mathewhe/aqua_rat huggingface dataset:
Question: A BAG CONTAINS 6 WHITE AND 4 BLACK BALLS .2 BALLS ARE DRAWN AT RANDOM. FIND THE PROBABILITY THAT THEY ARE OF SAME COLOUR.
(A) 8/9
(B) 75/4
(C) 7/15
(D) 3/7
(E) 4/3
Rationale: LET S BE THE SAMPLE SPACE
THEN N(S)=NO OF WAYS OF DRAWING 2 BALLS OUT OF (6+4)=10C2=(10*9)/(2*1)=45
LET E=EVENT OF GETTING BOTH BALLS OF SAME COLOUR
THEN N(E)=NO OF WAYS(2 BALLS OUT OF SIX) OR(2 BALLS OUT OF 4)
=(6C2+4C2)=(6*5)/(2*1)+(4*3)/(2*1)=15+6=21
P(E)=N(E)/N(S)=21/45=7/15
Ans: C
Answer: (C) 7/15
Question: A certain company had a total annual expenditure of 1.47∗10^7 on employee salaries last year. If the company employed 420 people, what was the average employee salary?
(A) $20,000
(B) $25,000
(C) $35,000
(D) $40,000
(E) $45,000
Rationale: Given: Total annual expenditure of 1.47∗10^7 on employee salaries
Total employees = 420
Observe that 420*3.5 = 1470
Therefore try to bring the numerator in terms of 1470
Average salary = (1470*10^4) /420 = 3.5*10^4 = 35,000
Option C
Answer: (C) $35,000
Question: which number need to add to 859622 to get a number exactly divisible by 456?
(A) 544365
(B) 465674
(C) 345465
(D) 675644
(E) 859622
Rationale: Dividend = Quotient * Divisor + Reminder
859622 / 456 gives quotient = 1885 and reminder = 62.
So, the next number divisible by 456 is 456 places infront of 456 * 1885
Which means 456 – 62 = 394 should be added to 859622.
E
Answer: (E) 859622
Question: A rectangular with dimensions 16 inches by 20 inches is to be divided into squares of equal size. Which of the following could be a length of a side of the squares?
(A) a) 4 inches
(B) b) 6 inches
(C) c) 7 inches
(D) d) 8 inches
(E) e) 10 inches
Rationale: you need to divide the width and length of the rectangular to equal pieces where L = W
you can solve this using GCF
16=2*2*2*2
20=2*2*5
GCF = 2*2= 4
P.S you can make squares with side of 2,4 and we choose 4 because 2 is not in the answers
Answer : A
Answer: (A) a) 4 inches
Question: A woman invested $1,000, part at 5% and the rest at 6%. Her total investment with interest at the end of the year was $1,054. How much did she invest at 5%?
(A) $500
(B) $600
(C) $700
(D) $900
(E) $950
Rationale: et x be the portion invested at 5% and
Let (1-x) be the rest which is invested at 6%
The question states that the return after 1 year is (1054/1000)-1 = 0.054 = 5.4%
We want to find the dollar amount invested in X
Using our defined variables, put together the equation and solve for x (the percentage of 1000 invested at 5%)
0.05x+0.06(1-x)= 0.054
(0.05)x +0.06 - (0.06)x = 0.054
-0.01x = -0.006
x= -0.006/-0.01 = 6/10 = 60%
So X = 60% of the 1000 which is 600
ANSWER:B
Answer: (B) $600
Question: CX, EV, GT, IR, ?
(A) JH
(B) UU
(C) KP
(D) UY
(E) IS
Rationale: ANSWER:C
Answer: (C) KP
Question: The figure shown can be folded into the shape of a cube. In the resulting cube, which of the lettered faces is opposite the face marked x?
(A) D
(B) H
(C) J
(D) H
(E) W
Rationale: Explanation: If you fold the above picture at the dotted lines, X and C are opposite to each other.
Answer:A
Answer: (A) D
Question: A cylinder and a cone have the same height and same radius of base. The ratio between the volumes of the cylinder and the cone is:
(A) 4:1
(B) 2:1
(C) 7:1
(D) 5:1
(E) 3:1
Rationale: Volume of the cylinder = πr(power2)h
Volume of the cone = 1/3 πr(power2)h
(πr(power2)h)/(1/3 πr(power2)h) = 3/1 = 3 : 1
Answer is E.
