mathewhe/aqua_rat huggingface dataset:
Question: z is a positive integer and multiple of 2; w = 4^z, what is the remainder when w is divided by 10?
(A) 10
(B) 6
(C) 4
(D) 0
(E) It Cannot Be Determined
Rationale: It is essential to recognize that the remainder when an integer is divided by 10 is simply the units digit of that integer. To help see this, consider the following examples:
4/10 is 0 with a remainder of 4
14/10 is 1 with a remainder of 4
5/10 is 0 with a remainder of 5
105/10 is 10 with a remainder of 5
It is also essential to remember that the z is a positive integer and multiple of 2. Any integer that is a multiple of 2 is an even number. So, z must be a positive even integer.
With these two observations, the question can be simplified to:what is the units digit of 4 raised to an even positive integer?
The units digit of 4 raised to an integer follows a specific repeating pattern:
4^1 = 4
4^2 = 16
4^3 = 64
4^4 = 256
4^(odd number) --> units digit of 4
4^(even number) --> units digit of 6
There is a clear pattern regarding the units digit. 4 raised to any odd integer has a units digit of 4 while 4 raised to any even integer has a units digit of 6.
Since z must be an even integer, the units digit of w=4^z will always be 6. Consequently, the remainder when w=4^z is divided by 10 will always be 6.
In case this is too theoretical, consider the following examples:
z=2 --> w=4^z=16 --> w/10 = 1 with a remainder of 6
z=4 --> w=4^z=256 -->w/10 = 25 with a remainder of 6
z=6 --> w=4^z=4096 --> w/10 = 409 with a remainder of 6
z=8 --> w=4^z=65536 --> w/10 = 6553 with a remainder of 6
Answer: B.
Answer: (B) 6
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) 37 min
(B) 55 min
(C) 47 min
(D) 67 min
(E) 49 min
Rationale: E
49 min
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) 49 min
Question: In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 12 percent of revenues. The profits in 2009 were what percent of the profits in 2008?
(A) 96%
(B) 105%
(C) 120%
(D) 124.2%
(E) 138%
Rationale: x = profits
r= revenue
x/r = 0,1
x= 10
r=100
2009:
r=80
x/80 = 0,12 = 12/100
x= 80*12/100
x= 9.6
9.6/10 = 0.96 = 96%, Answer A
Answer: (A) 96%
Question: Which of the following fractions is the largest?
(A) 7/8
(B) 7/7
(C) 7/2
(D) 7/5
(E) 7/6
Rationale: L.C.M of 8, 16, 40 and 80 = 80.
7/8 = 70/80; 13/16 = 65/80; 31/40 = 62/80
Since, 70/80 > 63/80 > 65/80 > 62/80,
So, 7/8 > 63/80 > 13/16 > 31/40
So, 7/8 is the largest.
Answer: A
Answer: (A) 7/8
Question: The value of ((x – y)³ + (y - z)³ + (z – x)³)/(15 (x – y) (y – z) (z – x))
is equal to :
(A) 0
(B) 1/12
(C) 1
(D) 1/5
(E) 1/3
Rationale: Since (x – y) + (y – z) + (z – x) = 0,
so (x – y)³ + (y – z)³ + (z – x)³= 3 (x – y) (y – z) (z – x).
(3 (x – y) (y – z) (z – x))/(15(x – y) (y – z) (z – x)) = 1/5.
ANSWER:D
Answer: (D) 1/5
Question: A crate of apples contains 1 bruised apple for every 20 apples in the crate. Three out of every 4 bruised apples are considered not fit to sell, and every apple that is not fit to sell is bruised. If there are 12 apples not fit to sell in the crate, how many apples are there in the crate?
(A) 270
(B) 360
(C) 480
(D) 600
(E) 320
Rationale: as given 3 out of every 4 bruised apple is not fit to sell
or, 75% of the bruised apples are not fit to sell.
as per the question 12 are not fit to sell
or,
0.75x=12
x=1200/75=16
thus total number of bruised apples =16
total number of apples =20*16=320
Answer: E
Answer: (E) 320
Question: If x = y+3+4.5x and y = x+33, what is the value of x/y ?
