mathewhe/aqua_rat huggingface dataset:
Question: Shekhar started a business investing Rs. 25,000 in 1999. In 2000, he invested an additional amount of Rs. 10,000 and Rajeev joined him with an amount of Rs. 35,000. In 2001, Shekhar invested another additional amount of Rs. 10,000 and Jatin joined them with an amount of Rs. 35,000. What will be Rajeev’s share in the profit of Rs. 1,50,000 earned at the end of 3 years from the start of the business in 1999?.
(A) Rs. 10000
(B) Rs. 20000
(C) Rs. 30000
(D) Rs. 40000
(E) Rs. 50000
Rationale: Shekhar : Rajeev : Jatin = (25000 X 12 + 35000 X 12 + 45000 X 12) : (35000 X 24) : (35000 X 12)
= 1260000 : 840000 : 420000 = 3 : 2 : 1.
Rajeev’s share = Rs.(150000×2/6) = Rs. 50000
Answer E
Answer: (E) Rs. 50000
Question: Maximum no of unsuccessful attempts, a thief can do in order to break a number locking system of 4 digits.
(A) 9988
(B) 9999
(C) 9799
(D) 9685
(E) 6545
Rationale: From 0 to 9999 there are 10000 four digit numbers
So maximum number of unsuccessful attempts = 10000 - 1 = 9999
ANSWER:B
Answer: (B) 9999
Question: If a coin has an equal probability of landing heads up or tails up each time it is flipped , what is the probability that the coin will land Tails up exactly twice in 2 consecutive flips ?
(A) 0.125
(B) 0.25
(C) 0.375
(D) 0.5
(E) 0.666
Rationale: Total number of ways in which H or T can appear in 3 tosses of coin is
= 2 * 2 = 4 ways
For 2 H
TT,
Thus probability is
= P(TT)
= 1/4
= .25
Answer : B
Answer: (B) 0.25
Question: A woman took some money for borrowed, for 3 years the total will be Rs.4000 and 5 years it will be Rs.5000/-. Then how much amount she borrowed?
(A) Rs.2500/-
(B) Rs.2550/-
(C) Rs.2590/-
(D) Rs.2600/-
(E) Rs.2650/-
Rationale: 3 years --------> Rs.4000/-
5 years --------> Rs.5000/-
~ ~
------------------------------
2 years ---------> Rs.1000/-
1 year ----------> Rs.500/-
3years * Rs.500/- = Rs.1500/-
P = Rs.4000/- - Rs.1500/- = Rs.2500/-
P = Rs.2500/-
A
Answer: (A) Rs.2500/-
Question: If we have 5 people in a meeting, in how many ways they can sit around a table?
(A) 10*9!
(B) 9*8!
(C) 8*7!
(D) 7*6!
(E) 4*3!
Rationale: If there arenpeople sitting around a table, there are(n-1)!possible arrangements:
Here, n=5
(n-1)!=4!=4*3!
Ans:E
Answer: (E) 4*3!
Question: How many seconds will a 500 meter long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 878 meters
(B) 154 meters
(C) 500 meters
(D) 184 meters
(E) 157 meters
Rationale: Let length of tunnel is x meter
Distance = 800+x meter
Time = 1 minute = 60 seconds
Speed = 78 km/hr = 78*5/18 m/s = 65/3 m/s
Distance = Speed*Time
800+x = (65/3) * 60
800+x = 20 * 65 = 1300
x = 1300 - 800
=500 meters
Answer:C
Answer: (C) 500 meters
Question: Approximately how many revolutions will be made by a car tire with a 12-inch diameter if the car travels 1 mile?
(A) 1,205
(B) 1,800
(C) 1,356
(D) 1,672
(E) 1,440
Rationale: Diameter of car tire = 12 inches
Radius of car tire = 6 inches = 6*2.54 cm = 15.24 cm
Circumference of the car tire = 2*pi * 15.24 = 2 *3.14 *15.24= 95.71 cm
Distance traveled by car =1 mile = 1 *1.6 km = 1.6 km = 1600 m = 1.6 * 10^5 cm
Number of revolutions =Distance traveled / Circumference of tire = 1.6 * 10^5 / 95.71 = 1671.72
Since the answer choices are far apart we should use estimation in this question .
