mathewhe/aqua_rat huggingface dataset:
Question: A bag contains 12 red marbles. If someone were to remove 2 marbles from the bag, one at a time, and replace the first marble after it was removed, the probability that neither marble would be red is 36/49. How many marbles are in the bag?
(A) 24
(B) 48
(C) 84
(D) 72
(E) 80
Rationale: ok let me see if i can explain what went on in the previous post
lets say i have x marbles in the bag in total --> out of them 12 are red
so the probability of pulling a non-red marble is (x -12) / x
now the marble is placed back in the bag and we have x marbles again, of which again 12 are red. so the probability of pulling a non-red marble out is (x-12) / x
probability theorm states that if the probability of event A occuring is m and the probability of event B occuring is n then the probability of both A and B occuring is m*n
so therefore the probability of 2 non-red marbles getting pulled out is [(x-12)/x ] * [(x-12)/x]
this is given as 36/49
-->(x-12)^2= 36/49
x^2
square rooting u have x-12/x = 6/7 or 7x-6x =84 or x =84
C
Answer: (C) 84
Question: What is the smallest positive perfect square that is divisible by 9, 15, and 25?
(A) 100
(B) 225
(C) 900
(D) 1,600
(E) 4,900
Rationale: The number needs to be divisible by 3^2, 3*5, and 5^2.
The smallest such perfect square is 3^2*5^2 = 225
The answer is B.
Answer: (B) 225
Question: 10 play kabadi, 25 play kho kho only, 5 play both gmaes. Then how many in total?
(A) 30
(B) 35
(C) 38
(D) 40
(E) 45
Rationale: 10 play kabadi =>n(A)=10,
5 play both gmaes.=> n(AnB)=5
25 play kho kho only,=>n(B)=n(B only)+n(AnB)=25+5=30
Total => n(AUB)= n(A)+n(B)-n(AnB)
= 10+30-5
= 35
ANSWER:B
Answer: (B) 35
Question: A train speeds past a pole in 15 sec and a platform 100 m long in 25 sec, its length is?
(A) 100
(B) 150
(C) 160
(D) 170
(E) 180
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 15 => y = x/15
(x + 100)/25 = x/15 => x = 150 m.
Answer: Option B
Answer: (B) 150
Question: The area of a parallelogram is 98sq m and its altitude is twice the corresponding base. Then the length of the base is?
(A) 8
(B) 9
(C) 7
(D) 62
(E) 2
Rationale: 2x * x = 98 => x= 7
Answer: C
Answer: (C) 7
Question: A certain amount earns simple interest of Rs. 1750 after 6 years. Had the interest been 2% more, how much more interest would it have earned?
(A) Rs. 350
(B) Rs. 35
(C) Rs. 245
(D) Cannot be determined
(E) None of these
Rationale: We need to know the S.I., principal and time to find the rate. Since the principal is not given, so data is inadequate.
ANSWER:D
Answer: (D) Cannot be determined
Question: Twenty percent of Country Y's yearly exports come from fruit exports. One-fourth of all fruit exports from Country Y are orange exports. If country Y generates $20 million from its orange exports, how much money does it generate from its yearly total of exports?
(A) $21.25m
(B) $25.5m
(C) $106.25m
(D) $400m
(E) $153m
Rationale: 20/100*1/4*(total) = 20
1/20*(total) = 20
(total) = 20*20 = 400
Answer: D.
Answer: (D) $400m
Question: The present population of a town is 240. Population increase rate is 10% p.a. Find the population of town after 1 years?
(A) 100
(B) 120
(C) 200
(D) 220
(E) 264
Rationale: P = 240
R = 10%
Required population of town = P*(1 + R/100)^T
= 240*(1 + 10/100)
= 240*(11/10)
= 264
Answer is E
Answer: (E) 264
Question: The average of runs of a cricket player of 10 innings was 34. How many runs must he make in his next innings so as to increase his average of runs by 4 ?
(A) 78
(B) 79
(C) 85
(D) 87
(E) 89
Rationale: Explanation:
Average = total runs / no.of innings = 34
So, total = Average x no.of innings = 34 x 10 = 340.