(A) -6/5.
(B) -8/25
(C) 1/4.
(D) 5/6.
(E) 1.5.
Rationale: (1) x = y + 3 + 4.5x
Substitute y for y = x + 33 (Eq. we are given)
x = x + 33 + 3 + 4.5x
Combine like terms
x = 5.5x +36 --> -4.5x = 36 --> x = -8
(2) y = x + 18
Substitute x for x = -8
y = (-8) + 33 = 25
(3) x/y = ?
Substitute x and y we found above
x/y = (-8) / (25) =-8/25
My answer: B
Answer: (B) -8/25
Question: Working alone at its constant rate, machine K took 3 hours to produce 1/6 of the units produced last Friday. Then machine M started working and the two machines, working simultaneously at their respective constant rates, took 6 hours to produce the rest of the units produced last Friday. How many hours would it have taken machine M, working alone at its constant rate, to produce all of the units produced last Friday?
(A) 8
(B) 12
(C) 16
(D) 24
(E) 30
Rationale: Machine K works at a rate of 1/18 of the units per hour.
The rate of K + M together is 5/6 * 1/6 = 5/36 of the units per hour.
The rate of machine M is 5/36 - 1/18 = 1/12.
It would have taken machine M a total time of 12 hours.
The answer is B.
Answer: (B) 12
Question: If y ≠ 3 and 2b/y is a prime integer greater than 2, which of the following must be true?
I. b = y
II. y = 1
III. b and y are prime integers.
(A)  None
(B)  I only
(C)  II only
(D)  III only
(E)  I and II
Rationale: Note that we are asked which of the following MUST be true, not COULD be true. For such kind of questions if you can prove that a statement is NOT true for one particular set of numbers, it will mean that this statement is not always true and hence not a correct answer.
So we should try to make the listed statements not true for some b and y (which satisfy y≠3 and 2b/y=prime>2).
I. b = y --> not necessarily true: b=3 and y=2 (2b/y=3=prime>2);
II. y=1 --> not necessarily true: b=3 and y=2 (2b/y=3=prime>2);
III. b and y are prime integers --> not necessarily true: b=10 and y=4 (2b/y=5=prime>2).
Answer: A.
Answer: (A)  None
Question: Let S be the set of all positive integers that, when divided by 8, have a remainder of 5. What is the 72th number in this set?
(A)  573
(B)  608
(C)  613
(D)  616
(E)  621
Rationale: The set S = {5, 13, 21, 29, ..................... }
1st Number = 8 * 0 + 5 = 5
2nd Number = 8 * 1 + 5 = 13
3rd Number = 8 * 2 + 5 = 21
72th Number = 8 * (72-1) + 5 = 573
Answer = A
Answer: (A)  573
Question: what is the compound interest on rs:80,000 for 4 months at the rate of 5% per annum
(A) 1341.69
(B) 1342.69
(C) 1343.69
(D) 1344.69
(E) 1345.69
Rationale: it is monthly compound
rate=5/12% per month
80000*(1+5/1200)^4-80000=1341.69
ANSWER:A
Answer: (A) 1341.69
Question: The length of the bridge, which a train 130 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
(A) m
(B) m
(C) m
(D) m
(E) m
Rationale: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (130 + X)/30 = 25/2 ==> 2(130 + X) = 750 ==> X
= 245 m.
Answer:C
Answer: (C) m
Question: What is the least number that should be added to 1077, so the sum of the number is divisible by 23?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: (1077 / 23) gives a remainder 19 so we need to add 4.
The answer is D.
Answer: (D) 4
Question: Tough and Tricky questions: Number Properties.
What is the smallest positive integer x such that 500x is the cube of a positive integer?
(A) 2
(B) 3
(C) 5
(D) 10
(E) 15
Rationale: We want to know the smallest x that will make 500x a CUBE of some number. Let's call that number y.
