mathewhe/aqua_rat huggingface dataset:
Question: The probability that a family with 6 children has exactly four boys is:
(A) 1/3
(B) 1/64
(C) 15/64
(D) 3/8
(E) none of the above
Rationale: Now let's find the # of combinations where there's a BGB combination. Let the sequence of BG=A:
BBAA
BAAB
BABA
ABBA
ABAB
AABB
So there are 6 combinations here. But since BG can also be GB, we have to multiply by 2. We have to multiply by another 2 because there are 2 As. Therefore, there are 6x2x2=24 combinations.
We also have to include the instances where GG occurs at the end or the front, that is:
GGBBBB
BBBBGG
(all the other instances such as BBGGBB have been taken care of in the calculation at the top)
So we have 24+2=26 possibilities of 4 boys and 2 girls.
The total number of possibilities is 2^6=64. Therefore, the probability is 26/64, which is 13/32. The answer is E
Answer: (E) none of the above
Question: A certain board game is played by rolling a pair of fair six-sided dice and then moving one's piece forward the number of spaces indicated by the sum showing on the dice. A player is frozen if her opponent's piece comes to rest in the space already occupied by her piece. If player A is about to roll and is currently nine spaces behind player B, what is the probability that player B will be frozen after player A rolls?
(A) 1/12
(B) 5/36
(C) 1/9
(D) 1/3
(E) 17/36
Rationale: no. of possible outcomes = 6*6 = 36
no. of outcomes that result a total of 9 (as A is 9 spaces behind B) = 4 ( (3,6), (4,5), (5,4), (6,3) )
So, the probability = 4/36=1/9 (Option C)
Answer: (C) 1/9
Question: 9 spheres of the same size are made from melting a solid cylinder of 8 cm diameter and 48 cm height. What is the diameter of each sphere?
(A) 4 cm
(B) 6 cm
(C) 8 cm
(D) 10 cm
(E) 12 cm
Rationale: Volume of cylinder = pi*r^2*h
Volume of a sphere = 4*pi*R^3 / 3
9*4*pi*R^3 / 3 = pi*r^2*h
R^3 = r^2*h / 12 = 64 cm^3
R = 4 cm
D = 8 cm
The answer is C.
Answer: (C) 8 cm
Question: A can do a work in 7 days. B is 20% more efficient than A. How many days does B alone take to do the same job?
(A) 28/6
(B) 25/6
(C) 35/6
(D) 33/6
(E) 39/6
Rationale: Ratio of times taken by A and B = 120:100 = 6:5
suppose B alone to take x days to do the work
then, 6:5::7:x
6x= 5*7
x=35/6 days
correct option is C
Answer: (C) 35/6
Question: The average (arithmetic mean) of the even integers from 0 to 60 inclusive is how much greater than the average (arithmetic mean) of the even integers from 0 to 30 inclusive?
(A) 10
(B) 15
(C) 20
(D) 25
(E) 30
Rationale: The sum of even numbers from 0 to N is 2 + 4 +...+ N
= 2(1 + 2 + ...+ N/2)
= 2(N/2)(N/2+1)/2 = (N/2)(N/2+1)
The average is (N/2)(N/2+1)/(N/2+1) = N/2
The average of the even numbers from 0 to 60 is 60/2 = 30
The average of the even numbers from 0 to 30 is 30/2 = 15
The answer is B.
Answer: (B) 15
Question: What is the are of an equilateral triangle of side 8 cm?
(A) 64√5
(B) 64√9
(C) 16√3
(D) 64√3
(E) 64√2
Rationale: Area of an equilateral triangle = √3/4 S2
If S = 8, Area of triangle = √3/4 * 8 * 8 = 16√3 cm2;
Answer: C
Answer: (C) 16√3
Question: Soymilk are sold in packages of two or three only. If Hannah bought 17 Soymilk exactly, what could be the number of large packs Hannah bought?
(A) 1
(B) 4
(C) 3
(D) 5
(E) 8
Rationale: Let number of packs of three = t
let number of packs of two = w
3t + 2w = 17
Now , we need to test for values of w .