Now increase in avg = 4runs. So, new avg = 34+4 = 38runs
Total runs = new avg x new no. of innings = 38 x 11 = 418
Runs made in the 11th inning = 418 - 340 = 78 Answer: A
Answer: (A) 78
Question: In one can of mixed nuts, 60% is peanuts. In another can of mixed nuts that is one-half the size of the first one, 40% is peanuts. If both cans are emptied into the same bowl, what percentage of the mixed nuts in the bowl is peanuts?
(A) 16 2/3%
(B) 20%
(C) 25%
(D) 53 1/3%
(E) 35%
Rationale: Can 1: size 1; 60% nuts
Can 2: size 0.5 and 40% nuts
(1x0.6+0.5x0.4)/1.5=53.33
D
Answer: (D) 53 1/3%
Question: The difference between compound interest and simple interest on a sum for two years at 8% per annum, where the interest is compounded annually is Rs.16. if the interest were compounded half yearly , the difference in two interests would be nearly
(A) 24.64
(B) 24.69
(C) 24.62
(D) 24.6
(E) 24.61
Rationale: Explanation:
For 1st year S.I =C.I.
Thus, Rs.16 is the S.I. on S.I. for 1 year, which at 8% is thus Rs.200
i.e S.I on the principal for 1 year is Rs.200
Principle = = Rs.2500
Amount for 2 years, compounded half-yearly
C.I = Rs.424.64
Also,
Hence, [(C.I) - (S.I)] = Rs. (424.64 - 400) = Rs.24.64
Answer:A
Answer: (A) 24.64
Question: If the quantity 8^2+ 8^4 + 8^6 is written as (a + b)(a – b), in which both a and b are integers, which of the following could be the value of b?
(A) 51
(B) 64
(C) 49
(D) 29
(E) 37
Rationale: (a+b)(a-b) = a^2 - b^2
8^2+ 8^4 + 8^6 = 8^2 (1+8^2+8^4)
if the above expression is solved even then every term of the expression will remain a multiple of 8^2 which is out of parenthesis
hence, b must be a multiple of 8^2 i.e. 64
Answer: option B
Answer: (B) 64
Question: A train running at a speed of 36 kmph crosses an electric pole in 12 seconds. In how much time will it cross a 370 m long platform?
(A) 19
(B) 27
(C) 29
(D) 47
(E) 49
Rationale: Let the length of the train be x m.
When a train crosses an electric pole, the distance covered is its own length.
So, x = 12 * 36 * 5 /18 m = 120 m.
Time taken to cross the platform = (120 +370)/ 36 * 5/18
= 49 min.
Answer:E
Answer: (E) 49
Question: The prime sum of an integer n greater than 1 is the sum of all the prime factors of n, including repetitions. For example , the prime sum of 12 is 7, since 12 = 2 x 2 x 3 and 2 +2 + 3 = 7. For which of the following integers is the prime sum greater than 30 ?
(A) 440
(B) 512
(C) 550
(D) 620
(E) 750
Rationale: Large numbers are made in two ways:
Either by taking small prime numbers and raising them to higher powers or taking large prime numbers in the first place.
31*2 = 62 (large prime number)
2^6 = 64 (many small prime numbers)
To get a sum as large as 30 or more, you would need some large prime numbers. So options such as 512, 700 and 750 which have small prime numbers as factors should be ignored first. 440 also splits into 11, 4( which is 2*2), 2, 5 - relatively small prime numbers.
You are left with 620 which is 31*2*2*5 (sum greater than 30)
Answer (D)
Answer: (D) 620
Question: A, B and C enter into a partnership investing Rs 35000, Rs 45000 and Rs 55000 resp. The respective share of A,B and C in an annual profit of Rs 40500 are.
(A) Rs. 11500, Rs. 13500, Rs. 16500
(B) Rs. 10500, Rs. 12500, Rs. 16500
(C) Rs. 10500, Rs. 13500, Rs. 15500
(D) Rs. 10500, Rs. 13500, Rs. 16500
(E) None of these
Rationale: Explanation:
A:B:C = 35000:45000:55000
= 7:9:11
Now we are having the ratio.
to get the share, first make total of above ratio.
then get each share.