Let's first figure out what we're working with. The prime factorization of 500 can be visualized:
...........500
......../.......\
......50.......10
...../..\....../...\
...25...2...2.....5
.../..\
..5....5
So, we have 5 * 5 * 5 * 2 * 2 that can be multiplied together to get 500. Now we need to figure out what we need to make 450 * x into a cube of y (y^3=500*x).
We have two 5s, two 3s, and one 2. To arrange these numbers in identical sets (2,5), we need at least one more 2. Each of these numbers will give us the value of y (2*5=10), which, multiplied by itself three times, gives us 500 * x.
Looking at the factors we need to complete the sets, we get x= 2. We know this is the smallest number possible because prime factors by definition cannot be broken down any further.
Therefore, we can go with answer choice A.
If time permits, we can do a sanity check. We calculated that y should be 2 * 5, or 10. 10 * 10 * 10 = 1000. Also, 500 * 2 = 1000.
Answer: (A) 2
Question: Profits in the partnership of Bess, Bill and Bob are shared in the ratio 1 : 2 : 3. If Bill's share of the profits is $300, what is Bob's share?
(A) $150
(B) $900
(C) $600
(D) $450
(E) None
Rationale: Ans is D
Given profit ratio, Bess : Bill : Bob = 1 : 2 : 3 To make Bill's portion $300, multiply by $150 => Bess : Bill : Bob = $150 : $300 : $450 => Bob's share = $450
Answer: (B) $900
Question: A, B and C enter into a partnership and theirs shares are in the ratio 1/2 : 1/3 : 1/4. After two months, A withdraws half of his capital and after 10 months, a profit of Rs.378 is divided among them. What is B’s share?
(A) Rs.129
(B) Rs.144
(C) Rs.156
(D) Rs.168
(E) Rs.178
Rationale: Ratio of initial investments = 1/2 : 1/3 : 1/4 = 6 : 4 : 3.
Let their initial investments be 6x, 2x and 3x respectively.
A : B : C = (6x * 2 + 3x * 10) : (4x * 12) : (3x * 12) = 42 : 48 : 36 = 7 : 8 : 6.
Therefore, B’s share = Rs. 378 * 8/21
= Rs.144.
ANSWER:B
Answer: (B) Rs.144
Question: A certain sum amounts to Rs.7350 in 2 years and to Rs.8575 in 3 years.find the sum and rate percent
(A) 3488
(B) 7789
(C) 5400
(D) 2887
(E) 1881
Rationale: Explanation:
Interest for 1 year is the same whether it's simple interest or the compound interest.
Now interest of third year = 8575 - 7350 = 1225; means principal for this interest is 7350 if comound interest is takenIf 7350 is the principal interest = 1225
if 100 is the principal interest =(1225/7350) * 100 = 50/3 %
When a thing increases for two successive times the overall increase on initial amount = a + b + (a * b)/100
Therefore overall interest for two years = 50/3 + 50/3 + [(50/3)*(50/3)]/100 = 325/9 %
Therefore amount after 2 years = 100 + 325/9 = 1225/9
If 1225/9 is the amount principal =100
if 7350 is the amount principal =(900/1225)*7350 =5400
So sum = 5400; Rate = 50/3 %
Answer: C) 5400
Answer: (C) 5400
Question: Look at this series: 3, 1, (1/3), (1/9),... What number should come next?
(A) 1/27
(B) 1/18
(C) 1/61
(D) 2/27
(E) None
Rationale: Explanation: This is a simple division series; each number is divisible by 3 of the previous number. In other terms to say, the number is divisible by 3 successively to get the next result.
9/3 = 3
3/3 = 1
1/3 = 1/3
(1/3)/3 = 1/9
(1/9)/3 = 1/27 and so on.
Answer: Option A
Answer: (A) 1/27
Question: A rectangular photograph is surrounded by a border that is 1 inch wide on each side. The total area of the photograph and the border is M square inches. If the border had been 3 inches wide on each side, the total area would have been (M + 52) square inches. What is the perimeter of the photograph, in inches?