Answer: (E) 3:1
Question: A 10-by-5 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?
(A) The volume of the cylinder with height 10 is 50/pi cubic inches greater than the volume of the cylinder with height 6.
(B) The volume of the cylinder with height 5 is 50/pi cubic inches greater than the volume of the cylinder with height 10.
(C) The volume of the cylinder with height 10 is 50pi cubic inches greater than the volume of the cylinder with height 6.
(D) The volume of the cylinder with height 5 is 50pi cubic inches greater than the volume of the cylinder with height 10.
(E) The volume of the cylinder with height 5 is 250/pi cubic inches greater than the volume of the cylinder with height 10.
Rationale: Pretty straightforward. Plug in the values to compute the volume of the cylinder. Keep in mind 5 and 10 are the circumference of the base and not the radius. B is the right answer.
Answer: (B) The volume of the cylinder with height 5 is 50/pi cubic inches greater than the volume of the cylinder with height 10.
Question: A BUS is running at a speed of 40 km/hr and it crosses a post in 18 seconds. What is the length of the BUS ?
(A) metres
(B) metres
(C) metres
(D) metres
(E) metres
Rationale: Explanation:
Speed of the BUS, v = 40 km/hr = 40000/3600 m/s = 400/36 m/s
Time taken to cross, t = 18 s
Distance Covered, d = vt = (400/36)× 18 = 200 m
Distance covered is equal to the length of the BUS= 200 m
Answer: Option C
Answer: (C) metres
Question: The average age of the mother and her six children is 8 years which is reduced by 5 years if the age of the mother is excluded. How old is the mother?
(A) 38
(B) 41
(C) 42
(D) 43
(E) 44
Rationale: Total age of mother and 6 children = avg x n = 8 x (6+1)= 56
If mother is excluded new average is (8 - 5) = 3
so for 6 children = 6 x 3 =18
so mother's age is 56 - 18 =38
Answer: Option A
Answer: (A) 38
Question: If a and b are positive real numbers, and a^3 + b^3 = 25, then the greatest possible value of a is between:
(A) 0 and 3
(B) 3 and 4
(C) 4 and 5
(D) 5 and 7
(E) 7 and 9
Rationale: If a > 3, then a^3 + b^3 > 25.
The answer is A.
Answer: (A) 0 and 3
Question: The “length of integer x” refers to the number of prime factors, not necessarily distinct, that x has. (If x = 60, the length of x would be 4 because 60 = 2 × 2 × 3 × 5.) What is the greatest possible length of integer z if z < 1,080?
(A) 13
(B) 10
(C) 9
(D) 7
(E) 6
Rationale: To maximize the length of z we should minimize its prime base. The smallest prime is 2 and since 2^10=1,024<1,080 then the greatest possible length of integer z is 10.
Answer: B.
Answer: (B) 10
Question: How many distinct integer values of n satisfy the inequality||n-3| + 2| ≤ 12?
(A) 15
(B) 16
(C) 12
(D) 18
(E) 19
Rationale: so i can write this as In-3I+2<=12
or In-3I<=10
so n can have -7 to 13 = 12 true values....
C
Answer: (C) 12
Question: How is 2% expressed as a decimal fraction?
(A) 0.2
(B) 0.02
(C) 0.002
(D) 0.0002
(E) 2
Rationale: 2/100= 0.02
ANSWER:B
Answer: (B) 0.02
Question: There are 1200 jelly beans divided between two jars, Jar X and Jar Y. If there are 400 fewer jelly beans in jar X than three times the number of beans in jar Y, how many beans are in jar X?
(A) 650
(B) 700
(C) 750
(D) 800
(E) 850
Rationale: X+Y=1200 so Y=1200-X
X=3Y-400
X=3(1200-X)-400
4X=3200
X=800
The answer is D.
Answer: (D) 800
Question: f n = 3^4 - 2^4, which of the following is NOT a factor of n?
(A) 13
(B) 22
(C) 65
(D) 169
(E) 130
Rationale: ( 3^2+2^2)(3^2-2^2) = 13*5*1 . 13 and 5 prime number and factor any thing not having 13 and 5 as factor will not be a factor.
