mathewhe/aqua_rat huggingface dataset:
Question: Given the two equations 5r + s = 26 and r + 5s = 10, by how much does r exceed s?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Solve by Simultaneous Equations.
My Answer is B.
r=5
s=1
Answer: (B) 4
Question: The sum of first six prime numbers is?
(A) 12
(B) 23
(C) 24
(D) 28
(E) 41
Rationale: Required sum = (2 + 3 + 5 + 7 + 11+13) = 41.
Note: 1 is not a prime number.
Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.
E
Answer: (E) 41
Question: The average speed of a car is 1 4/5 times the avg speed of a bike. A tractor covers 575km in 23hrs. How much distance will the car cover in 4hrs if the speed of the bike is twice speed of the tractor?
(A) 300 km
(B) 320 km
(C) 360 km
(D) 430 km
(E) 670 km
Rationale: Sol. Average speed of a tractor = 25 km / h
The speed of a bus in an hour = 25 × 2 = 50 km
The speed of a car in an hour = 9/5 * 50 = 90 km
So, the distance covered by car in 4 h is
90 × 4 = 360 km
Ans.(C)
Answer: (C) 360 km
Question: 15% of a certain number is subtracted from 299, the result is the same number. What is the number?
(A) 199
(B) 260
(C) 365
(D) 175
(E) 238
Rationale: 299 - (15/100) * X = X
299 - .15*X = X
299 = 1.15 * X
X = 260
Answer: B
Answer: (B) 260
Question: Set S consists of integers {1,2,3,4}. If two numbers are chosen from set S at random, what is the probability that the sum of 2 numbers is more than 6?
(A) 1/3
(B) P(E)=1/6
(C) 2/3
(D) 2/5
(E) 3/7
Rationale: Number of ways you can choose 2 from 4 = 4C2 = 6
E = event of getting the 2 numbers is more than 6 = (3,4) = 1
probability = 1/6
Answer is B
Answer: (B) P(E)=1/6
Question: Three hoses work to fill a tub at at different rate. Hose P and B, working together, can fill the tub in 6/5 of an hour. Hoses P and C can fill it in 3/2 an hour. Houses B and C can fill it in 2 hours. How long does it take all 3 hoses, working together, to fill the tub?
Edited for accurate solution
(A) 3/10
(B) 2/5
(C) 1/2
(D) 1
(E) 6/5
Rationale: Convert the given time to rate and you will be able to add it up.
Total Rate of P and B = Rate of P + Rate of B = 1/(6/5) = 5/6
Total Rate of P and C = Rate of P + Rate of C = 1/(3/2) = 2/3
Total Rate of B and C = Rate of B + Rate of C = 1/2
Adding all three,
2(Rate of P + Rate of B + Rate of C) = 5/6 + 2/3 + 1/2 = 2
Rate of P + Rate of B + Rate of C = 1 tub/hour
Time taken by all three together to fill up the tub is 1 hour=D
Answer: (D) 1
Question: In a rectangular coordinate system, points O (2,0), P (2,8), and Q (8,0) represent the sites of three proposed housing developments. If a fire station can be built at any point in the coordinate system, at which point would it be equidistant from all three developments?
(A) (3,5)
(B) (4,3)
(C) (5,4)
(D) (4,4)
(E) (5,3)
Rationale: All points equidistant from O and Q lie on the line x = 5, so the fire station should lie on this line.
All points equidistant from O and P lie on the line y = 4, so the fire station should lie on this line.
These two intersect at (5,4) and that will be the point equidistant from all 3 points.
The answer is C.
Answer: (C) (5,4)
Question: The population of a town is 10000. It increases annually at the rate of 10% p.a. What will be its population after 2 years?