Ideally ,in the GMAT the conversion between units would be provided .
Answer D
Answer: (D) 1,672
Question: The present ages of Lewis and Brown are in the ratio 1:2. Three years from now, the ages will be in the ratio 3:5. Find the present age of Brown.
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: l:b=1:2 & (l+3):(b+3)=3:5
then 2l=b & 5l+15=3b+9
by solving above we get
b=12
ANSWER:E
Answer: (E) 12
Question: A crew can row a certain course up the stream in 84 minutes; they can row the same course down stream in 6 minutes less than they can row it in still water. How long would they take to row down with the stream
(A) 45 or 23 minutes
(B) 63 or 12 minutes
(C) 78 minutes
(D) 19 minutes
(E) 25 minutes
Rationale: A method has been discussed here to nullify the calculations though.
All I can input here is,
speed of a crew in still water = 1/2 ( speed upstream + speed downstream)
approximating this for time,
t = 1/2(84+ (t-6))
giving t = 78
C.
Answer: (C) 78 minutes
Question: If k and y are integers, and 10k + y is odd, which of the following must be true?
(A) k is odd
(B) k is even
(C) y is odd integer
(D) y is even
(E) both k and y are odd
Rationale: 10k will be always even as 10 has 2 as one of its factors
if 10k+y is odd, then the only possible explanation is that y is odd
correct answer C
Answer: (C) y is odd integer
Question: what is the minimum possible range in scores of the three test-takers?Three people each took 5 tests. If the ranges of their scores in the 5 practice tests were 17, 25 and 36.
(A) 36
(B) 17
(C) 25
(D) 40
(E) 35
Rationale: I simply looked at the 3 different possible scores for each individual test: 17,36,25
We have to find the minimum range:
36-17=9
36-25=11
25-17=8
The find the minimum range, you have to make the set of the 5 scores as small as possible.
Which means that 4 of the 5 scores of each individual person is zero.
8*5 = 40
Answer:D
Answer: (D) 40
Question: At a supermarket, John spent 1/2 of his money on fresh fruits and vegetables, 1/3 on meat products, and 1/10 on bakery products. If he spent the remaining $10 on candy, how much did John spend at the supermarket?
(A)  $60
(B)  $80
(C)  $90
(D)  $120
(E)  $150
Rationale: Let's let T = total number of dollars spent at the supermarket. With this variable we can set up an equation and determine T.
We are given that John spent 1/2 of his money on fresh fruits and vegetables, or (1/2)T, 1/3 on meat products, or (1/3)T, and 1/10 on bakery products, or (1/10)T. We are also given that he spent the remaining $10 on candy. Since we know where all his money was allocated, we can sum these values together and set the sum to T. So we have:
(1/2)T + (1/3)T + (1/10)T + 10 = T
To get rid of the fractions we can multiply the entire equation by 30, and we obtain:
15T + 10T + 3T + 300 = 30T
28T + 300 = 30T
300 = 2T
T = 150
John spent $90 at the supermarket.
Answer: E
Answer: (E)  $150
Question: If A : B = 4 : 5 and B : C = 6 : 7 then A : B : C is :
(A) 20 : 35 : 63
(B) 35 : 36 : 63
(C) 30 : 35 : 65
(D) 25 :34: 68
(E) None of these
Rationale: Expl : A : B = 4 : 5
B : C = 6 :7 = 6*5/6 : 7 *5/6 = 5 : 35/6
A : B : C = 4 : 5 : 36/6 = 24 : 30 : 36 = 4 : 5 : 6
Answer: E
Answer: (E) None of these
Question: What is the probability that a two digit number selected at random will be a multiple of '3' and not a multiple of '5'?
(A) 2/15
(B) 4/15
(C) 1/15
(D) 4/90
(E) 5/60
Rationale: Solution:
There are a total of 90 two digit numbers. Every third number will be divisible by '3'. Therefore, there are 30 of those numbers that are divisible by '3'.