B
Answer: (B) 22
Question: The banker's discount on a bill due 4 months hence at 15% is $6.20. The true discount is:
(A) $5.90
(B) $6.80
(C) $6.60
(D) $6.70
(E) $6.10
Rationale: T.D.	=	B.D. x 100/100 + (R x T)
= $ [6.20 x 100/100 +15 x 1/3]
= $	[6.20 x 100/105]
= $ 5.90
ANSWER:A
Answer: (A) $5.90
Question: Find the area of the quadrilateral of one of its diagonals is 10 cm and its off sets 7 cm and 3 cm?
(A) 50 cm2
(B) 100 cm2
(C) 150 cm2
(D) 200 cm2
(E) 250 cm2
Rationale: 1/2 * 10(7 + 3)
= 50 cm2
Answer: A
Answer: (A) 50 cm2
Question: If ab > 0, which of the following must be negative?
(A) a + b
(B) |a| + b
(C) b - a
(D) a/b
(E) -a/b
Rationale: If ab > 0 the we Infer that a and b both have same sign i.e. either both a and b are Positive or Both a and b are Negative
Now Checking Options:
(A) a + b will be positive for both a and b to be positive hence INCORRECT OPTION
(B) |a| + b will be positive for both a and b to be positive hence INCORRECT OPTION
(C) b - a May be positive for both a and b to be positive (e.g. b=3 and a=2) henceINCORRECT OPTION
(D) a/b will be positive for both a and b to be positive or Negative hence INCORRECT OPTION
(E) -a/b will always be Negative because an and b have same sign so a/b will be positive therefore -a/b will be Negative hence CORRECT
Answer: Option E
Answer: (E) -a/b
Question: Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak's share is :
(A) Rs. 5400
(B) Rs. 700
(C) Rs. 8400
(D) 2Rs. 9600
(E) Rs. 8000
Rationale: Explanation:
Ratio of their shares = 22500 : 35000 = 9 : 14.
Deepak's share = Rs.
(13800âˆ—14/23)
= Rs. 8400.
ANSWER IS C
Answer: (C) Rs. 8400
Question: Some persons can do a piece of work in 12 days. Two times the number of these people will do half of that work in?
(A) 2 days
(B) 3 days
(C) 1 days
(D) 5 days
(E) 7 days
Rationale: B
3 days
12/ (2 * 2) = 3 days
Answer: (B) 3 days
Question: Find the value of x: 2x² + 9x − 5.
(A) 1/2
(B) 1/3
(C) 2/3
(D) 2/5
(E) 3/5
Rationale: That quadratic is factored as follows:
2x² + 9x − 5 = (2x − 1)(x + 5).
Lesson 17.
Now, it is easy to see that the second factor will be 0 when x = −5.
As for the value of x that will make
2x − 1	=	0,
we must solve that little equation. (Lesson 9.)
We have:
2x	=	1
x	=	1
2
The solutions are:
x	=	1/2 or −5
A
Answer: (A) 1/2
Question: Ram's age and Shyam's age are in the ratio 3:4. Seven years ago the ratio of their ages was 2:3. Find the ratio of their ages five years hence?
(A) 26/73
(B) 26/39
(C) 26/93
(D) 26/33
(E) 26/13
Rationale: Let ages of Ramu and Shyam be x and y respectively.
x/y = 3/4 => x = 3/4 y
(x- 7)/(y - 7) = 2/3
=> 3x - 21 = 2y - 14 => 3x = 2y + 7
But x = 3/4 y
3 * 3/4 y = 2y + 7
9y = 8y + 28 => y = 28years
=> x = 21 years
Ratio of their ages five years hence, (21 + 5)/(28 + 5) = 26/33.
Answer: D
Answer: (D) 26/33
Question: A salesman`s commission is 5% on all sales upto Rs.10,000 and 4% on all sales exceeding this.He remits Rs.31,100 to his parent company after deducing his commission . Find the total sales.
(A) 32500
(B) 33400
(C) 44000
(D) 40000
(E) 45000
Rationale: Let his total sales be Rs.x.Now(Total sales) – (Commission )=Rs.31,100
x-[(5% of 10000 + 4% of (x-10000)]=31,100
x-[((5/100)*10000 + (4/100)*(x-10000)]=31,100
x-500-((x-10000)/25)=31,100
x-(x/25)=31200  24x/25=31200x=[(31200*25)/24)=32,500.
Total sales=Rs.32,500
ANSWER A
Answer: (A) 32500
Question: What is the remainder when 263251 is divided by 9?