(A) 12300
(B) 12350
(C) 12100
(D) 12500
(E) 12600
Rationale: Formula :
( After =100 denominator
Ago = 100 numerator)
10000 Ã— 110/100 Ã— 110/100 = 12100
C
Answer: (C) 12100
Question: The HCF and LCM of two numbers m and n are respectively 6 and 210. If m + n = 72, then 1/m + 1/n is equal to
(A) 1/35
(B) 3/35
(C) 5/37
(D) 2/35
(E) None
Rationale: Answer
We have, m x n = 6 x 210 = 1260
∴ 1/m + 1/n = (m + n)/mn = 72/1260 = 4/70 = 2/35
Correct Option: D
Answer: (D) 2/35
Question: The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides?
(A) 3
(B) 6
(C) 4
(D) 9
(E) 1
Rationale: S = (1 + 2 + 3)/2
= 3
Answer:A
Answer: (A) 3
Question: When a random experiment is conducted, the probability that event A occurs is 1/4. If the random experiment is conducted 4 independent times, what is the probability that event A occurs exactly twice?
(A) 14/65
(B) 27/128
(C) 33/140
(D) 37/165
(E) 41/187
Rationale: One case is: 1/4*1/4*3/4*3/4=9/256
The total number of possible cases is 4C2 = 6
P(event A occurs exactly twice) = 6*(9/256) = 27/128
The answer is B.
Answer: (B) 27/128
Question: A man whose speed is 5.5 kmph in still water rows to a certain upstream point and back to the starting point in a river which flows at 1.5 kmph, find his average speed for the total journey?
(A) 7
(B) 5.1
(C) 6
(D) 9
(E) 3
Rationale: M = 5.5
S = 1.5
DS = 7
US = 4
AS = (2 * 7 * 4) /11 = 5.1
Answer:B
Answer: (B) 5.1
Question: A coin is tossed 6 times. What is the probability of getting exactly 5 heads?
(A) 3/8
(B) 3/16
(C) 5/16
(D) 3/32
(E) 7/64
Rationale: The number of possible outcomes is 2^6 = 64
There are 6 ways to get exactly 5 heads.
P(exactly 5 heads) = 6/64 = 3/32
The answer is D.
Answer: (D) 3/32
Question: If a + b = x and a - b = y , then 3ab =
can someone explain!
(A) (3x^2 - 3y^2)/4
(B) (3y^2 - 3x^2)/4
(C) 3x+3y/2
(D) 3x - 3y/2
(E) 3x^2 - 3y^2/2
Rationale: plugging numbers is quite fast in this case:
Let
a=1
b=2
Then; x= 1+2=> 3 and Y= 1-2=> -1
Question asks 3ab=.........
As our number 3ab= 3*1*2=6
now plug the value of x and y in the answer choices. Option A gives 6 and that is the number we need.
Hence: Ans is A.
Answer: (A) (3x^2 - 3y^2)/4
Question: Set A contains all the even numbers between 32 and 80 inclusive. Set B contains all the even numbers between 62 and 110 inclusive. What is the difference between the sum of elements of set B and the sum of the elements of set A?
(A) 450
(B) 550
(C) 650
(D) 750
(E) 850
Rationale: Each term in set B is 30 more than the corresponding term in set A.
The difference of the sums = 25 * 30 = 750.
The answer is D.
Answer: (D) 750
Question: When Q is divided by 9, the remainder is 4. All of the following are possible values of Q, except for which of the following?
(A) 13
(B) 31
(C) 49
(D) 57
(E) 67
Rationale: The number can be expressed in the form of 9x+4 where x can 0,1,2,3,4....