Since sum 17 is odd and 2w will always be even, therefore w can't be even .
Now , we can test for values w = 1 , 3 and 5
2*4 + 3*3 = 8 + 9 = 17
Answer C
Answer: (C) 3
Question: Robert ate 10 chocolates, Nickel ate 5 chocolates. How many more chocolates did Robert ate than nickel?
(A) A)4
(B) B)7
(C) C)9
(D) D)5
(E) E)2
Rationale: 10-5=5. Answer is D
Answer: (D) D)5
Question: In the fifth grade at Parkway elementary school there are 500 students. 350 students are boys and 250 students are playing soccer. 86% of the students that play soccer are boys. How many girl student are in Parkway that is not playing soccer?
(A) 69.
(B) 73.
(C) 81.
(D) 91.
(E) 115.
Rationale: Total students = 500
Boys = 350, Girls = 150
Total playing soccer = 250
86%of 250 = 215 are boys who play soccer.
Girls who play soccer = 35.
Total girls who do not play soccer = 150 - 35 = 115.
Correct option: E
Answer: (E) 115.
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) 776
(B) 298
(C) 245
(D) 266
(E) 256
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) 245
Question: Virginia, Adrienne, and Dennis have taught history for a combined total of 87 years. If Virginia has taught for 9 more years than Adrienne and for 9 fewer years than Dennis, for how many years has Dennis taught?
(A)  23
(B)  32
(C)  38
(D)  41
(E)  44
Rationale: Let number of years taught by Virginia = V
number of years taught by Adrienne = A
number of years taught by Dennis = D
V+A+D = 96
V= A+9
=>A = V-9
V= D-9
=> A = (D-9)-9 = D-18
D-9 + D-18 + D = 87
=> 3D = 87+ 27 = 114
=> D = 38
Answer C
Answer: (C)  38
Question: Find the number of square tiles to cover the floor of a room measuring 4 m * 9 m leaving 0.25 m space around the room. A side of square tile is given to be 25 cms?
(A) 478
(B) 476
(C) 472
(D) 471
(E) 445
Rationale: 3 1/2 * 8 1/2 = 1/4 * 1/4 * x => x
= 476
Answer:B
Answer: (B) 476
Question: In a cricket team, the average of eleven players is 28 years. Out of these, the average ages of three groups of three players each are 25 years, 28 years and 32 years respectively. If in these groups, the captain and the youngest player are not included, and the captain is eleven years older than the youngest player, what is the age of the captain ?
(A) 32 years
(B) 34 years
(C) 35 years
(D) 36 years
(E) 37 years
Rationale: Explanation :
Let the age of youngest player be x.
Then, age of the captain = (x + 11).
=> 3*25 + 3*28 + 3*32 + x + x + 11 = 11*28.
=> 75+84+96+2x+11=308
so 2x = 42
so x = 21.
Age of the captain = (x+11)
= 32 years.
Answer : A
Answer: (A) 32 years
Question: Two trains are running in opposite directions with the same speed. If the length of each train is 100 m and they cross each other in 12 sec, then the speed of each train is?
(A) 30
(B) 35
(C) 36
(D) 37
(E) 38
Rationale: Let the speed of each train be x m/sec.
Then, relative speed of the two trains = 2x m/sec.
So, 2x = (100 + 100)/12 => x = 8.33
Speed of each train = 10 m/sec.
= 8.33 * 18/5 = 30 km/hr.
Answer: Option A
Answer: (A) 30
Question: In a school of 850 boys, 34% of Muslims, 28% Hindus, 10% Sikhs and the remaining of other communities. How many belonged to the other communities?
(A) A)125
(B) B)627
(C) C)153
(D) D)238
(E) E)159
Rationale: 34 + 28 + 10 = 72%
100 – 72 = 28%
850 * 28/100 = 238
Answer:D
Answer: (D) D)238
Question: If a farmer wants to plough a farm field on time, he must plough 120 hectares a day. For technical reasons he ploughed only 85 hectares a day, hence he had to plough 2 more days than he planned and he still has 40 hectares left. What is the area of the farm field and how many days the farmer planned to work initially?