(A) 8
(B) 3
(C) 6
(D) 1
(E) 9
Rationale: If the sum of the digits of a number is divisible by 9, the number will be divisible by 9.
2 + 6 + 3 + 2 + 5 + 1 = 19
The nearest multiple of 9 is 18.
19 - 18 = 1.
ANSWER:D
Answer: (D) 1
Question: A set of numbers has the property that for any number x in the set, x+4 is also in the set. If -4 is in the set, which of the following must also be in the set
1. 0
2. -8
3. 8
(A) 1 only
(B) 2 only
(C) 1 and 2 only
(D) 2 and 3 only
(E) 1,2 and 3
Rationale: If X is in the set than X+ 4 is also in the set
If -4 in the set than
-4+4= 0 is also in the set
Since + 4 is Present, 4 + 4= 8 Is also present in the set .
Therefore Ans C
Answer: (C) 1 and 2 only
Question: A began business with Rs.45000 and was joined afterwards by B with Rs.5400. When did B join if the profits at the end of the year were divided in the ratio of 2:1?
(A) 7
(B) 8
(C) 9
(D) 6
(E) 5
Rationale: 45*12 : 54*x = 2: 1
x = 5
12 -5 = 7.Answer: A
Answer: (A) 7
Question: If 40% of a number is greater than 80% of 5 by 2, what is the number?
(A) 3
(B) 15
(C) 20
(D) 2
(E) 5
Rationale: Explanation:
40/100 * x - 80/100 * 5 = 2
40/100 * x - 4 = 2
40/100 * x = 6
x = 6 * 100 / 40
x = 15
Answer: Option B
Answer: (B) 15
Question: If a coin is flipped, the probability that the coin will land tails is 1/2. If the coin is flipped 5 times, what is the probability that it will land tails up on the first 2 flips and not on the last 3 flips?
(A) 3/5
(B) 1/32
(C) 1/5
(D) 1/4
(E) 1/2
Rationale: (1/2) * (1/2) * (1/2) * (1/2) * (1/2) = 1/32 Answer: B
Answer: (B) 1/32
Question: If a is a positive integer then 4^(2a) + (64^a)/(2^(2a)) =
(A) 0
(B) 16^16
(C) 8^15
(D) 2 × 16^a
(E) 18^a
Rationale: 4^(2a) + 64^a/ 2^(2a) = 16^a + 36^a/4^a = 16^a + (64/4)^a = 16^a + 16^a = 2 × 16^a
Answer : D
Answer: (D) 2 × 16^a
Question: There are 5 locks and 5 keys and each of the 5 keys matches each of the 5 locks. What is the minimum and the maximum trial numbers of attempts needed to confirm that each of the 5 keys matches each of the 5 locks?
(A) 5,15
(B) 4,15
(C) 5,10
(D) 4,10
(E) 5,20
Rationale: the actual number of tries that we need to "unlock" all the lockers, and got into the trap 5-15.
of course, if we do not need to unlock the lockers, but just simply to check..
minimum # of attempts is 4.
maximum is 10,
ANS:D
Answer: (D) 4,10
Question: A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 19 months?
(A) 18:11
(B) 18:15
(C) 18:19
(D) 18:121
(E) 19:11
Rationale: A invests Rs.8000 for 19 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only.
A : B
8000*19 : (8000*4) + (4000*14)
152000 : 88000
A:B = 19:11.Answer:E
Answer: (E) 19:11
Question: In the set of positive integers from 1 to 60, what is the sum of all the odd multiples of 5?
(A) 180
(B) 185
(C) 190
(D) 160
(E) 165
Rationale: 1 - 60
5 - 15 - 25 - 35 - 45 are valid multiples of 5. Add them
5+15+25+35+45+55 =180
A
Answer: (A) 180
Question: Two bus tickets from city A to B and three tickets from city A to C cost Rs. 154 but three tickets from city A to B and two tickets from city A to C cost Rs. 146. What are the fares for cities B and C from A ?
(A) s. 4, Rs. 23
(B) s. 13, Rs. 17
(C) s. 15, Rs. 14
(D) s. 17, Rs. 13
(E) s. 26, Rs. 34
Rationale: If fares for cities B and C from A are x and y respectively, then
2x+3y=154 or 6x+9y= 462
3x+2y =146 or 6x+4y= 292
subtracting
5y = 170
y= Rs 34
Hence E. Rs. 26, Rs. 34
ANSWER:E
Answer: (E) s. 26, Rs. 34
Question: If the difference between the length and breadth of a rectangle is 23 m and its perimeter is 206 m, what is its area?