A's Share=40500∗7/27=Rs.10500
B's Share=40500∗927=Rs.13500
B's Share=40500∗1127=Rs.16500
Option D
Answer: (D) Rs. 10500, Rs. 13500, Rs. 16500
Question: Employees of a certain company are each to receive a unique 5-digit identification code consisting of the digits 0, 1, 2, 3, and 4 such that no digit is used more than once in any given code. In valid codes, the second digit in the code is exactly twice the first digit. How many valid codes are there?
(A) 10
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: There are 3! ways to make codes starting with 12.
There are 3! ways to make codes starting with 24.
The number of codes is 2*3! = 12.
The answer is B.
Answer: (B) 12
Question: x^2 + rx + 72 = 0 has two distinct integer roots; how many values are possible for r?
(A) 3
(B) 6
(C) 8
(D) 12
(E) 24
Rationale: For a quadratic equation ax^2+rx+c=0, we know that -r/a is sum of roots and c/a is product of roots.
The quadratic equation here is x^2 + rx + 72 = 0, where product of roots is 72.
If we find all the factors of 72, we have the answer.
By prime factorization, we get 72= 2^3*3^2.
We know that total factors are (3+1)*(2+1) = 12 (Reason: with 2^n, we have n+1 possibilities. n^0 to n^n. so n+1)=D
Answer: (D) 12
Question: An investor opened a money market account with a single deposit of $6000 on Dec. 31, 2001. The interest earned on the account was calculated and reinvested quarterly. The compound interest for the first 3 quarters of 2002 was $125, $130, and $145, respectively. If the investor made no deposits or withdrawals during the year, approximately what annual rate of interest must the account earn for the 4th quarter in order for the total interest earned on the account for the year to be 10 percent of the initial deposit?
(A) 3.1%
(B) 9.3%
(C) 10.0%
(D) 10.5%
(E) 12.5%
Rationale: We know 10% of 6000 is 600
already earned is Rs. 400 in 3 quarters
balance to be earned is 200 on amount of 6400 (6000+400 intt)
we get quarterly Rate of Interest as 3.125% (200/6400).
annually it would be 3.125*4 = 12.5%
ANSWER:E
Answer: (E) 12.5%
Question: If the remainder is 10 when the integer n is divided by 18, what is the remainder when 2n is divided by 9?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: n = 18k+10
2n = 2(18k+10) = 4k*9 + 20 = 4k*9 + 2*9 + 2 = 9j + 2
The answer is C.
Answer: (C) 2
Question: Find the compound ratio of (1:2), (1:3) and (3:5) is
(A) 1:10
(B) 2:3
(C) 3:4
(D) 4:5
(E) 3:2
Rationale: Required ratio = 1/2 * 1/3 * 3/5 = 1/10 = 1:10
Answer is A
Answer: (A) 1:10
Question: Four of the following five parts numbered (a), (b), (c), (d) and (e) are exactly equal. The number of the part which is not equal to the other four parts is your answer.
(A) 85 ÷ 17 × 110
(B) 45 × 6 + 75 × 4
(C) 175 ÷ 25 × 75 + 5(2)
(D) 36 × 4 + 21(2) – 7 × 5
(E) 65 × 12 – 46 × 5
Rationale: Except it, others are equal to 550.
Answer B
Answer: (B) 45 × 6 + 75 × 4
Question: A small, rectangular park has a perimeter of 560 feet and a diagonal measurement of 100 feet. What is its area, in square feet?
(A) 4,800
(B) 19,600
(C) 20,000
(D) 20,400
(E) 20,800
Rationale: you can avoid a lot of work in this problem by recognizing that, with the info provided, the diagonal forms a triangle inside the rectangle with sides that have a 3:4:5 ratio.
diagonal = 200
2x + 2y = 560, or x + y = 280
a^2 + b^2 = c^2 for each the sides of the triangle
using the ratio 3:4:5 for sides, and knowing c = 100, you can deduce the following
a=60
b=80
60x80=4,800
A is the answer.