(A) 334
(B) 720
(C) 667
(D) 261
(E) 181
Rationale: Let xx be the number of days in the initial plan. Therefore, the whole field is 120⋅x120⋅x hectares. The farmer had to work for x+2x+2 days, and he ploughed 85(x+2)85(x+2) hectares, leaving 4040 hectares unploughed. Then we have the equation:
120x=85(x+2)+40120x=85(x+2)+40
35x=21035x=210
x=6x=6
So the farmer planned to have the work done in 6 days, and the area of the farm field is 120⋅6=720120⋅6=720 hectares
Answer:B
Answer: (B) 720
Question: What number should replace the question mark? 11, 15, 16, 12, 21, 9, ---?
(A) 21
(B) 29
(C) 28
(D) 27
(E) 26
Rationale: Answer: E
11, 15, 16, 12, 21, 9, ---?
There are two alternate sequences: +5 and -3.
Answer: (E) 26
Question: David works at a science lab that conducts experiments on bacteria. The population of the bacteria multiplies at a constant rate, and his job is to notate the population of a certain group of bacteria each hour. At 1 p.m. on a certain day, he noted that the population was 600 and then he left the lab. He returned in time to take a reading at 4 p.m., by which point the population had grown to 4,800. Now he has to fill in the missing data for 2 p.m. and 3 p.m. What was the population at 3 p.m.?
(A) 2400
(B) 3600
(C) 3000
(D) 2800
(E) 2500
Rationale: let the rate be x, then population of the bacteria after each hour can be given as 600,600x, 600(x^2), 600(x^3)
now population at 4pm =4800
thus we have 600(x^3) = 4800 =8
thus x=2
therefore population at 3pm = 600(4) = 2400
Answer : A
Answer: (A) 2400
Question: What is the sum of the 1st 6 prime numbers greater than 10?
(A) 112
(B) 111
(C) 212
(D) 115
(E) 113
Rationale: Required numbers are= (11 + 13 + 17 + 19 + 23+ 29) = 112
Note: 1 is not a prime number
Answer A
Answer: (A) 112
Question: A train travels from station A to station B. If it travels at a speed of 80 miles per hour, it ends up reaching the station 30 minutes late. If it travels at 120 miles per hour, it reaches the station 15 minutes early. What is the amount of time that the train is scheduled to take for the journey and what is the distance between the stations?
(A) 	2 hours, 225 miles
(B) 	3 hours, 350 miles
(C) 	1.75 hours, 180 miles
(D) 	5 hours, 550 miles
(E) 	6 hours, 650 miles
Rationale: Let t be the usual time and x be the distance between AB. So we need to find t and Distance x. The question gives us 2 combinations of speedtime, but the distance remains the same for both condition.
Equation 1 - x= 80 (t+.5) (converted 30 mins into hr) added .5 hrs because it is late or took more time than usual.
Equation 2 - x= 120 (t-.25) subtracted .25 hrs because it is early or took less time than usual.
Now equating 12 we get 100(t+.5)=120(t-.25)
=> 8t +4 = 12t - 3
=> 4t=7 => t= 1.75 hrs.
Hence x= 80(1.75+.5) =>80 X 2.25 => 180 miles.
Hence correct answer C.
Answer: (C) 	1.75 hours, 180 miles
Question: Dawson is going with 14 friends on a trip to Washington D.C for spring break. Airfare and hotel costs a total of $13500.00 for the group of 15 friends. How much does each person have to pay for their hotel and airfare?
(A) $900
(B) $800
(C) $850
(D) $950
(E) $920
Rationale: Answer= A
The total cost of the trip ($13500.00) divided by 15 equals $900.00.
Answer: (A) $900
Question: What is the average of first 21 multiples of 7 ?