(A) 10
(B) 36
(C) 38
(D) 40
(E) 42
Rationale: Let Length and Breadth of photograph be L and B respectively.
Perimeter is given by 2*(L+b) -----(1)
According to the question:
(L+2)(B+2) = m ----(2)
and
(L+6)(B+6) = m + 52 ---------> (L+6)(B+6) - 52 = m ------(3)
Equating (2) and (3)
(L+2)(B+2) = (L+6)(B+6) - 52
LB + 2L + 2B + 4 = LB + 6L + 6B + 36 -52
Simplify
4L + 4B = 20 ------> 2(L+B) = 10 (Check eq (1))
Answer is A
Answer: (A) 10
Question: 8, 19, 30, 41, 52, ….
Given the sequence above, what is the sum of the 15th and the 20th terms?
(A) 324
(B) 335
(C) 346
(D) 357
(E) 379
Rationale: The first term is 8 = 11 – 3. The second term is 19 = 22 – 3, the third term is 30 = 3 × 11 – 3, the fourth term is 41 = 4 × 11 – 3, etc.
Thus, 11n – 3 describes the values in the sequence where n is the number of the term.
The 15th term is 15 × 11 – 3 = 162
The 20th term is 20 × 11 – 3 = 220 – 3 = 217.
The sum of these two values is 376
The correct answer is choice (E).
Answer: (E) 379
Question: Three numbers are in the ratio 1 : 2 : 3 and their H.C.F is 12. The numbers are
(A) 12, 24, 30
(B) 12, 24, 38
(C) 12, 24, 362
(D) 12, 24, 36
(E) 12, 24, 321
Rationale: Explanation:
Let the required numbers be x, 2x, 3x. Then, their H.C.F =x. so, x= 12
\inline \fn_jvn \therefore The numbers are 12, 24, 36
Answer: D) 12, 24, 36
Answer: (D) 12, 24, 36
Question: How many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3 and 4, if repetition of digits is allowed?
(A) 376
(B) 377
(C) 236
(D) 228
(E) 212
Rationale: The smallest number in the series is 1000, a 4-digit number.
The largest number in the series is 4000, the only 4-digit number to start with 4.
The left most digit (thousands place) of each of the 4 digit numbers other than 4000 can take one of the 3 values 1 or 2 or 3.
The next 3 digits (hundreds, tens and units place) can take any of the 5 values 0 or 1 or 2 or 3 or 4.
Hence, there are 3 x 5 x 5 x 5 or 375 numbers from 1000 to 3999.
Including 4000, there will be 376 such numbers.
Answer: A
Answer: (A) 376
Question: A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is
(A) 7/19
(B) 7/18
(C) 7/12
(D) 7/19
(E) 7/15
Rationale: Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways.
Similarly from eight white balls two can be drawn in ⁸C₂ ways.
P = 7C2/`5C2 + 8C2/15C2
= 7/15
Answer: E
Answer: (E) 7/15
Question: 78, 64, 48, 30, 10, (...)
(A) -12
(B) -14
(C) 2
(D) 8
(E) 6
Rationale: Explanation :
78 - 14 = 64
64 - 16 = 48
48 - 18 = 30
30 - 20 = 10
10 - 22 = -12
Answer : Option A
Answer: (A) -12
Question: According to the direction on a can of frozen orange juice concentrate is to be mixed with 3 cans of water to make orange juice . How many 10 - ounce cans of the concentrate are required to prepare 200 6-ounce servings of orange juice?