Answer: (A) 4,800
Question: A security guard at a certain store is instructed to check the receipt of one out of every five customers as they are leaving the store. If, on the guard's shift, 10 customers leave the store, how many different samples of customers could have been selected to have their receipts checked?
(A) 20
(B) 45
(C) 59
(D) 90
(E) 100
Rationale: If the guard is instructed to select 1 of every 5 receipts and the question is asking how many different sets of customers could be selected out of 10 then the guard will select 2 of the 10 customers to review.
10C2 = 45.
ANS:B
Answer: (B) 45
Question: The average weight of 6 students decreases by 3 kg when one of them weighing 80 kg is replaced by a new student. The weight of the student is
(A) 62 kg
(B) 60 kg
(C) 70 kg
(D) 72 kg
(E) None of these
Rationale: Explanation :
Let the weight of student be x kg.
Given, Difference in average weight = 3 kg
=> (80-x)/6 = 3
=> x = 62
Answer : A
Answer: (A) 62 kg
Question: A sun is divided among X, Y and Z in such a way that for each rupee X gets, Y gets 45 paisa and Z gets 30 paisa. If the share of Y is RS. 45, what is the total amount?
(A) 166
(B) 105
(C) 175
(D) 177
(E) 169
Rationale: x:y:z = 100:45:30
20:9:6
9 --- 45
35 --- ? => 175
Answer: C
Answer: (C) 175
Question: How many 6 digit even numbers can be formed from digits 1, 2, 3, 4, 5, 6, and 7 so that the digit should not repeat and the second last digit is even?
(A) 6480
(B) 320
(C) 2160
(D) 720
(E) 620
Rationale: 5x4x3x2x2x3= 720
last digit can be 2 or 4 or 6 ie 3ways since the no is even
and second last digit 2 ways bcz no cannot be repeated similarly remaining 5,4,3,2 ways
multipling all we get 720
ANSWER:D
Answer: (D) 720
Question: The price of a T.V. set worth Rs. 70000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?
(A) 22678
(B) 26699
(C) 69000
(D) 19000
(E) 26711
Rationale: Money paid in cash = Rs. 1000
Balance payment = (70000 - 1000) = Rs. 69000
Answer: C
Answer: (C) 69000
Question: One year ago, the ratio of Sooraj's and Vimal's age was 6:7 respectively. Four years hence, this ratio would become 7:8. How old is Vimal?
(A) 35
(B) 36
(C) 37
(D) 38
(E) 39
Rationale: 1 year ago
Age of Sooraj and Vimal, 6x and 7x respectively.
After 4 years ratio would become 7:8
(6x+5):(7x+5)=7:8
8(6x+5)=7(7x+5)
48x+40=49x+35
x=5 Vimal's present age
=7x+1=7×5+1=36
answer :B
Answer: (B) 36
Question: Solve for X, log10X + log√10 X + log3√100 X = 27.
(A) 1
(B) 106
(C) 104
(D) 10
(E) 15
Rationale: Changing the base to 10, we get
log√10 X = log10X / log10√10 = 2log10X
log3√X = log10X / log103√100 = 3log10X / 2.
Thus, log10X + 2log10X + 3/2 log10X = 27
=> 9/2 log10X = 27
=> log10X = 6
ANSWER:B
Answer: (B) 106
Question: A sum of Rs.4600 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
(A) Rs.2990
(B) Rs.3120
(C) Rs.3320
(D) Rs.2760
(E) None of these
Rationale: Let A be the amount received at the end of the three years.
A = 4600[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4600 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.7590
So the interest = 7590 - 4600 = Rs.2990
ANSWER:A
Answer: (A) Rs.2990
Question: Rs.160 contained in a box consists of one rupee, 50 paisa and 25 paisa coins in the ratio 4:5:8. What is the number of 25 paisa coins?