Of these 30 numbers, the numbers that are divisible by '5' are those that are multiples of '15'. i.e. numbers that are divisible by both '3' and '5'.
There are 6 such numbers -- 15,30,45,60,75 and 90.
We need to find out numbers that are divisible by '3' and not by '5', which will be:
30âˆ’6=24
24 out of the 90 numbers are divisible by '3' and not by '5'.
The required probability is therefore,
=24/90
=4/15
ANSWER IS B
Answer: (B) 4/15
Question: In a maths test, students were asked to find 5/16 of a certain number. One of the students by mistake found 5/6th of that number and his answer was 50 more than the correct answer. Find the number.
(A) 96
(B) 280
(C) 384
(D) 400
(E) 500
Rationale: Explanation:
Let the number be x.
5*x/6 = 5*x/16 +50
25*x/48 = 50
x = 96
ANSWER A
Answer: (A) 96
Question: man is 20 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
(A) 14years
(B) 26 years
(C) 17 years
(D) 18 years
(E) 22 years
Rationale: Let the son's present age be x years. Then, man's present age = (x + 20) years.
(x + 20) + 2 = 2(x + 2)
x + 22 = 2x + 4
x = 18.
answer :D
Answer: (D) 18 years
Question: A company consists of 6 senior and 5 junior staff officers. If a committee is created with 3 senior and 3 junior staff officers, in how many ways can the committee be formed?
(A)  12
(B)  30
(C)  45
(D)  80
(E)  200
Rationale: Choose 3 senior from 6 senior and choose 3 junior from 5 junior:
6C3 * 5C3 = 20*10 = 200
Ans: E
Answer: (E)  200
Question: From the word 'LAPAROSCOPY' how many independent meaningful words can be made without changing the order of the letters and using each letter only once ?
(A) 8
(B) 7
(C) 6
(D) 2
(E) 3
Rationale: Explanation:
The words are LAP and COPY.
Answer: D) 2
Answer: (D) 2
Question: Find (7x + 5y ) / (x-2y) if x/2y = 3/2 ?
(A) 24
(B) 25
(C) 26
(D) 27
(E) 29
Rationale: x/2y=3/2
=>x=6y/2=3y
=>(7x+5y)/(x-2y)=((7*(3y))+5y)/(3y-2y)
=>26y/y=26
ANSWER:C
Answer: (C) 26
Question: When positive integer n is divided by 4, the remainder is 2. When n is divided by 7, the remainder is 5. How many values less than 100 can n take?
(A)  0
(B)  2
(C)  3
(D)  4
(E)  5
Rationale: a quick approac to this Q is..
the equation we can form is.. 3x+2=7y+5..
3x-3=7y... 3(x-1)=7y...
so (x-1) has to be a multiple of 7 as y then will take values of multiple of 3..
here we can see x can be 1,8,15,22,29 so 5 values till 100 is reached
as (29-1)*3=84 and next multiple of 7 will be 84+21>100..
ans 3.. C
Answer: (C)  3
Question: The number of cars present at a particular time was measured at 3,999 different locations on Tuesday and on Wednesday. The number of locations that had more cars on Wednesday was 10% higher than the number of locations that had more cars on Tuesday. How many of the locations had more cars on Tuesday?
(A) 1,159
(B) 1,333
(C) 1,860
(D) 1,904
(E) 2,829
Rationale: The question states that all these 3,999 locations were measured twice, once on each day.
It also breaks the 3,999 into two groups, the higher-on-Tuesday locations and the higher-on-Wednesday locations, which we can call T and W.
Therefore, we can write two equations:
For each of the first and second day count of locations, T + W = 3999
But, for the second day count, W = 1.10 T
i.e. for Second day count, T + 1.10T = 3999
i.e. 2.10 T = 3999
i.e. T = 1904
D
Answer: (D) 1,904
Question: A train 360 m long runs with a speed of 45 km/hr. What time will it take to pass a platform of 340 m long?