(A) 25
(B) 30
(C) 50
(D) 67
(E) 100
Rationale: Orange juice concentrate: water::1:3
total quantity of orange juice = 200*6 = 1200 oz
so Orange juice concentrate: water :: 300 oz:900 oz
no. of 10 oz can = 300 oz/10 oz = 30
Answer B, 30 cans
Answer: (B) 30
Question: The ratio of sum of squares of first n natural numbers to square of sum of first n natural numbers is 17:325. the value of n is
(A) 15
(B) n=25
(C) 35
(D) 30
(E) none of these
Rationale: sum of 1st n natural no.s is n(n+1)/2,
sum of sqaures of 1st n natural no.s is n(n+1)(2n+1)/6,
The ratio of sum of squares of first n natural numbers to square of sum of first n natural numbers=n(n+1)(2n+1)*2*2/(n*n*(n+1)*(n+1))
=2(2n+1)/(3n(n+1))
now by hit and trial for the given options,if we put 25 then this will give 17/325
therefore the answer is 25
ANSWER:B
Answer: (B) n=25
Question: An office supply store stocks two sizes of notebooks, each in five colors: blue, green, yellow, red, or pink. The store packs the notebooks in packages that contain either 4 notebooks of the same size and the same color or 4 notebooks of the same size and of 4 different colors. If the order in which the colors are packed is not considered, how many different packages of the types described above are possible?
(A) 10
(B) 12
(C) 20
(D) 24
(E) 28
Rationale: First let's consider the small notebooks.
There are 5 ways to choose notebooks of the same color.
The number of ways to choose four notebooks with different colors is 5C4=5.
There are 10 different packages we can make with the small notebooks.
We can use the same process to find 10 different packages with large notebooks.
The total number of different packages is 20.
The answer is C.
Answer: (C) 20
Question: How many pieces of 0.85 meteres can be cut from a rod 42.5 meteres long
(A) 30
(B) 40
(C) 50
(D) 60
(E) 70
Rationale: Explanation:
We need so simple divide 42.5/0.85,
=(4250/85) = 50
Option C
Answer: (C) 50
Question: What is 120% of 13/24 of 360?
(A) 52
(B) 117
(C) 234
(D) 312
(E) 576
Rationale: 120% * 13/24 * 360 = 1.2 * 13 * 15 = 234
The answer is C.
Answer: (C) 234
Question: How many odd numbers between 10 and 1,000 are the squares of integers?
(A) 12
(B) 13
(C) 14
(D) 15
(E) 16
Rationale: The square of an odd number is an odd number:
10 < odd < 1,000
10 < odd^2 < 1,000
3.something < odd < 31.something (by taking the square root).
So, that odd number could be any odd number from 5 to 31, inclusive: 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, and 31.
14 numbers.
Answer: C.
Answer: (C) 14
Question: Two trains each 150m in length each, are running on two parallel lines in opposite directions. If one goes at the speed of 95km/h while the other travels at 85km/h. how long will it take for them to pass each other completely.
(A) 25 sec
(B) 23 sec
(C) 34 sec
(D) 22 sec
(E) 6 sec
Rationale: Explanation:
D = 150 m + 150 m = 300 m
RS = 95 + 85 = 180 * 5/18 = 50
T = 300 * 1/50 = 6 sec
Answer: Option E
Answer: (E) 6 sec
Question: The duplicate ratio of 6:4 is?
(A) 1:2
(B) 9:4
(C) 1:8
(D) 1:18
(E) 1:13
Rationale: 36^2: 4^2 = 36:16=9:4
ANSWER:B
Answer: (B) 9:4
Question: A leak in the bottom of a tank can empty the full tank in 6 hours. An inlet pipe fills water at the rate of 4 liters per minute. When the tank is full in inlet is opened and due to the leak the tank is empties in 8 hours. The capacity of the tank is?
(A) 2877
(B) 5760
(C) 1797
(D) 1797
(E) 2972
Rationale: Explanation:
1/x - 1/6 = -1/8
x = 24 hrs
24 * 60 * 4 = 5760
Answer:B
Answer: (B) 5760
Question: A clothing store originally bought 100 jackets at a total cost of j dollars. If each jacket was sold for 50 percent more than its original cost, what was the individual price, in terms of j, of each jacket sold?
(A) j/67
(B) 7j/500
(C) 140j
(D) j/100+40
(E) 140j/100
Rationale: lets take j=1000, as decided by you..
now 50% increase makes it 1500..
this is the price for 100 jackets, so selling price for each jacket=1500/100=$15..