(A) 100
(B) 110.14
(C) 140.24
(D) 120.34
(E) 170.64
Rationale: 4x 5x 8x
100 50 25
400x + 350x + 200x = 16000
x = 21.33
6x = 170.64
ANSWER:E
Answer: (E) 170.64
Question: Henry eats X scones in X percent of the time it takes Rachel to eat Y scones. If Rachel eats four scones in ten minutes, then the number of minutes it takes Henry to eat 20 scones must be equal to which of the following?
(A) Y/2
(B) 20/Y
(C) 100Y/(15X)
(D) XY/250
(E) Y/(5X)
Rationale: Rachel eats 4 scones/10 minutes = 2/5 scones per minute
The time for Rachel to eat 1 scone is 5/2 minutes.
The time for Rachel to eat Y scones is 5Y/2 minutes.
The time for Henry to eat X scones is 5YX/200 minutes.
The time for Henry to eat 1 scone is 5Y/200 minutes.
The time for Henry to eat 20 scones is 100Y/200 = Y/2 minutes.
The answer is A.
Answer: (A) Y/2
Question: Jill works as a waitress at the local diner where she earns an hourly wage of $4.00 per hour and a standard tip rate of 15% of the cost of the orders she serves. If she worked one 8-hour shifts this week and averaged $40 in orders per hour, how much did Jill earn this week?
(A) 280
(B) 300
(C) 80
(D) 350
(E) 400
Rationale: Jill earns 4 dollars/hour and the hourly tip is (3/20)*40.
Jill thus earns 4*8+8*2*3 per day(or 4(8)+6(8)=10(8)=80).
Jill has worked for 1 days -> 80*1=80.
This matches answer choice C.
Answer: (C) 80
Question: Annie has 3 times the number of stamps that Doris does and Jane has 7 stamps more than Doris does. If Annie, Doris, and Jane each increase their number of stamps by 4, which of the following must be true after each person increases her number of stamps?
Annie has more stamps than Jane.
Jane has 3 more stamps than Doris.
The sum of the numbers of stamps that Annie and Doris have is a multiple of 4.
(A) None
(B) IIIonly
(C) and III only
(D) and III only
(E) II, and III
Rationale: Given that:
A=3D;
J=D+7;
After increase:
Alice: A=3D+4;
Jane: J=D+11;
Doris: D+4.
Analyze each option:
Alice has more stamps than Jane.
3D+4>D+11 --> D>7/3=3.5. Thus this statement will be true if D is more than or equal to 4. Since we don't know that, then this statement is not always true.
Jane has 3 more stamps than Doris.
D+11=(D+4)+3. This is not true for ANY value of D.
The sum of the numbers of stamps that Alice and Doris have is a multiple of 4.
The sum of the numbers of stamps that Alice and Doris have is (3D+4)+(D+4)=4D+8=4(D+2). So, this sum is a multiple of 4 for ANY value of D, which smeans that this statement is always true.
Answer: B (III only).
Answer: (B) IIIonly
Question: Two equal triangles constitute rhombus A. If the diagonals of rhombus are 15cm and 20cm long. What is the area of each triangle?
(A) 300
(B) 150
(C) 75
(D) 40
(E) 20
Rationale: Area of rhombus =0.5 x 15 x 20
=150 cmÂ²
Area of triangle= 150/2=75 cmÂ²
Answer: C
Answer: (C) 75
Question: If Ryan and Smith car ratio is 5:8. Ryan bought 6 new car and Smith bought 2 new car. Now,Smith has 18 car.what is their car ratio now?
(A) 5:4
(B) 3:2
(C) 8:9
(D) 6:5
(E) 7:5
Rationale: current no. of Smith car=8x+2=18,8x=16,x=2.
current car ratio= 10+6/18=16/18=8:9.
answer C
Answer: (C) 8:9
Question: Rs.1170 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
(A) Rs.528
(B) Rs.542
(C) Rs.528
(D) Rs.540
(E) Rs.549
Rationale: A+B+C = 1170
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 1170 = Rs.540
Answer: D
Answer: (D) Rs.540
Question: The banker's discount on Rs.1550 due a certain time hence is Rs.155. Find the true discount and the banker's gain.