(A) 38 sec
(B) 35 sec
(C) 44 sec
(D) 40 sec
(E) 56 sec
Rationale: Explanation:
Speed = 45 km/hr = 45×(10/36) m/s
= 150/12 = 50/4 = 25/2 m/s
Total distance = length of the train + length of the platform
= 360 + 340 = 700 meter
Time taken to cross the platform = 700/(25/2) = 700×2/25 = 56 seconds
Answer: Option E
Answer: (E) 56 sec
Question: Mixture of milk & water has been kept in two separate bowl. Ratio of milk to water in one of the bowls is 5 : 1 and that in the other bowl 7 : 2. In what ratio the mixtures of these 2 bowl should be added together so that the quantity of milk in the new mixture may become 80%?
(A) 2:3
(B) 1:3
(C) 2:5
(D) 2:7
(E) 3:8
Rationale: Lett. mixtures of the two containers be added together in the ratio of x
= = [ixoox l00%
Since the percentage quantity ofmilk in the new mixture is SO% — so% (45x + 42y) x 5 4 x 54(x y) 225x 210y 216.3E+216y
9x=6y
x:y=2:3
A
Answer: (A) 2:3
Question: Find the value of y from (12)^3 x 6^4 ÷ 432 = y?
(A) 2234
(B) 4350
(C) 4560
(D) 5132
(E) y=5184
Rationale: Given Exp. = (12)3 x 64 = (12)3 x 64 = (12)2 x 62 = (72)2 = 5184
432 12 x 62
E
Answer: (E) y=5184
Question: Numbers from 1 to 10^2012 are given, there are 'm' no of 1's and 'n' no of 2's.
Then what is (m-n).
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: let us consider 1-100 here no of 1's m =21 and no.of 2's n = 20 there by m-n=1 similary from 1 to (10^2012-1) no.of 1's=no.of 2's but in last term 10^2012 a one is added there by the ans is 1.
ANSWER:B
Answer: (B) 1
Question: In a fuel station the service costs $1.75 per car, every liter of fuel costs 0.65$. Assuming that a company owns 12 cars and that every fuel tank contains 57 liters and they are all empty, how much money total will it cost to fuel all cars?
(A) 320.50$
(B) 380.50$
(C) 425.50$
(D) 450.50$
(E) 465.60$
Rationale: Total Cost = ( 1.75*12 ) + ( 0.65 * 12 * 57 ) = 465.60
Hence answer will be (E)
Answer: (E) 465.60$
Question: If z2 + 4y2 = 4zy, then z : y is :
(A) 2 : 1
(B) 1 : 2
(C) 1 : 1
(D) 1 : 4
(E) 1 : 5
Rationale: as the coefficient of z is 1 and coefficient of y is 4
ANSWER:D
Answer: (D) 1 : 4
Question: A sells a bicycle to B at a profit of 50% and B sells it to C at a loss of 40%. Find the resultant profit or loss.
(A) -4%
(B) 5%
(C) -5%
(D) 6%
(E) -10%
Rationale: The resultant profit or loss = 50 - 40 - (50*40)/100 = -10%
loss = 10%
Answer is E
Answer: (E) -10%
Question: The sum of three consecutive even numbers is 42. Find the middle number of the three?
(A) 14
(B) 86
(C) 16
(D) 28
(E) 23
Rationale: Three consecutive even numbers (2P - 2), 2P, (2P + 2).
(2P - 2) + 2P + (2P + 2) = 42
6P = 42 => P = 7.
The middle number is: 2P
= 14.
Answer:A
Answer: (A) 14
Question: Arabica coffee costs $0.5 per ounce while Robusta coffee costs $0.3 per ounce. If the blend of Arabica and Robusta costs $0.33 per ounce, what is the share of Arabica in this blend?