=j/67
so ans is correct as A..
Answer: (A) j/67
Question: Three unbiased coins are tossed, what is the probability of getting at least 2 tails ?
(A) 1/5
(B) 1/7
(C) 1/8
(D) 1/2
(E) 1/10
Rationale: Total cases are = 2^3=8
favoured cases =[TTH,THT,HTT,TTT]=4
Probability = 4/8=1/2
ANSWER D
Answer: (D) 1/2
Question: The diameter of the driving wheel of a bus in 140 cm. How many revolutions per minute must the wheel make in order to keep a speed of 14 kmph?
(A) 53.03
(B) 50.01
(C) 23.23
(D) 24.23
(E) 41.23
Rationale: distance covered in 1 min=(14*1000)/60=233.33m
circumference of the wheel=(2*(22/7)*.70)=4.4m
no of revolution per min=233.33/4.4=53.03
ANSWER:A
Answer: (A) 53.03
Question: Find number which is 70% less than 80.
(A) 18
(B) 22
(C) 24
(D) 26
(E) 98
Rationale: Explanation:
70% less is 30% of the given number
Therefore, 30% of 80 is 24.
ANSWER: C
Answer: (C) 24
Question: In a BCCI meeting there are ten people. All shake hands with each other once. How many handshakes will be there altogether?
(A) 38
(B) 676
(C) 278
(D) 28
(E) 21
Rationale: Answer:B
Answer: (B) 676
Question: A can do a piece of work in 10 days and B can do the same work in 12 days. A and B worked together for 2 days. How many more days are required to complete the remaining work if they work together?
(A) 3 (5/18)
(B) 3 (5/16)
(C) 3 (5/11)
(D) 3 (5/13)
(E) 3 (5/21)
Rationale: A can do 1/10 of the work in a day.
B can do 1/12 of the work in a 1 day.
Both of them together can do (1/10 + 1/12) part of work in 1 day = (6 + 5)/60 = 11/60
They take 60/11 days to complete the work together.
Given that they already worked for 2 days.
The number of days required to complete remaining work => 60/11 - 2 = 38/11 = 3 (5/11) days.
Answer:C
Answer: (C) 3 (5/11)
Question: The sum of money at compound interest amounts to thrice itself in 2 years. In how many years will it be 6 times itself?
(A) 8 years
(B) 9 years
(C) 2 years
(D) 6 years
(E) 4 years
Rationale: 100 ---- 300 --- 2
600 --- 2
----
4 years
Answer: E
Answer: (E) 4 years
Question: Three pounds of 05 grass seed contain 1 percent herbicide. A different type of grass seed, 20, which contains 20 percent herbicide, will be mixed with three pounds of 05 grass seed. How much grass seed of type 20 should be added to the three pounds of 05 grass seed so that the mixture contains 15 percent herbicide?
(A) 3
(B) 3.75
(C) 4.5
(D) 8.4
(E) 9
Rationale: 05 grass seed contains 5% herbicide and its amount is 3 pound
20 grass seed contains 20% herbicide and its amount is x
when these two types of grass seeds are mixed, their average becomes 15%
thus we have
3(1)+x(20)/(x+3) = 15
3+20x=15x +45
5x=42
or x=8.4
D
Answer: (D) 8.4
Question: One night 17 percent of the female officers on a police force were on duty. If 204 police officers were on duty that night and half of these were female officers, how many female officers were on the police force?
(A) 420
(B) 480
(C) 540
(D) 600
(E) 660
Rationale: Let x be the number of female police officers on the police force.
The number of female police officers on duty was 102.
0.17x = 102
x = 600
The answer is D.
Answer: (D) 600
Question: The blood groups of 100 people is distributed as follows: 15 have type A blood, 20 have B blood type, 60 have O blood type and 5 have type AB blood. If a person from this group is selected at random, what is the probability that this person has AB blood type?