(A) 14
(B) 15
(C) 18
(D) 21
(E) None
Rationale: Solution
Sum	=B.D x T.D/ B.D - T.D
= B.D x T.D/ B.G
T.D / B. G	=Sum / B.D
= 1550 / 155
= 10 / 1
If B.D is Rs. 11,T.D= Rs.10.
If B.D is Rs.155,
T.D	= Rs.(10 / 11 x 155)
= Rs.140.
And, B.G	= Rs(155 - 140)
= Rs.14.
Answer A
Answer: (A) 14
Question: What number should replace the question mark? 2, 16, 4, 14, 6, 12, ---?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: Answer: A
2, 16, 4, 14, 6, 12, 8?
There are two alternate sequences: +2 and -2.
Answer: (A) 8
Question: In a can, there is a mixture of milk and water in the ratio 4 : 5. If it is filled with an additional 4 litres of milk the can would be full and ratio of milk and water would become 6 : 5. Find the capacity of the can?
(A) 40
(B) 44
(C) 48
(D) 22
(E) None of these
Rationale: Let the capacity of the can be T litres.
Quantity of milk in the mixture before adding milk = 4/9 (T - 4)
After adding milk, quantity of milk in the mixture = 6/11 T.
6T/11 - 4 = 4/9(T - 4)
10T = 396 - 176 => T = 22.
ANSWER:D
Answer: (D) 22
Question: Total dinning bill for 8 people was $211.00.If they add 15% tip and divided the bill evenly ,approximate.What was each persons find share
(A) $30.14
(B) 45.14
(C) 34.66
(D) 32.29
(E) 30.33
Rationale: 211*15=3165/100=31.65
211+31.65=242.65
242.65/8=30.33
ANSWER:E
Answer: (E) 30.33
Question: Which of the following can be a perimeter e of a triangle inscribed in a circle of radius 1?
I. 0.001
II. 0.010
III. 0.100
(A) I only
(B) III only
(C) II and III only
(D) I, II, and III
(E) Not I, II, or III
Rationale: Yes,the length of any side of a triangle must be larger than the positive difference of the other two sides, but smaller than the sum of the other two sides.
But how do you use the above property to solve the question?
The lower limit of the perimeter of an inscribed triangle in a circle of ANY radius is 0: e>0.
Answer is D.
Answer: (D) I, II, and III
Question: By selling 100 pencil, a trader gains the cost of 30 Pencil. Find his gain percentage?
(A) 26 1/3%
(B) 51 1/3%
(C) 30%
(D) 53 1/3%
(E) 34 1/3%
Rationale: C
30%
Let the CP of each pencil be Rs. 1.
CP of 100 pens = Rs. 100
Profit = Cost of 30 pencil = Rs. 30
Profit% = 30/100 * 100 =30%
Answer: (C) 30%
Question: If $ 5,000 is invested in an account that earns 6% interest compounded semi-annually, then the interest earned after one year would be how much greater than if the $ 5,000 had been invested at 8% simple yearly interest?
(A) $ 6
(B) $ 8
(C) $ 12
(D) $ 16
(E) $ 432
Rationale: ANS A
Solution
Amount (CI) = P+(1+r/n)^nt = 5000+(1+0.06/2)^2= 5406
Amount (SI) = P+PTR/100 = 5000+(5000*1*8/100)=5400
Difference = 5406-5400=6 $
A
Answer: (A) $ 6
Question: 80% of Ram's marks is equal to 20% of Rahim's marks which percent is equal to 30% of Robert's marks. If Robert's marks is 80, then find the average marks of Ram and Rahim?
(A) 70
(B) 97
(C) 87
(D) 90
(E) 75
Rationale: Given, 80% of Ram's marks = 20% of Rahim's marks = 30% of Robert's marks.
Given, marks of Robert = 80
30% of 80 = 30/100 * 8 = 24
Given, 80% of Ram's marks = 24.
=> Ram's marks = (24 * 100)/80 = 30
Also, 20% of Rahim's marks = 24
=> Rahim's marks = (24 * 100)/20 = 120
Average marks of Ram and Rahim = (30 + 120)/2 = 75.