(A) 2520
(B) 2510
(C) 2525
(D) 2025
(E) 2020
Rationale: l-b=23...(1)
perimeter = 206
2(l=b)= 206
l+b = 103...(2)
(1)+(2)
2l=23+103=126
l =126/2=63 metre
Substituting the value of l in (1), we get
63-b=23
b=63-23=40 metre
area=lb=63Ã—40 =2520 m2
ANSWER:A
Answer: (A) 2520
Question: If Yury has been writing programming code for 11 hours at a rate of 5 lines of code per 20 seconds, how many lines of code has he written?
(A) 126(10^2)
(B) 126(10^3)
(C) 12.6(10^5)
(D) 1.26(10^7)
(E) 99(10^2)
Rationale: 5 LINES IN 20 SECONDS
SO FOR 1 MINUTE ( 5 X 3 = 15 LINES )
I HOUR = 60 MINUTES
15 X 60 = 900 LINES IN AN HOUR
11 HOURS = 900 X 11 = 99(10^2)
ANSWER E
Answer: (E) 99(10^2)
Question: The sum of five numbers is 750. The average of the first two numbers is 75 and the third number is 130. Find the average of the two numbers?
(A) 220
(B) 225
(C) 230
(D) 235
(E) 240
Rationale: Let the five numbers be P, Q, R, S and T.
=> P + Q + R + S + T = 750.
(P + Q)/2 = 75 and R = 130
P + Q = 150 and R = 130
P + Q + R = 280
S + T = 750 - (P + Q + R) = 470
Average of the last two numbers
= (S + T)/2 = 235
Answer:D
Answer: (D) 235
Question: The number of sequences in which 7 players can throw a ball, so that the youngest player may not be the last is?
(A) 4389
(B) 8369
(C) 4320
(D) 4356
(E) 3537
Rationale: x Not younger_______ ↑
The last ball can be thrown by any of the remaining 6 players. The first 6 players can throw the ball in ⁶P₆ ways.
The required number of ways = 6(6!) = 4320
Answer:C
Answer: (C) 4320
Question: If Jake loses 8 pounds, he will weigh twice as much as his sister Kendra. Together they now weigh 287 pounds. What is Jake’s present weight, in pounds?
(A) 178
(B) 182
(C) 186
(D) 190
(E) 194
Rationale: J + K = 287 and so K = 287 - J
J - 8 = 2K
J - 8 = 2(287-J)
3J = 582
J = 194
The answer is E.
Answer: (E) 194
Question: A number x is mistakenly divided by 10 instead of being multiplied by 10. what is the percentage error in the result?
(A) -99%
(B) -100%
(C) +99%
(D) +100%
(E) None
Rationale: Solution: Actual result = 10x
By mistake it has been divided by 10 = x /10
% change = [10x -(10 /x) /10x] *100 = 99
= - 99%.
Since, actual value is greater than the wrong value.
Alternatively,
Let, x = 10
Actual result = 10 * 10 = 100
wrong result = 10 /10 = 1.
Change = (1 -100) = -99
% change = -99%.
Answer: Option A
Answer: (A) -99%
Question: A man buys an item at Rs. 1200 and sells it at the loss of 20 percent. Then what is the selling price of
that item
(A) Rs. 660
(B) Rs. 760
(C) Rs. 860
(D) Rs. 960
(E) None of these
Rationale: Explanation:
Here always remember, when ever x% loss,
it means S.P. = (100 - x)% of C.P
when ever x% profit,
it means S.P. = (100 + x)% of C.P
So here will be (100 - x)% of C.P.
= 80% of 1200
= 80/100 * 1200
= 960
Answer: D
Answer: (D) Rs. 960
Question: 10 books are placed at random in a shelf. The probability that a pair of books will always be together is?
(A) 1/7
(B) 1/9
(C) 1/5
(D) 1/8
(E) 1/2
Rationale: 10 books can be rearranged in 10! ways consider the two books taken as a pair then number of favourable ways of getting these two books together is 9! 2!