(A) 70
(B) 77
(C) 79
(D) 81
(E) 82
Rationale: Required average = 7(1+2+....+21) / 21
(7/21)X ( (21x22) / 2 ) (because sum of first 21 natural numbers)
= 77
B
Answer: (B) 77
Question: A train 275 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
(A) 7 sec
(B) 5 sec
(C) 15 sec
(D) 6 sec
(E) 12 sec
Rationale: Speed of train relative to man
= (60 + 6) km/hr
= 66 km/hr
[66 * 5/18] m/sec
= [55/3] m/sec.
Time taken to pass the man
= [275* 3/55] sec
= 15 sec
Answer:C
Answer: (C) 15 sec
Question: A candidate got 35% of the votes polled and he lost to his rival by 2280 votes. How many votes were cast?
(A) 7500
(B) 3388
(C) 2665
(D) 2888
(E) 7600
Rationale: 35%-----------L
65%-----------W
------------------
30%----------2280
100%---------? => 7600
Answer: E
Answer: (E) 7600
Question: 3th/4 of 1th/5 of a number is 60. The number is
(A) 300
(B) 400
(C) 450
(D) 1200
(E) None
Rationale: Explanation:
Let the number be N. Then
3/4×1/5×N=60⇒3N=1200⇒N=400
Correct Option: B
Answer: (B) 400
Question: A clothing store originally bought 100 jackets at a total cost of j dollars. If each jacket was sold for 60 percent more than its original cost, what was the individual price, in terms of j, of each jacket sold?
(A) j/62
(B) 7j/500
(C) 140j
(D) j/100+40
(E) 140j/100
Rationale: lets take j=1000, as decided by you..
now 60% increase makes it 1600..
this is the price for 100 jackets, so selling price for each jacket=1600/100=$16..
j/62
so ans is correct as A..
Answer: (A) j/62
Question: What is the sum of all possible 3-digit numbers that can be constructed using the digits 2, 3, and 5 if each digit can be used only once in each number?
(A) 2210
(B) 2220
(C) 2230
(D) 2240
(E) 2250
Rationale: There are 6 possible arrangements of the three numbers.
Then each number will be in the hundreds, tens, and ones place two times each.
The sum is 2(222) + 2(333) + 2(555) = 2220
The answer is B.
Answer: (B) 2220
Question: At a certain organisation, the number of male members went up by 13% in the year 2001 from year 2000, and the number of females members went down by 6% in the same time period. If the total membership at the organisation went up by 1.2% from the year 2000 to 2001, what was the ratio of male members to female members in the year 2000?
(A) 1:2
(B) 1:3
(C) 2:3
(D) 3:5
(E) 2:1
Rationale: men increase by 13% ==> 1.13M = males in 2001
women decrease by 6% ==> 0.94F = women in 2001
total employees increase by 1.2% ==> 1.012*(M + F) = total number of employees in 2001
Obviously
(males in 2001) + (females in 2001) = total number of employees in 2001
1.13M + 0.94F = 1.012*(M + F)
1.13M + 0.94F = 1.012M + 1.012F
1.13M - 1.012M = 1.012F - 0.94F
0.108M = 0.072F
M/F = (0.072)/(0.118) = 72/118 = 3/5
Answer =(D)
Answer: (D) 3:5
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 320 m long platform?
(A) 44 min
(B) 55 min
(C) 47 min
(D) 67 min
(E) 45 min
Rationale: A
44 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 +320)/ 36 * 5/18 = 44 min.
Answer: (A) 44 min
Question: Two goods trains each 400 m long are running in opposite directions on parallel tracks. Their speeds are 45 km/hr and 30 km/hr respectively. Find the time taken by the slower train to pass the driver of the faster one?
(A) 38.4
(B) 32.6
(C) 48
(D) 27.4
(E) 21
Rationale: Relative speed = 45 + 30 = 75 km/hr.
75 * 5/18 = 125/6 m/sec.
Distance covered = 400 + 400 = 800 m.
Required time = 800 * 6/125 = 38.40 sec.
Answer:A
Answer: (A) 38.4
Question: The banker's gain of a certain sum due 2 years hence at 10% per annum is Rs. 24. The present worth is:
(A) 480
(B) 520
(C) 600
(D) 960
(E) 840
Rationale: T.D. = B.G. x 100 / Rate x Time
= Rs.(24 x 100/10 x 2)= Rs. 120.