by evaluating the answer choices carefully we can clearly observe that 57 is the only number which can't be expressed Q in the form of 9x+4
In other words we can also say that the (answer - 4) will not be divisible by 9.57 is the number which doesn't follow this condition
Correct Answer - D
Answer: (D) 57
Question: The price of 80 apples is equal to that of 120 oranges. The price of 60 apples and 75 oranges together is Rs.1320. The total price of 25 apples and 40 oranges is
(A) 680
(B) 620
(C) 720
(D) 480
(E) 700
Rationale: Let the price of one apple = a and price of one orange = b
The price of 80 apples is equal to that of 120 oranges
80a = 120b
=> 2a = 3b ==> b=2a/3 ------------(1)
price of 60 apples and 75 oranges together is Rs.1320
=>60a + 75b = 1320
=> 4a + 5b = 88 ==> 4a + 5(2a/3) = 88 -------(from equation 1)
=> 12a + 10a = 88 × 3
=> 6a + 5a = 44 × 3
=> 11a = 44 × 3
=> a = 4 × 3 = 12
b = 2a/3
b = 2*12/3
b = 8
Total price of 25 apples and 40 oranges
= 25a + 40b = (25 × 12) + (40 × 8) = 300 + 320 = 620
Ans - B
Answer: (B) 620
Question: In a bag, there are coins of 25 p, 10 p and 5 p in the ratio of 1 : 2 : 3. If there is
Rs. 30 in all, how many 5 p coins are there?
(A) 150
(B) 130
(C) 120
(D) 110
(E) 140
Rationale: Let the number of 25 p, 10 p and 5 p coins be x, 2x, 3x respectively.
Then, sum of their values = Rs. (25X/100 + 10X2X/100 + 5X3X/100) = RS 60X/100
60X/100 = 30 X =30 X 10/60 = 50
Hence, the number of 5 p coins = (3 x 50) = 150.
ANSWER A 150
Answer: (A) 150
Question: Sally has $100 in pennies. She wants to stack her pennies into three large piles and five small piles. The large piles are all the same size, and the small piles are all the same size. Additionally, Sally wants all of the small piles put together to equal one of the large piles. How many pennies does Sally put in one of the small piles?
(A) 2500 pennies
(B) 500 pennies
(C) 250 pennies
(D) 100 pennies
(E) 50 pennies
Rationale: B. Each large pile gets 1/4 of the total pennies. Each small pile gets 1/5 of the remaining 1/4 of the total pennies. So each small pile gets 1/20 of the total pennies. $100 is 10,000 pennies. 1/20 of 10,000 is 500, so the correct answer is B: 500 pennies.
Answer: (B) 500 pennies
Question: If 32.5% of the 880 students at a certain college are enrolled in biology classes, how many students at the college are NOT enrolled in a biology class?
(A) 110
(B) 330
(C) 550
(D) 594
(E) 880
Rationale: Students enrolled in biology are 32.5% and therefore not enrolled are 67.5%. so of 880 is 880*.675 = 594
Answer is D 594
Answer: (D) 594
Question: The average of temperatures at noontime from Monday to Friday is 50; the lowest one is 45, what is the possible maximum range of the temperatures?
(A) 20
(B) 25
(C) 40
(D) 45
(E) 75
Rationale: Average=50, Sum of temperatures=50*5=250
As the min temperature is 45, max would be 250-4*45=70 --> The range=70(max)-45(min)=25
Answer: B.
Answer: (B) 25
Question: A and B entered into a partnership investing Rs. 13,000 and Rs. 12,000 respectively.After 3 months, A withdrew Rs. 5000 while B invested Rs. 5000 more, After 3 more months, C joins the business with a capital of Rs. 21,000, The share of B exceeds that of C, out of a total profit of Rs. 26,400 after one year by?
(A) 8340
(B) 3600
(C) 2787
(D) 1287
(E) 3627
Rationale: A : B : C = (16000 * 3 + 11000 * 9) : (12000 * 3 + 17000 * 9) : (21000 * 6)
= 147 : 189 : 126
= 7 : 9 ; 6.
Difference of B and C's shares = Rs. ( 26400 * 9/22 - 26400 * 6/22 )
= Rs. 3600.
Answer: B
Answer: (B) 3600
Question: A certain sum is invested at simple interest at 15% p.a. for two years instead of investing at 12% p.a. for the same time period. Therefore the interest received is more by Rs. 900. Find the sum?
(A) s. 7000
(B) s. 9000
(C) s. 15000
(D) s. 17000
(E) s. 27000
Rationale: Let the sum be Rs. x.
(x * 15 * 2)/100 - (x * 12 * 2)/100 = 900
=> 30x/100 - 24x/100 =900
=> 6x/100 = 900
=> x = 15000.
