kingsifhers = 650. So all others are 1000 - 650= 350 or 35% of total birds.
The main job here to to identify the smart number to start the question with. This can be time consuming, but once identified, this question can be solved fairly quickly.
2. Another method: If X is total --> Non Hawks = 0.7X --> Warbs = 0.4(0.7X) --> KFs = 0.25(0.4(0.7X)).
Our job is to find out W: (0.3X + 0.28X + 0.07X)/ X. OR 0.65X/X = 0.65. We need to find 1-0.65 = 0.35 or 35%.B
Answer: (B) 35%
Question: A man rows his boat 70 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
(A) 1 kmph
(B) 6 kmph
(C) 5 kmph
(D) 8 kmph
(E) 7 kmph
Rationale: Speed downstream = d/t = 75/(2 1/2) = 28 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (28 - 18)/2 = 5 kmph
Answer:C
Answer: (C) 5 kmph
Question: A sum of Rs. 2500 amounts to Rs. 3500 in 4 years at the rate of simple interest. What is the rate of interest?
(A) 7%
(B) 9%
(C) 5%
(D) 6%
(E) 10%
Rationale: S.I. = (3500- 2500) = Rs. 1000
Rate = (100 * 1000) / (2500* 4)
= 10%
Answer: E
Answer: (E) 10%
Question: The H.C.F of two numbers is 19 and their L.C.M is 4263. If one of the numbers is 399, then the other is?
(A) 202
(B) 203
(C) 204
(D) 205
(E) 206
Rationale: Other number = (19 * 4263)/399
= 203.
Answer: B
Answer: (B) 203
Question: Three years ago the average age of a family of seven members was 20 years. A boy have been born, the average age of the family is the same today. What is the age of the boy?
(A) A)8
(B) B)7
(C) C)6
(D) D)5
(E) E)4
Rationale: 7 * 23 = 161
7 * 19 = 153
--------------
8
Answer: A
Answer: (A) A)8
Question: The value of (68.237)2 – (31.763)2 is :
(A) 3.6474
(B) 36.474
(C) 364.74
(D) 3647.4
(E) None of these
Rationale: Solution
Given expression = (a2 - b2) = (a + b)(a - b)
= (68.237 + 31.763) (68.237 - 31.763)
= (100 × 36.474)
= 3647.4. Answer D
Answer: (D) 3647.4
Question: The price of a mobile was increased by 40 percent. The new price was then decreased by 15 percent. A single increase of what percent is equivalent to these two successive changes?
(A) 25%
(B) 19%
(C) 30%
(D) 22.5%
(E) 15%
Rationale: consider base price - $100
25% increase = 1.40*100 = $140
Then a 15% decrease on new price = 0.85* 140 = $119
so final price of radio - $119
therefore a 19% increase
correct option - B
Answer: (B) 19%
Question: Two employees X and Y are paid a total of Rs. 550 per week by their employer. If X is paid 120 percent of the sum paid to Y, how much is Y paid per week?
(A) A)Rs.200
(B) B)Rs.220
(C) C)Rs.250
(D) D)Rs.300
(E) E)Rs.350
Rationale: Let the amount paid to X per week = x
and the amount paid to Y per week = y
Then x + y = 550
But x = 120% of y = 120y/100 = 12y/10
∴12y/10 + y = 550
⇒ y[12/10 + 1] = 550
⇒ 22y/10 = 550
⇒ 22y = 5500
⇒ y = 5500/22 = 500/2 = Rs.250
C
Answer: (C) C)Rs.250
Question: In how many ways can live boys and three girls sit in a row such that all boys sit together?
(A) 2882
(B) 2880
(C) 7276
(D) 2786
(E) 2661
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: B
Answer: (B) 2880
Question: When the positive integer y is divided by 11, the quotient is z and the remainder 3. When y is divided by 19, the remainder is also 3. What is the remainder when z is divided by 19?
(A) 4
(B) 3
(C) 2
(D) 1
(E) 0
Rationale: Any Number which when divided by divisor d1,d2, etc. leaving same remainderrtakes the form ofK+r
where k = LCM (d1,d2)
In this case the divisors are 1119 and remainder is 3.
so LCM (11,19) = 209
So N= 209+3 = 212
Also y=d1q+3 ; which means d1q=209d1=11 therefore q=19
And ( z divided by 19)19/19 leaves remainder 0.
Answer is E
Answer: (E) 0
Question: Divide Rs. 2379 into 3 parts so that their amounts after 2, 3 and 4 years respectively may be equal, the rate of interest being 5% per annum at simple interest. The first part is?
(A) 388
(B) 3769
(C) 8782
(D) 828
(E) 271
Rationale: Let the parts be x, y and [2379 - (x + y)]
x + (x * 2 * 5/100) = y + (y * 3 * 5/100) = z + (z * 4 * 5/100)
11x/10 = 23y/20 = 6z/5 = k
x = 10k/11, y = 20k/23, z = 5k/6
But x + y + z = 2379
10k/11 + 20k/23 + 5k/6 = 2379
k = (2379 * 11 * 23 * 6)/3965 = (3 * 11 * 23 * 6)/5
x = [10/11 * (3 * 11 * 23 * 6)/5] = 828
Hence, the first part is Rs. 828.
Answer: D
Answer: (D) 828
Question: If A,B is 20%,30% smaller than C then how much percentage is B greater than A?
(A) 10%
(B) 11%
(C) 12 3/4%
(D) 12 1/2 %
(E) 13%
Rationale: A = 80 %
B = 70 %
C = 100 %
A-B/A × 100 = 10/80 × 100 = 12 1/2 % greater than A
D)
Answer: (D) 12 1/2 %
Question: A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by :
(A) 3
(B) 5
(C) 9
(D) 11
(E) 13
Rationale: Solution
Let the ten's digit be x and units digit be y. Then, number = 10x + y.
Number obtained by interchanging the digits = 10y + x.
∴ (10x + y) + (10y + x) = 11 (x + y), which is divisible by 11.
Answer D
Answer: (D) 11
Question: What is the 149th digit to the right of the decimal point in the decimal form of 30/33?
(A) 5
(B) 6
(C) 9
(D) 0
(E) 1
Rationale: To solve ,we first have to use some long division.Long division allows us to get 30/33 in decimal form, which is 0.909090… where “90” is repeating.
We see that the 1st, 3rd, 5th digit to the right of the decimal point is a 9 and that the 2nd, 4th, 6th digit to the right of the decimal point is a 0. In other words, each odd-positioned digit is a 9, and each even-positioned digit is a 0.
Then the 149th digit to the right of the decimal point and we see that 149 is odd, then 149th digit is a 9.
Answer C.
Answer: (C) 9
Question: A, B and C play a cricket match. The ratio of the runs scored by them in the match is A:B = 2:3 and B:C = 2:5. If the total runs scored by all of them are 75, the runs scored by B are?
(A) 33
(B) 18
(C) 99
(D) 787
(E) 65
Rationale: A:B = 2:3
B:C = 2:5
A:B:C = 4:6:15
6/25 * 75 = 18
Answer: B
Answer: (B) 18