Required probability = 1/5
Answer: C
Answer: (C) 1/5
Question: An automobile parts supplier charges $25 per package of gaskets. When a customer orders more than 10 packages of gaskets, the supplier charges 4/5 the price for each package in excess of 10. During a certain week, the supplier sold 60 packages of gaskets. If 25 percent of the gaskets went to Company X, 15 percent to Company Y, and the rest to Company Z, what was the total amount, in dollars, that the parts supplier received in payment for the gaskets?
(A) 1305
(B) 1545
(C) 1375
(D) 1345
(E) 1455
Rationale: $25 per packet of gasket in case a customer orders less than 10
in case a customer orders > 10 price per gasket = 25*4/5=20
a certain week the supplier sold 60 gasket
1.he sold 25 % of the gaskets to X = 15 gaskets = 25*10 + 20 *5 = 250 + 100 = 350
2.he sold 15 % of the gaskets to Y = 9 gaskets = 25*9= 225
3.he sold remaining 60% to z =36 gaskets = 25*10 =250 + 20*26=770
thus ,total money earned
350+225+770 = 1345
Answer is D
Answer: (D) 1345
Question: Cost is expressed by the formula tb^4. If b is doubled, the new cost is what percent T of the original cost?
(A) T=200
(B) T=600
(C) T=800
(D) T=1600
(E) T=50
Rationale: Original Cost C1=t1*b1^4
New Cost C2=t2*b2^4....only b is doubled so t2=t1 and b2=2b1
C2=t2*(2b1)^4
=16(t1 * b1^4)
=16C1
16 times C1=>1600% of C1
Ans D=1600
Answer: (D) T=1600
Question: Find the value of 72519 x 9999 = m?
(A) 234567745
(B) 674225565
(C) 570909643
(D) 725117481
(E) 768965324
Rationale: 72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
D
Answer: (D) 725117481
Question: A is twice as good a workman as B and together they complete a work in 12 days. In how many days A alone can do the work?
(A) 32
(B) 33
(C) 34
(D) 35
(E) 36
Rationale: A’s one day’s work : B’s one day’s work= 2:1
(A+B)’s one day’s work= 1/12
B’s one day’s work= 1/12 *1/3 = 1/36
B alone can do the work in 36 days
ANSWER:E
Answer: (E) 36
Question: In how many ways can a group of 4 men and 2 women be made out of a total of 6 men and 4 women?
(A) 63
(B) 67
(C) 70
(D) 90
(E) 80
Rationale: We need to select 4 men from 6 men and 2 women from 4 women. Number of ways to do this= 6C4 × 4C290D)
Answer: (D) 90
Question: What will come in place of the x in the following Number series? 11, 14, 19, 22, 27, 30, x
(A) 29
(B) 31
(C) 23
(D) 35
(E) 39
Rationale: (D)
The pattern is + 3, + 5, + 3, + 5, …………
So the missing term is = 30 + 5 = 35.
Answer: (D) 35
Question: what is the angle between the hands of a clock when time is 10:20?
(A) 90deg
(B) 75deg
(C) 45deg
(D) 15deg
(E) 30deg
Rationale: Angle between two hands =
20h - 11/2 m = 20*10 - 20*11/2 = 200 - 110 = 90deg
ANSWER:A
Answer: (A) 90deg
Question: Two hoses are pouring water into an empty pool. Hose 1 alone would fill up the pool in 6 hours. Hose 2 alone would fill up the pool in 5 hours. How long would it take for both hoses to fill up two-thirds of the pool?
(A) 5/12 hours
(B) 5/8 hours
(C) 20/11 hours
(D) 12/7 hours
(E) 12/5 hours
Rationale: Hose 1 would fill the pool alone in 6 hours
i.e. 1 Hour work of Hose 1 = 1/6
Hose 2 would fill the pool alone in 5 hours
i.e. 1 Hour work of Hose 2 = 1/5
i.e. 1 Hour work of Hose1 and Hose2 together = (1/6)+(1/5) = (11/30)
i.e. (11/30) work can be finished by Hose1 and Hose2 together in 1 hour
i.e. (2/3) work can be finished by Hose1 and Hose2 together in 1*(30/11)*(2/3) = 20/11hour
Answer: Option C
Answer: (C) 20/11 hours
Question: The difference between the simple interest and the compound interest (compounded yearly)earned on a sum of money at the end of four years at the rate of 10 percent per annum is Rs.256.40. Find the sum.