ANSWER:C
Answer: (C) s. 15000
Question: If an integer n is divisible by3, 5, 12. what is the next larger integer divisible by all these numbers
(A) n+3
(B) n+5
(C) n+12
(D) n+60
(E) n+15
Rationale: If n is divisible by 3, 5 and 12 it must a multiple of the lcm of 3, 5 and 12 which is 60.
n=60k
n + 60 is also divisible by 60 since
n + 60 = 60 k + 60 = 60(k + 1)
The answer is D.
Answer: (D) n+60
Question: If it is 6:12 in the evening on a certain day, what time in the morning was it exactly 1,440,711 minutes earlier? (Assume standard time in one location.)
(A) 6:12
(B) 6:15
(C) 6:18
(D) 6:21
(E) 6:24
Rationale: 6:12 minus 1,440,711 must end with 1, the only answer choice which ends with 1 is D.
Answer: D.
Answer: (D) 6:21
Question: x^2-y^2= 16 and 2. xy=4 so find out x+y=? tell that both statement are required to find out the value of x+Y
(A) 6
(B) 7
(C) 8
(D) 9
(E) 5
Rationale: x^2-y^2= 16 = 25-9 =5^2-3^2
=> (x+y)*(x-y)=(5+3)*(5-3)
=> (x+y)=(5+3)=8
ANSWER:C
Answer: (C) 8
Question: A number increased by 20% gives 480. The number is
(A) 250
(B) 400
(C) 450
(D) 500
(E) 520
Rationale: Formula = TOTAL=100% ,INCRESE = "+" DECREASE= "-"
A number means = 100 %
That same number increased by 20 % = 120 %
120 % -------> 480 (120 × 4 = 480)
100 % -------> 400 (100 × 4 = 400)
B)
Answer: (B) 400
Question: n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4 ?
(A) 6
(B) 3
(C) 2
(D) 1
(E) 8
Rationale: Let n=4q+3.Then, 2n=8q+6=4(2q+1)+2.
Thus when 2n is divided by 4, the remainder is 2.
Answer is C
Answer: (C) 2
Question: A company has two models of computers, model P and model Q. Operating at a constant rate, a model P computer can complete a certain task in 12 minutes and a model Q computer can complete the same task in 6 minutes. If the company used the same number of each model of computer to complete the task in 1 minute, how many model P computers were used?
(A) 3
(B) 4
(C) 1
(D) 5
(E) 6
Rationale: Let's say 1 work is processing 12 gb of data.
Model P : 1 gb per min
Model Q : 2 gb per min
Working together, 1 P and 1 Q = 3 gb per min
So, 4 times as many computers would work at 12 gb per min.
So no. of P = 4
Answer is B
Answer: (B) 4
Question: The area of a triangle will be when a = 1m, b = 2m, c = 3m, a, b, c being lengths of respective sides?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: S = (1 + 2 + 3)/2 = 3
=> No triangle exists
Answer: A
Answer: (A) 3
Question: mr. depak has $459,774 in his bank account. What is the least amount of money (in whole number of dollars) that he must add to his account if he wants to split this money evenly among her six best friends?
Options:
(A) $0
(B) $2
(C) $3
(D) $4
(E) $6
Rationale: To find the least amount deepak should add to his saving account to split the money evenly among his 6 best friends,
he needs to make the total divisible by 6
Simply add the individual digits of the total = 4+5+9+7+7+4 = 36
If you add 0 , the number is divisible by 6 (36+ 0)
Correct Option : A
Answer: (A) $0
Question: A person standing on a railway platform noticed that a train took 21 seconds to completely pass through the platform which was 84m long and it took 9 seconds in passing him.Find the speed of the train?
(A) 6m/sec
(B) 5m/sec
(C) 12m/sec
(D) 7m/sec
(E) None
Rationale: Let the length of the train be x m.
then, then train covers x meters in 9 seconds and (x+84)m in 21 seconds.