(A) 15%
(B) 24%
(C) 30%
(D) 33%
(E) 40%
Rationale: a= amount of arabica coffee
1-a = amount of robusta coffee. because if you subtract a from the 1 ounce, the remaining amount is robusta
therefore:
.5a + .3(1-a) = .33
.5a + .3 - .3a = .33
a= .3/2
therefore: .3/2/1 ounce = 15%. Therefore, the answer should be A
Answer: (A) 15%
Question: A shopkeeper sold an article offering a discount of 4% and earned a profit of 44%. What would have been the percentage of profit earned if no discount was offered?
(A) 24
(B) 28
(C) 30
(D) 32
(E) 50
Rationale: Let C.P. be Rs. 100.
Then, S.P. = Rs. 144
Let marked price be Rs. x. Then, 96/100 x = 144
x = 14400/96 = Rs. 150
Now, S.P. = Rs. 150, C.P. = Rs. 100
Profit % = 50%.
ANSWER:E
Answer: (E) 50
Question: What is the least number of squares tiles required to pave the floor of a room 15 m 17 cm long and 9 m 2 cm broad
(A) 814
(B) 256
(C) 3258
(D) 896
(E) 745
Rationale: Explanation:
Length of largest tile = H.C.F. of 1517 cm and 902 cm = 41 cm.
Area of each tile = (41 x 41) cm^2.
Required number of tiles =(1517 x 902/41*41)= 814.
Answer : A
Answer: (A) 814
Question: Jerry’s average (arithmetic mean) score on the first 3 of 4 tests is 81. If Jerry wants to raise his average by 2 points, what score must he earn on the fourth test?
(A) 87
(B) 89
(C) 90
(D) 93
(E) 95
Rationale: Total score on 3 tests = 81*3 = 243
Jerry wants the average to be = 83
Hence total score on 4 tests should be = 83*4 = 332
Score required on the fourth test = 332 - 243 = 89
Option B
Answer: (B) 89
Question: What is remainder of the division (1625*1627*1629)/12?
(A) 3
(B) 2
(C) 1
(D) 0
(E) 4
Rationale: remainder will be number/ 100 here as the divisor is two digit number = 12.
hence checking for the last two digits = 5*7*9 = 15
Thus remainder = 3.
Answer : A
Answer: (A) 3
Question: Machine X takes 60 hours longer than machine Y to produce 1080 Widgets. Machine Y produces 20 percent more widgets in an hour than machine x does in an hour. How many widgets per hour does machine X produce
(A) 100
(B) 65
(C) 25
(D) 11
(E) 3
Rationale: Machine Y produces 20 percent more widgets in an hour than machine x does in an hour.
So if machine X produces 100 widgets, then machine Y produces 120 widgets.
Ratio of 120/100 = 6/5.
This is their speed of work (Y:X).
i.e. speed of their work (X:Y) = 5/6
Now, time is inversely proportional to speed.
Hence the ratio of the time spent (X:Y)= 6/5
Let us assume that they spend 6x and 5x hours.
Given that 6x-5x = 60
So, x = 60.
Hence 6x = 6*60 = 360 hours.
Hence X takes 120 hours to produce 1080 widgets.
So, in 1 hour, it can produce (1 * 1080)/360
= 3
Hence option (E).
Answer: (E) 3
Question: There are 12 balls in a bag; 8 are blue balls and the other 4 are yellow balls. If 3 balls are to be selected at random from the 12 balls, what is the probability that at least one of the yellow ball will be selected?
(A) 57/55
(B) 56/55
(C) 54/55
(D) 53/55
(E) 52/55
Rationale: Total probability=12C3=220
8C3 +8C2*4C1+8C1*4C2=56+112+48=216
therefore the probability that at least one of the yellow ball will be selected= 216/220=54/55
answer is C
Answer: (C) 54/55
Question: A certain quantity of 40% concentration solution is replaced with 25% concentration solution such that the concentration of the combined amount is 35%.
What's the ratio of the amount of solution that was replaced to the amount of solution that was not replaced?