(A) 0.4
(B) 0.5
(C) 0.05
(D) 0.1
(E) 0.01
Rationale: Blood group -	frequency
A	- 15
B	- 20
O	- 60
AB	- 5
Let P(E) be the event of getting AB blood group
P(E) = Frequency for AB blood group / Total frequencies in the above table
= 5 / (5+60+20+15)
= 5 / 100
= 0.05
My answer is (C)
Answer: (C) 0.05
Question: A traveler changes 150 pounds into rupees at the rate of Rs. 7000 for 100 pounds. He spends Rs. 9060 and changes the remaining amount back to pounds at the rate of 100 pounds to Rs. 7200. How many pounds will he get?
(A) 18 pounds
(B) 20 pounds
(C) 25 pounds
(D) 30 pounds
(E) None of these
Rationale: Explanation:
Amount of rupees for exchange of 150 pounds = (150/100)*(7000/1) = Rs. 10,500
Out of these Rs.10,500, traveler spent Rs. 9060
Remaining balance in rupees = 10,500 – 9060 = Rs. 1440
Now these Rs. 1440 are exchanged back to pounds with the rate of 100 pounds for Rs. 7200
Amount in pounds = (1440 * 100) / 7200 = 20 pounds
ANSWER: B
Answer: (B) 20 pounds
Question: Bill downloads the movieRevenge of the Avengersto his computer in 2.5 hours, using a download manager that downloads from 3 sources marked A, B and C. Each source provides download at a constant rate, but the rates of different sources are not necessarily identical. If the movie was downloaded from sources A and C alone, it would take 4 hours to complete the download. The next day, source B is available, but the other sources are inactive. How long will it take to download the trailer of the movie, a file that is 80 times smaller, from source B alone?
(A) 6 hours and 40 minutes
(B) 15 minutes
(C) 12 minutes
(D) 10 minutes
(E) 5 minutes
Rationale: Let the movie size be 400 u.
Given,A+C=4 hrs.
A+C=100 u/hr
And A+B+C=2.5 hrs or 400/2.5=160 u/hr
B alone=160-100=60 u/hr
Trailer=80 times smaller or400/80=5 u
B will take 5/60 hrs or 5 minutes.
Ans E
Answer: (E) 5 minutes
Question: A is twice as good workman as B, and together they complete a work in 15 days. In how many days can the work be complete by B alone?
(A) 35 days
(B) 65 days
(C) 45 days
(D) 75 days
(E) 95 days
Rationale: C
45 days
Answer: (C) 45 days
Question: In one alloy there is 12% chromium while in another alloy it is 8%. 15 kg of the first alloy was melted together with 35 kg of the second one to form a third alloy. Find the percentage of chromium in the new alloy.
(A) 8.8%
(B) 9%
(C) 9.2%
(D) 8.6%
(E) 8.4%
Rationale: The amount of chromium in the new 15+35=50 kg alloy is 0.12*15+0.08*35=4.6 kg, so the percentage is 4.6/50*100=9.2%.
Answer: C.
Answer: (C) 9.2%
Question: What is the probability of getting a sum 9 from two throws of a dice?
(A) 1/6
(B) 1/9
(C) 1/8
(D) 5/8
(E) 2/9
Rationale: In two throws of a dice, n(S) = (6 x 6) = 36.
Let E = event of getting a sum ={(3, 6), (4, 5), (5, 4), (6, 3)}.
P(E)=n(E)/n(S)
=4/36
=1/9
The answer should be B
Answer: (B) 1/9
Question: A shopkeeper purchased 70 kg of potatoes for Rs. 420 and sold the whole lot at the rate of Rs. 6.70 per kg. What will be his gain percent?
(A) 8 1/7 %
(B) 2 1/3 %
(C) 11 2/3 %
(D) 8 1/8 %
(E) 8 1/9 %
Rationale: C.P. of 1 kg = 420/70 = Rs. 6
S.P. of 1 kg = Rs. 6.70
Gain % = 0.70/6 * 100 = 35/3
= 11 2/3 %
Answer:C
Answer: (C) 11 2/3 %