Therefore, x/9=(x+84)/21 =63m
So, the length of the train=63m
Speed of the train=63/9=7m/sec
Answer: Option D
Answer: (D) 7m/sec
Question: If A is a positive integer, which of the following must be odd?
(A) A+1
(B) A^2+A
(C) A^2+A+1
(D) x^2−1
(E) 3x^2−3
Rationale: A. A+1 = can be odd or even. Since O + O =E or E + O = O
B. A^2 + A = A(A+1). Since from the above derivation we already know the term A+1 can be Odd or Even, directly substitute here. A(ODD) = Even (When A is Even) or A(EVEN) = EVEN [When A is ODD]
C. Here's the answer. Since we know the term A^2 + A can always take a EVEN number, EVEN + 1 = ODD
Hence C.
Answer: (C) A^2+A+1
Question: 6, 11, 21, 36, 56, 81, 111, 146, 186, 231 ?
(A) 511
(B) 711
(C) 811
(D) 611
(E) 281
Rationale: The pattern is + 5, + 10, + 15, + 20, + 25, + 30, + 35, + 40, + 45, + 50,....
Answer : E.
Answer: (E) 281
Question: How many different four letter words can be formed (the words need not be meaningful) using the letters of the word MEDITERRANEAN such that the first letter is E and the last letter is R?
(A) 59
(B) 11!/(2!*2!*2!)
(C) 56
(D) 23
(E) 11!/(3!*2!*2!*2!)
Rationale: Available letters:
M E D I T R A N (8 letters)
E _ _ R
We have 1 combination for E and 1 combination for R, and also we have 8 combinations for the 2nd letter and 7 combinations for the last letter, so:
E 8 7 R = 1 * 8 * 7 * 1 = 56
ANSWER:C
Answer: (C) 56
Question: George has 8 candies in a bag, 3 of which are sweet while the other 5 are sour. He pulls out 2 of the candies simultaneously, and at random. What is the probability that exactly one of the candies he picked is sour?
(A) 2/8
(B) 3/15
(C) 2/28
(D) 3/5
(E) 15/28
Rationale: The probability is equal to the number of desired choices divided by the total number of possibilities.
Probability = Favorable/Total
Total = 8C2 = 8*7/2 = 28
Favorable:
Pick 1 sour out of 3 sour
AND
pick 1 sweet out of 5 sweet.
3C1*5C1=3*5=15
P=15/28
When you use combination method, it is picking all possible cases and the order doesn't matter. Whereas, upon choosing probability method to solve, order matters.
Thus,
Total Probability:
Probability of choosing sour candy first AND Probability of choosing sweet candy
OR
Probability of choosing sweet candy first AND Probability of choosing sour candy
Answer: E
Answer: (E) 15/28
Question: A train crosses a platform of 150 m in 15 sec, same train crosses another platform of length 250 m in 20 sec. then find the length of the train?
(A) 150
(B) 788
(C) 267
(D) 266
(E) 123
Rationale: Length of the train be ‘X’
X + 150/15 = X + 250/20
4X + 600 = 3X + 750
X = 150m
Answer:A
Answer: (A) 150
Question: A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 21 hrs and a machine of type S does the same job in 42 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Rationale: Type R completes 1/21 of the job each hour.
Type S completes 1/42 of the job each hour.
Together R and S complete 1/21 +1/42 = 1/14 of the job each hour.
Let n be the number of each type of machine.
2*n*(1/14) = 1 job completed
n = 7
The answer is B.
Answer: (B) 7
Question: A cow was standing on a bridge, 5m away from the middle of the bridge. A train was coming towards the bridge from the end nearest to the cow. Seeing this cow ran towards the train and managed to escape when the train was 2m away from the bridge. If it had run in opposite direction(i.e away from the train) it would have been hit by the train 2m before the end of the bridge. What is the length of bridge in meters assuming speed of the train is 4 times that of the cow.
(A) 32
(B) 36
(C) 40
(D) 44
(E) 50
Rationale: Explanation :
Explation:
Let length of bridge is X
then middle of bridge is X/2.
and Cow is standing at X/2-5 from the end so
After seeing the train it would run opposite direction and cover distance of X/2-5 when the train is 2m away from other side.