P.W. =(100 x T.D./Rate x Time)
= Rs.(100 x 120/10 x 2)= Rs. 600.
Correct answer is C.
Answer: (C) 600
Question: In the rectangular coordinate system, what is the area of triangle CDE with points
C=(5,8)
D=(4,2)
E=(8,0)
(A) 13
(B) 12
(C) 12.8
(D) 14
(E) 20
Rationale: Use the formula of the distance formula
square root (x2-x1)^2+(y2-y1)^2
Do this for each of the sides and then the value is given as A.
Answer: (A) 13
Question: A distributor sells a product through an on-line store, which take a commission of 20% of the price set by the distributor. The distributor obtains the product from a producer at the price of $15 per item. What is the price that the buyer observers on-line if the distributor wants to maintain a 25% profit on the cost of the item?
(A) 18
(B) 21.6
(C) 22
(D) 22.5
(E) 24
Rationale: Producer price = $15;
The distributor wants to maintain a 20% profit on the cost of the item, thus he must get $15*1.2 = $18 after the store takes a commission of 25% of the final price --> (final price)*0.75 = $18 --> (final price) = $24.
Answer: E.
Answer: (E) 24
Question: Which symbol would be exactly at the middle of the fifth symbol from the right and ninth symbol from the left end of the following sequence of symbols ?
& * ∧ % $ # @ + - ! ∼ μ Ω Δ ± ∈ ≈ ∫ → √ ∞ ∧ @ ↓ ≥ ∈ $ + @
(A) +
(B) _
(C) ≈
(D) "
(E) ?
Rationale: Explanation:
& * ∧ % $ # @ + - ! ∼ μ Ω Δ ± ∈ ≈ ∫ → √ ∞ ∧ @ ↓ ≥ ∈ $ + @
The fifth symbol from the right end of the given sequence is “≥”, while the ninth symbol from the left end of the sequence is “-”.
The symbol at the middle of “≥” and “-” is “ ≈ ”.
ANSWER:C
Answer: (C) ≈
Question: In a 1000 m race Usha beats Shiny by 50 m. In the same race, by what time margin Shiny beat Mercy.
who runs at 4 m/s ?
(A) 100 sec.
(B) 50 sec
(C) 25 sec
(D) Data not sufficient
(E) None of these
Rationale: Explanation:
Speed of Shiny = 50/ 10 = 5m/s
Time taken by shiny to complete the race is B = 1000/5 = 200 sec.
Time taken by Baley to complete the race is D = 1000/4 = 250 sec.
Hence, D-B = 50 sec
Answer : B
Answer: (B) 50 sec
Question: The perimeter of a rhombus is 68 cm and one of its diagonals is 16 cm. Find its area?
(A) 299
(B) 240
(C) 277
(D) 266
(E) 121
Rationale: 4a = 68 => a = 17
172 – 82 = 152
1/2 * 16 * 30 = 240
Answer: B
Answer: (B) 240
Question: One fourth of one third of two fifth of a number is 20. What will be40% of that number
(A) A)140
(B) B)150
(C) C)180
(D) D)240
(E) E)220
Rationale: Explanation:
(1/4) * (1/3) * (2/5) * x = 20
then x = 20 * 30 = 600
40% of 600 = 240
Answer: Option D
Answer: (D) D)240
Question: Find the area of a parallelogram with base 24 cm and height 16 cm.
(A) 200
(B) 384
(C) 345
(D) 244
(E) 242
Rationale: Area of a parallelogram = base * height = 24 * 16 = 384 cm2
Answer: Option B
Answer: (B) 384
Question: 18 litres of mixture contains 20% alcohol and the rest water. If 3litres of water be mixed with it, the percentage of alcohol in the new mixture would be?