(A) 1:3
(B) 1:2
(C) 2:3
(D) 2:1
(E) 3:1
Rationale: From the wording in the prompt, we're essentially mixing two liquids:
Liquid X is 40% concentrate
Liquid Y is 25% concentrate
We're supposed to mix some of each and end up with a solution that is 35% concentrate. The prompt doesn't give us specific amounts of liquids to work with and the question itself asks for the ratio of the two liquids, so we could even TEST VALUES if doing it that way made it easier for you. For now though, here's the Algebra:
X = # of ounces of liquid X
Y = # of ounces of liquid Y
(.4X + .25Y) / (X + Y) = .35
.4X + .25Y = .35X + .35Y
.05X = .1Y
5X = 10Y
From here, you have to be CAREFUL to answer the question that is ASKED.
5X = 10Y
Y/X = 5/10 = 1/2
ANSWER:B
Answer: (B) 1:2
Question: A company has 16 equally qualified applicants for 4 open positions. How many different groups of 4 applicants can be chosen by the company to fill the positions if the order of selection does not matter?
(A) 1780
(B) 1820
(C) 1860
(D) 1900
(E) 1940
Rationale: 16C4=1820
The answer is B.
Answer: (B) 1820
Question: Tough and Tricky questions: Exponents.
If 6^(3x+4)*2^(2y+1) = 36^x*16^y, then x + y =
(A) -7/2
(B) -1/7
(C) 3/7
(D) 7/2
(E) -3/7
Rationale: Here is my solution.
6^(3x+4)*2^(2y+1) = 36^x*16^y
Here RHS 36^x*16^y= 6^(2x)*2^(4y)
Equating powers on both sides-->
3x+4=2x , thus x=-4 and
2y+1=4y giving y=1/2
So, x+y=-7/2
Option: A
Answer: (A) -7/2
Question: If W is the set of all the integers between 49 and 76, inclusive, that are either multiples of 3 or multiples of 2 or multiples of both, then W contains how many numbers?
(A) 19
(B) 91
(C) 41
(D) 18
(E) 14
Rationale: Official Solution:
Number of multiples of 3
Step 1. Subtract the extreme multiples of 3 within the range (The greatest is 75, the smallest is 51): 75 - 51 = 24
Step 2. Divide by 3: 24 / 3 = 8
Step 3. Add 1: 8 + 1 = 9.
So there are 9 multiples of 3 within the range: examples are 51, 54, 57, 60, etc.
Number of multiples of 2
Step 1. Subtract the extreme multiples of 2 within the range (The greatest is 76, the smallest is 50): 76 - 50 = 26
Step 2. Divide by 2: 26 / 2 = 13
Step 3. Add 1: 13 + 1 = 14.
So there are 14 multiples of 2 within the range: examples are 50, 52, 54, 56, 58, 60 etc.
Add the 9 multiples of 3 and the 14 multiples of 2: 9+14=23.However, by adding the multiples of 2 and the multiples of 3, we are effectively counting several numbers twice: for example, 54 and 60 are parts of both the lists above. So we can't just take 9+14=23. Find the Number of multiples of 6 (which are the double counted, as 6 is divisible by both 2 and 3), and subtract it from 23:
Step 1. Subtract the extreme multiples of 6 within the range (The greatest is 72, the smallest is 54): 72 - 54 = 18
Step 2. Divide by 6: 18 / 6 = 3
Step 3. Add 1: 3 + 1 = 4.
So there are 4 multiples of 6 within the range: we counted 4 numbers twice.
Subtract the 4 multiples of 6 from the sum of the multiples of 2 and 3:
= 9 + 14 - 4
= 23 - 4
= 19
Therefore, the final number of multiples of 2, 3 or 6 is 19.
Hence, this is the correct answer. (A)
Answer: (A) 19
Question: Marcela, Karla, Isabel, and Viviana all got their math tests back. The average of Marcela, Karla, and Isabel's grades was an 85%. The average of Karla, Isabel, and Viviana's grades was a 78%. If Viviana got a 75%, what did Marcela get?
(A) 90%
(B) 92%
(C) 96%
(D) 88%
(E) 98%
Rationale: Solution: Average grade for Marcela, Karla, and Isabel = 85%
Total grade points= 3*85 = 255
Average grade for Karla, Isabel and Viviana = 78%
Total grade points = 3*78 = 234
Viviana got a 75%.