So, the bridge from one side to cow is {(X/2-5)+(X/2-5)}=X-10
so remaining distance is 10m
the cow is hit before 2m i.e cow covers 8m and train will cover 32 m.
Answer : A
Answer: (A) 32
Question: A fort had provision of food for 150 men for 30 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is:
(A) 29 1/5
(B) 24
(C) 42
(D) 54
(E) 48
Rationale: After 10 days : 150 men had food for 20 days.
Suppose 125 men had food for x days.
Now, Less men, More days (Indirect Proportion)
Therefore 125 : 150 :: 20 : x <=> 125 x x = 150 x 20
=> x =150 x 20/125
=> x = 24.
Correct answer is B
Answer: (B) 24
Question: The number of diagonals of a polygon of n sides is given by the formula q=n(n-3)/2. If a polygon has twice as many diagonals as sides, how many sides does it have?
(A)  3
(B)  5
(C)  6
(D)  7
(E)  8
Rationale: q=n(n-3)
q=2*n
2n=n(n-3)
=>2=n-3
=>n=5
Answer B
Answer: (B)  5
Question: Rs. 6000 is lent out in two parts. One part is lent at 4% p.a simple interest and the other is lent at 10% p.a simple interest. The total interest at the end of one year was Rs. 450. Find the ratio of the amounts lent at the lower rate and higher rate of interest?
(A) 5:1
(B) 5:5
(C) 5:7
(D) 5:4
(E) 5:2
Rationale: Let the amount lent at 4% be Rs. x
Amount lent at 10% is Rs. (6000 - x)
Total interest for one year on the two sums lent
= 4/100 x + 10/100 (6000 - x) = 600 - 3x/50
=> 600 - 3/50 x = 450 => x = 2500
Amount lent at 10% = 3500
Required ratio = 2500 : 3500 = 5:7
Answer:C
Answer: (C) 5:7
Question: What number comes next in the following number series? 12, 50, 202, 810, 3242, _____
(A) 12400
(B) 12800
(C) 12970
(D) 13015
(E) 16000
Rationale: 1212 × 4 + 2 = 5050 × 4 + 2 = 202202 × 4 + 2 = 810810 × 4 + 2 = 32423242 × 4 + 2 = 12970 C
Answer: (C) 12970
Question: A family I know has several children. Each boy in this family has as many sisters as brothers but each girl has twice as many brothers as sisters. How many brothers and sisters are there?
(A) 4 brothers and 2 sisters
(B) 4 brothers and 3 sisters
(C) 3 brothers and 3 sisters
(D) 4 brothers and 5 sisters
(E) 4 brothers and 6 sisters
Rationale: let no. of girls=g n boys=b
b=g+1 ..........(i) as each boy have equal no. of sisters and brothers and he is not included in brothers.so,1 is for him in g+1.
now ,
b=2(g-1)........(ii) as each girl have g-1 sisters.
solving (i) and(ii) we get g=3 and b=4
ANSWER:B
Answer: (B) 4 brothers and 3 sisters
Question: The ages of Old and Young total 48. Old is twice as old as Young was when Old was half as old as Young will be when Young is three times as Old was when Old was three times as old as Young. How old is Old?
(A) 23
(B) 27
(C) 12
(D) 43
(E) 37
Rationale: Explanation:
From the options itself,we can see that option c
old = 30
young = 18
30 + 18 = 48
By reducing this years only by one
Before 6years
old = 24 (half of young)
young = 12 (twice of old)
Answer: C
Answer: (C) 12
Question: In a sports club with 80 members, 48 play badminton and 46 play tennis and 7 do not play either. How many members play both badminton and tennis?
(A) 23
(B) 21
(C) 20
(D) 26
(E) 27
Rationale: 48+46=94
but where as total number is 80-7=73
therefore answer is 94-73=21
Hence Answer is B
Answer: (B) 21
Question: he population of a city is 110,000. If it increases at the rate of 6% per annum, then what will be its population 2 years hence?