(A) 16.67%
(B) 17.14%
(C) 18.3%
(D) 19.75%
(E) 21.23%
Rationale: Alcohol in the 18litres of mix. = 20% of 18litres = (20*18/100) = 3.6litres
water in it = 18-3.6 = 14.4litres
new quantity of mix. = 18+3 = 21 litres
Quantity of alcohol in it = 3.6litres
Percentage of alcohol in new mix. = 3.6*100/21 = 17.14%
Answer is B
Answer: (B) 17.14%
Question: a, b, and c are integers and a<b<c. S is the set of all integers from a to b, inclusive. Q is the set of all integers from b to c, inclusive. The median of set S is (3/4)*b. The median of set Q is (6/8)*c. If R is the set of all integers from a to c, inclusive, what fraction of c is the median of set R?
(A)  3/8
(B)  1/2
(C)  11/16
(D)  5/8
(E)  3/4
Rationale: The answer isC: 11/16.
The key to this problem is remembering that the median for a consecutive set of numbers is equivalent to its mean. For example, the mean and median of a set consisting of x, x+1, x+2, ... ,y will always be (x+y)/2.
For set S, consisting of numbers (a, a+1,...,b), the median is given to be 3/4*b:
(a+b)/2 = (3/4)*b
a = b/2
For set Q, consisting of numbers (b, b+1,...,c), the median is given to be 6/8*c:
(b+c)/2 = (6/8)*c
b = (1/2)*c
For set R, consisting of numbers (a, a+1,...c), the median needs to be found:
a = b/2 = (1/2*c)/2 = (1/4)*c
Median = (a + c)/2 = (1/4*c + c)/2 = (5/4)*c/2 = (5/8)*c (ANSWER D)
Answer: (D)  5/8
Question: A jogger running at 9 kmph along side a railway track is 240 metres ahead of the engine of a 120 metre long train running at 45 kmph in the same direction. In how much time will the train pass the jogger?
(A) 3.6 sec
(B) 18 sec
(C) 36 sec
(D) 72 sec
(E) None of these
Rationale: Speed of train relative to jogger
= (45 – 9) km/h = 36 km/h
= (36 × 5⁄18) m/sec = 10 m/sec
Distance to be covered = (240 + 120) m = 360 m.
∴ Time taken = (360⁄10) sec = 36 sec.
Answer C
Answer: (C) 36 sec
Question: A monkey ascends a greased pole 20 meters high. He ascends 2 meters in the first minute and then slips down 1 meter in the alternate minute. If this pattern continues until he climbs the pole , in how many minutes would he reach at the top of the pole ?
(A) 30th minute
(B) 31st minute
(C) 37th minute
(D) 32nd minute
(E) 33th minute
Rationale: The money is climbing 1meter in 2min. This pattern will go on till he reaches 10meters. I mean this will continue for first 18*2=36mins. he would have reached 18meters. After that he will climb 2meters and he will reach the pole. So total time taken = 36 + 1 = 37mins.
So, asnwer will be C
Answer: (C) 37th minute
Question: The area of the square formed on the diagonal of a rectangle as its side is 108 1/3 % more than the area of the rectangle. If the perimeter of the rectangle is 28 units, find the difference between the sides of the rectangle?
(A) 1m
(B) 5m
(C) 8m
(D) 2m
(E) 9m
Rationale: Let the sides of the rectangle be l and b respectively.
From the given data,
(√l2 + b2) = (1 + 108 1/3 %)lb
=> l2 + b2 = (1 + 325/3 * 1/100)lb
= (1 + 13/12)lb
= 25/12 lb
=> (l2 + b2)/lb = 25/12
12(l2 + b2) = 25lb
Adding 24lb on both sides
12l2 + 12b2 + 24lb = 49lb
12(l2 + b2 + 2lb) = 49lb
but 2(l + b) = 28 => l + b = 14
12(l + b)2 = 49lb
=> 12(14)2 = 49lb
=> lb = 48
Since l + b = 14, l = 8 and b = 6
l - b = 8 - 6 =2m.
Answer: D
Answer: (D) 2m
Question: There are 9 baskets numbered from 1 to 9 and filled with apples. 10 children are asked to pick apples one by one from each basket such that the number of apples picked by each child from each basket is equal to the number marked on the basket. If there were 1000 apples in total and the baskets were filled in such a way that none of the basket became empty in the process, how many apples were left in the end?