Answer:E
Answer: (E) 75
Question: An error 12% in excess is made while measuring the side of a square. Now What is the percentage of error in the calculated area of the square?
(A) 6.64%
(B) 16.64%
(C) 15.64%
(D) 25.44%
(E) 10.64%
Rationale: Percentage error in calculated area
=(12+12+(12Ã—12)/100)%=25.44%
ANSWER:D
Answer: (D) 25.44%
Question: ZYXW’ as coded as ‘ABCD’ then ‘STUV’ is coded as
(A) YU
(B) YY
(C) U
(D) H
(E) W
Rationale: Here each letter is coded with its opposite letter. i.e. Z – A, Y – B, X – C, W – D. Similarly, S – H, T – G, U – F, V – E.
Answer:D
Answer: (D) H
Question: A fort of 1000 soldiers has provisions for 25 days. After 5 days some of them left and the food was now enough for the same period of 25 days as before. How many of them left?
(A) 50
(B) 100
(C) 150
(D) 175
(E) 200
Rationale: 2000 ---- 50
1000 ---- 20
x ----- 25
x*25 = 1000*20
x=800
1000
-------
200
Answer: E
Answer: (E) 200
Question: There are 15 members in a family. it takes 180 days for a women to complete the work, however man completes in 120 days. They take 17days to complete the work if men work on alternate days and women work every third day. if all of them started together on the 1st day, then how many women are there in the family
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Let the number of men be m and so the number of women = 15-m
Out of 17 days, men and women work together on 1,4,7,10,13,16th days (Total of 6 days) from the start.
Men work on alternate days, that is 1,3,5,7,9,11,13,15,17th days (Total of 9 days).
Let the total work be 360 units (LCM of 180 and 120).
1 man does 360/120 = 3 units per day
1 woman does 360/180 = 2 units per day
Based on above facts,
Total work by men + women in these 17 days = 360 units
m*9*3 + (15-m)*6*2 = 360,
27m + 180 -12m = 360, Solving m=12.
Num of men = 12 and number of women = 15-12 = 3
ANSWER:C
Answer: (C) 3
Question: Mr. Smitherly leaves Cedar Rapids at 8:00 a.m. and drives north on the highway at an average speed of 50 km per hour. Mr. Dinkle leaves Cedar Rapids at 9:00 a.m. and drives north on the same highway at an average speed of 70 km per hour. Mr. Dinkle will
(A) overtake Mr. Smitherly at 9:30 a.m.
(B) overtake Mr. Smitherly at 10:30 a.m.
(C) overtake Mr. Smitherly at 11:30 a.m.
(D) be 30 miles behind at 9:35 a.m.
(E) never overtake Mr. Smitherly
Rationale: After one hour, Mr. Smitherly is ahead by 50 km.
Mr. Dinkle gains on Mr. Smitherly 20 km each hour.
2.5 hours after 9:00 a.m., Mr. Dinkle will catch Mr. Smitherly.
The answer is C.
Answer: (C) overtake Mr. Smitherly at 11:30 a.m.
Question: In how much time would the simple interest on a certain sum be 0.125 times the principal at 10% per annum?
(A) 1 1/4
(B) 1 1/6
(C) 1 1/5
(D) 1 1/3
(E) 1 1/9
Rationale: Let sum = x. Then, S.I. = 0.125x = 1/8 x, R = 10%
Time = (100 * x) / (x * 8 * 10) = 5/4 = 1 1/4 years.
Answer:A
Answer: (A) 1 1/4
Question: In a cinema hall for the matinee show which started at 2.30 pm and ended at 5.30 pm the vehicle parking lot had only three wheelers (auto rickshaws) and four wheelers. Today the wheels of the vehicles parked was counted and found to be 240. What could be the number of three wheelers parked therein?
(A) 41
(B) 43
(C) 42
(D) 45
(E) 48
Rationale: 3X+4y=240
by substitute through options 48 is correct
ANSWER:D
Answer: (D) 45