(A) 123596
(B) 1237723
(C) 123776
(D) 123728
(E) 123718
Rationale: Population after n years = P [1 + (R/100)]2
Population after 2 years = 110000 * [1 + 6/100]2 = (110000 x 53/50 x 53/50) = 123596
ANSWER: A
Answer: (A) 123596
Question: Combine terms: 6a + 26b -4b – 16a.
(A) 4a + 22b
(B) -28a + 30b
(C) -10a + 22b
(D) 28a + 30b
(E) 5a + 30b
Rationale: Solution:
6a + 26b -4b – 16a.
= 6a – 16a + 26b – 4b.
= -10a + 22b.
Answer: (C)
Answer: (C) -10a + 22b
Question: Saturn travels around the Sun at an approximate speed of 5.82 miles per second. This speed is how many kilometers per hour? (1 km = 0.6 miles)
(A) 30,560
(B) 31,650
(C) 32,740
(D) 33,830
(E) 34,920
Rationale: The speed is 5.82 miles/s. Then 5.82/0.6 = 9.7 km/s
9.7*3600 = 34,920 kph
The answer is E.
Answer: (E) 34,920
Question: A sum of money is sufficient to pay A's wages for 21 days and B's wages for 28 days. The same money is sufficient to pay the wages of both for?
(A) 10 days
(B) 12 days
(C) 15 days
(D) 20 days
(E) 18 days
Rationale: Let the total money be $x
A's 1 day work = $ x/21
B's 1 day work = $ x/28
A+B 1 day work = $ x/12
The money is sufficient to pay the wages of both for 12 days
Answer is B
Answer: (B) 12 days
Question: The bear alarm at Grizzly’s Peak ski resort sounds an average of once every thirty days, but the alarm is so sensitively calibrated that it sounds an average of ten false alarms for every undetected bear. Despite this, the alarm only sounds for three out of four bears that actually appear at the resort. If the alarm sounds, what is the probability that a bear has actually been sighted?
(A)  1/4
(B)  3/13
(C)  27/52
(D)  3/4
(E)  10/13
Rationale: How many times the alarm goes off --> 10 false + 3 true
How many of these alarms are true --> 3 true alarms
Therefore, p = true alarms/total alarms = 3/13
Or, we can calculate the p (of alarm sounding but no bear detected, i.e. false alarm),
10 times when the alarm goes off - no bear is seen
13 times in all the alarm goes off
So, 10/13 is the p that alarm is a false alarm
Subtracting 10/13 from 1 is the p that it's a true alarm --> (1-10/13) = 3/13....Answer B
Answer: (B)  3/13
Question: Find the number, when 15 is subtracted from 7 times the number, the result is 10 more than twice of the number
(A) 5
(B) 15
(C) 7.5
(D) 4
(E) 3
Rationale: Explanation:
Let the number be x.
7x -15 = 2x + 10 => 5x = 25 => x = 5
Option A
Answer: (A) 5
Question: What is the remainder when 980*1050*880*1010 is divided by 22?
(A) 15
(B) 10
(C) 12
(D) 8
(E) 3
Rationale: OA is 'C'.
OE:
take the remainder from each of 980/22, 1050/22 and so on..
980/22 gives remainder = 12
1050/22 gives remainder = 16
880/22 gives remainder = 0
1010/22 gives remainder = 20
the net remainder is the product of above individual remainders. i.e = 12*16*0*20
break them into pairs 12*16/22 gives remainder 16
and 0*20/22 gives remainder 20
so 16*20/22 gives remainder 12.
Answer: C
Answer: (C) 12
Question: If a person walks at 14 km/hr instead of 10 km/hr, he would have walked 20 km more. What is the actual distance travelled by him?
(A) 50
(B) 60
(C) 40
(D) 30
(E) 25
Rationale: Speed = x/10---1
x+20 km if travelled at 14 km/hr
speed = x+20/14---2
from 1 & 2
x = 50
ANSWER A
Answer: (A) 50