Now,
(Marcela+Karla+Isabel) - (Karla+Isabel+Viviana) = 255-234
Marcela-Viviana = 21
Marcela's score= Viviana's + 21 = 96%
Answer: Option C
Answer: (C) 96%
Question: If 6 parallel lines in a plane is intersected by a family of another 8 parallel lines, how many parallelograms are there in the network thus formed?
(A) 80
(B) 63
(C) 420
(D) 160
(E) 1260
Rationale: parallelogram can formed by 2 horizontal and 2 vertical lines
for horizontal 6c2
for vertical 8c2
total parallelogram is 6 c2*8c2=15*28
=420
ANSWER:C
Answer: (C) 420
Question: Here are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period?
(A) 1023
(B) 6000
(C) 1980
(D) 1800
(E) 1450
Rationale: 5 subjects can be arranged in 6 periods in 6P5 ways.
Any of the 5 subjects can be organized in the remaining period (5C1 ways).
Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.
Total number of arrangements
= 6P5× 5C1 /2!=1800
Option D
Answer: (D) 1800
Question: A dealer offers a cash discount of 20%. Further, a customer bargains and receives 20 articles for the price of 15 articles. The dealer still makes a profit of 20%. How much percent above the cost price were his articles marked?
(A) 100%
(B) 80%
(C) 75%
(D) 66+2/3%
(E) 50%
Rationale: Marked Price (M) = Cost Price (C) + Mark up...(EQN. A)
Selling price = 20% Discount over M = 0.8*M
Given that, a customer bargains and receives 20 articles for the price of 15 articles--> *a further loss of 25% to the dealer--> BUT a NET PROFIT of 20% over cost price (C)
0.75 * 0.8 * M = 1.2 * C
Hence, M/C = 2/1 = 200%
From Eqn. A , (C + Mark up)/C = 200% --> Mark up / C = 100%
Ans. A
Answer: (A) 100%
Question: The avg. age of a group of 28 students is 20 years.If 4 more students join the group,the avg age increases by 1 year.The avg age of the new student is?
(A) 22 years
(B) 23 years
(C) 24 years
(D) 25 years
(E) 28 years
Rationale: Total age of 28 students=28*20=560
If total age of 4 students=x
Then, (560+x)/(28+4) =(20+1), x=112
So average age of new students=112/4= 28 years
ANSWER:E
Answer: (E) 28 years
Question: There are 15 teams in the hockey league, and each team faces all the other teams 10 times each. How many games are played in the season?
(A) 650
(B) 750
(C) 850
(D) 950
(E) 1050
Rationale: The number of ways to choose two teams is 15C2 = 15*14/2 = 105
The total number of games in the season is 10*105 = 1050.
The answer is E.
Answer: (E) 1050
Question: The ratio of the amount of the oil bill for the month of February to the amount of the oil bill for the month of January was 3:2. If the oil bill for February had been $10 more, the corresponding ratio would have been 5:3. How much was the oil bill for January?
(A) $60
(B) $80
(C) $100
(D) $120
(E) $140
Rationale: 3:2 = 9:6 and 5:3 = 10:6.
An increase in $10 increases the ratio by 1:6.
Therefore, January's bill was 6($10) = $60.
The answer is A.
Answer: (A) $60
Question: The speed at which a man can row a boat in still water is 16 kmph. If he rows downstream, where the speed of current is 4 kmph, what time will he take to cover 100 metres?
(A) 23
(B) 27
(C) 28
(D) 12
(E) 18
Rationale: Speed of the boat downstream = 16 +4 = 20 kmph= 20 * 5/18 = 5.55 m/sHence time taken to cover 100 m = 100/5.55= 18 seconds.Answer:E
Answer: (E) 18
Question: A reduction of 40% in the price of bananas would enable a man to obtain 64 more for Rs.40, what is reduced price per dozen?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 40*(40/100) = 16 --- 64
? --- 12 => Rs.3
Answer:A
Answer: (A) 3