(A) Rs.6,000
(B) Rs.4,000
(C) Rs.5,000
(D) Rs.4500
(E) Rs.5500
Rationale: SI=(P*10*4)/100= 4p/10
CI=P(1+10/100)^4-P =4641P/100
CI-SI=
4641P/100-4P/100=256.40
P=4000
ANSWER:B
Answer: (B) Rs.4,000
Question: The cash realised on selling a 14% stock is Rs.105.25, brokerage being 1/4% is?
(A) 366
(B) 106
(C) 102
(D) 105
(E) 122
Rationale: Cash realised= Rs. (105.25 - 0.25)
= Rs. 106.
Answer: D
Answer: (D) 105
Question: Tom began driving from home on a trip averaging 30 miles per hour. How many miles per hour must Carla drive on average to catch up to him in exactly 3 hours if she leaves 30 minutes after Tom?
(A) 35
(B) 55
(C) 39
(D) 40
(E) 60
Rationale: Carla starts 30 minutes later and it takes 3 hr for carla to meet Tom
So Tom total time travelled = 3hr + 30 minutes
Tom distance = 30 * (3 1/2) = 105
so carla need to travle 105 to meet Tom in 3 hrs
speed of carla = 105/3 = 35 miles per hour
Answer is A
Answer: (A) 35
Question: The simple interest on Rs.12000 at a certain rate of interest in five years is Rs.7200. Find the compound interest on the same amount for five years at the same rate of interest?
(A) 3052.83
(B) 3052.22
(C) 3052.08
(D) 3052.8
(E) 3052.13
Rationale: R = 100 I / PT
=> R = (100 * 7200)/ (12000 * 5) = 12%
CI = P{ [1 + R /100]n - 1}
= 12000 { [ 1 + 12 / 100]2 - 1}
= Rs.3052.80
Answer: D
Answer: (D) 3052.8
Question: The smallest number which when added to 4, the sum is exactly divisible by 24, 36, 48 and 60 is:
(A) 327
(B) 716
(C) 256
(D) 299
(E) 111
Rationale: nation: 2 24 36 48 60 2 12 18 24 30 3 6 9 12 15 2 2 3 4 5 1 3 2 5 ∴ LCM of 24, 36, 48, 60 = 2 × 2 × 3 × 2 × 3 × 2 × 5 = 720. ∴ Required number = 716
Answer:B
Answer: (B) 716
Question: The sum of the first 50 positive even integers is 2550. What is the sum R of even integers from 102 to 200 inclusive?
(A) 5100
(B) 7550
(C) 10100
(D) 15500
(E) 20100
Rationale: My solution is:
First 50 even integers:
2
4
6
8
<...>
Integers from 102 to 200
102
104
106
108
<...>
We notice that each integer from the second set is 100 more than the respective integer in the first set. Since we have 50 even integers from 102 to 200, then:
R=2550+(100*50)=7550.B
Answer: (B) 7550
Question: A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 26 sec respectively. What is the speed of the train?
(A) 89
(B) 23
(C) 52.8
(D) 79.2
(E) 67
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 264)/26 = y
y = 14.67
Speed = 14.67 m/sec = 14.67 * 18/5 = 52.8 km/hr.
Answer: Option C
Answer: (C) 52.8
Question: If Susan takes 10 seconds to run y yards, how many minutes will it take her to run x yards at the same rate?
(A) xy/10
(B) 10x/(60y)
(C) 60xy/10
(D) xy/540
(E) 540x/y
Rationale: The answer is B.
She runs x yards in 10x/y seconds =10x/60y minutes.
Answer: (B) 10x/(60y)
Question: For how many values of M, is |||M - 5| -10| -5| = 2?
(Those ls are mods)
(A)  0
(B)  2
(C)  4
(D)  8
(E)  More than 8
Rationale: I think its 8
|||M-5|-10|-5| =2
let |M-5| = a which makes above
||a-10|-5| =2
let |a-10| = b which makes
|b-5| = 2
now for the above b can take 3, 7
for every b =3 a can have 13, 7
and for b = 7 a can have 17 and 3
so 'a' has four solutions 13, 7, 17 and 3
for a = 13; x has 18 or -8 thus has 2 for every combination hence 4x2 = 8
answer D
Answer: (D)  8