(A) 440
(B) 550
(C) 660
(D) 770
(E) 880
Rationale: Each child takes a total of 1+2+3+4+5+6+7+8+9 = 9*10/2 = 45 apples.
The total number of apples taken by 10 children is 10*45 = 450
The number of apples left in the end is 1000 - 450 = 550 apples.
The answer is B.
Answer: (B) 550
Question: A man sells an article at a gain 15%. If he had bought it at 10% less and sold it for 5 less, he would have gained 25%. Find the cost price of the article.
(A) 150
(B) 160
(C) 170
(D) 180
(E) 200
Rationale: Let the C.P. be 100
First S.P. = 115
Second C.P. = 90
Second S.P = 125% of 90 = 112.50
Difference of two selling prices is 115 – 112.50 = 2.50 and C.P. of the article is 100
But actual difference is 5.
∴ C.P. = 100⁄2.50 × 5 = 200.
Answer E
Answer: (E) 200
Question: A certain plant was 11 feet long on the day it was plantedthe length grows by a constant amount everyday(inc. the first day it was planted).
if this plant grew by 60% b/w the 4th day and 10 th day after it was planted ,how many feet per day does the plant grow
(A) a) 2
(B) b) 4.5
(C) c) 1.83
(D) d) 5.5
(E) e) 3
Rationale: If the plant is 11 feet tall when it is planted, it will be 11 + k feet tall at the end of the day (where k is the constant length it grows by every day).
Similarly, at the end of the 4th day the plant must be 11 + 4k feet tall and at the end of the 10th day it must be 11 + 10k feet tall.
Therefore 6k = 0.6 (11 + 4k)
=> k = 1.83
Therefore the plant grows by 1.83 feet every day.
Option (C)
Answer: (C) c) 1.83
Question: The equation y = ax*b* + c produces the
following (x, y) coordinate pairs: (0, 2),
(1, 7), and (2, 42). What is the value of abc?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 60
Rationale: To begin, plug x = 0 and y = 2 into the equation y = axb + c. Note that the first term
drops out:
2 = a(0)b + c
2 = c
Now you can substitute 2 for c in the original equation, giving you y = axb + 2. Next, plug in
x = 1 and y = 7. Notice that everything drops out except for the coefficient of the first term:
7 = a(1)b + 2
5 = a
You can now substitute 5 for a in the equation, giving you y = 5xb + 2. Now plug in x = 2
and y = 42:
42 = 5(2)b + 2
40 = 5(2)b
8 = 2b
23 = 2b
3 = b
Finally, you can see that abc = (5)(3)(2) = 30.
correct answer C)30
Answer: (C) 30
Question: What is the units digit of 18! + 4!?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: Check if there are trailing zeroes
4! /5 = Not divisible , hence there must be a numeric value of the units digit which is non zero
Calculate it 4! = 4*3*2*1 =>24
18! /5 is divisible m so it will have trailing zeroes
18! = Has units digit as 0
4! = Has units digit 4
So, Units digit of 18! + 4! will be 4
ANSWER:E
Answer: (E) 4
Question: Sheela deposits Rs. 3800 in bank savings account. If this is 22% of her monthly income. What is her monthly income in?
(A) 22000
(B) 20000
(C) 25123
(D) 17272
(E) None of these
Rationale: Explanation :
22% of income = Rs. 3800
100% of income = 3800 X 100/22 = Rs. 17272
Answer : D
Answer: (D) 17272
Question: Three distinct single digit no A,B and c are in G.M ,if abs(x) for real x is the absolute value of x(x , if x is positive or zero,and -x if x is negative), then the number of different possible values of abs (A+B -C) is;
(A) 3
(B) 6
(C) 5
(D) 4
(E) 1
Rationale: 1,2,4
2,4,8
4,2,1
8,4,2
1,3,9
9,3,1
total=6
ANSWER:B
Answer: (B) 6