mathewhe/aqua_rat huggingface dataset:
Question: A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?
(A) 9
(B) 14
(C) 25
(D) 30
(E) 44
Rationale: Since we need to find only an approximate value and the answer choices are quite widespread, then use:
80% instead of 82% (notice that this approximation gives the bigger tank capacity);
140 billion gallons instead of 138 billion gallons (notice that this approximation also gives the bigger tank capacity);
130 billion gallons instead of 124 billion gallons;.
Notice that the third approximation balances the first two a little bit.
So, we'll have that: capacity∗0.8=140 --> capacity=140/0.8=175
Hence, the amount of water the reservoirs were short of total capacity prior to the storm was approximately 175−130=45 billion gallons.
Answer: E.
Answer: (E) 44
Question: Two trains T1 and T2 start simultaneously from two stations X and Y respectively towards each other. If
they are 70 km apart both 3 and 6 hours after start, then find the distance between the two stations.
(A) 210 km
(B) 240 km
(C) 220km
(D) 180km
(E) 200km
Rationale: In first 3 hours T1 travels R km and T2 travels S km.
After 6 hours they traveled R+S+70+ 700
2(R+S ) = R+S +140
R+S = 140
Hence distance between XY is R+S+ 70 = 140 +70 =210
Answer : A
Answer: (A) 210 km
Question: A ranch has both horses and ponies. Exactly 3/10 of the ponies have horseshoes, and exactly 5/8 of the ponies with horseshoes are from Iceland. If there are 3 more horses than ponies, what is the minimum possible combined number of horses and ponies on the ranch?
(A) 130
(B) 141
(C) 152
(D) 163
(E) 174
Rationale: 3/10*P are ponies with horseshoes, so P is a multiple of 10.
5/8*3/10*P = 3/16*P are Icelandic ponies with horseshoes, so P is a multiple of 16.
The minimum value of P is 80. Then H = P+3 = 83.
The minimum number of horses and ponies is 163.
The answer is D.
Answer: (D) 163
Question: The ratio of cats to dogs to birds to fish is 8:9:10:11. There are no other types of animals in the pet store. which of the followingcannotbe the total number of animals in the store?
(A) 76
(B) 114
(C) 152
(D) 190
(E) 345
Rationale: The parts add up to 8 + 9 + 10 + 11 = 38, so we know that any possible number of total answers must be a multiple of 38. All five answer choices are multiples of 38:
(A) 76= 38*2
(B) 114= 38*3
(C) 152= 38*4
(D) 190= 38*5
(E) 345= not a multiple of 38
Answer: (E) 345
Question: The value of a stock is Y dollars. On Sunday the stock's value grew by half of its value, but on Monday its value dropped to a third of its new value. What is the stock's value at the end of Monday?
(A) Y.
(B) Y/2.
(C) 2Y/3.
(D) Y/3.
(E) Y/4.
Rationale: Stock value= Y
AT sunday end= y+.5Y= 1.5 Y
On monday the value drop to 1/3rd of its value on sunday
1.5y/3= .5y= Y/2
B is the answer
Answer: (B) Y/2.
Question: Find the missing number of the following series?
16 8 24 12 36 18 54 ? 81
(A) 27
(B) 28
(C) 29
(D) 26
(E) None
Rationale: Solution:
27
Explanation:
16/2 = 9
8*3 = 24
24/2 = 12
12*3 = 36
36/2 = 18
18*3 = 54
54/2 = 27
27*3 = 81
Answer A
Answer: (A) 27
Question: The volumes of two cones are in the ratio 1 : 10 and the radii of the cones are in the ratio of 1 : 2. What is the length of the wire?
(A) 2:5
(B) 2:9
(C) 2:2
(D) 2:2
(E) 2:8
Rationale: The volume of the cone = (1/3)πr2h
Only radius (r) and height (h) are varying.
Hence, (1/3)π may be ignored.
V1/V2 = r12h1/r22h2 => 1/10 = (1)2h1/(2)2h2
=> h1/h2 = 2/5
i.e. h1 : h2 = 2:5
Answer: A
Answer: (A) 2:5
Question: Benny goes to the market for buying some apples to be distributed between her nine kids equally.She takes 360 dollars with her .The cost of each apple is 2 dollars .How many apples does she buy to share them equally between her six kids?
(A) 8
(B) 30
(C) 3
(D) 7
(E) 10
Rationale: cost of each apple = 2 dollars
Apples that Benny can buy with the amount she has=360/2 = 180.
Apples that each kid gets evenly = 180/6 =30 Apples.
So the answer is B=30
Answer: (B) 30
Question: If the sum and difference of two numbers are 10 and 19 respectively, then the difference of their square is:
(A) 12
(B) 28
(C) 160
(D) 180
(E) 190
Rationale: Let the numbers be x and y.
Then, x + y = 10 and x - y = 19
x2 - y2 = (x + y)(x - y) = 10 * 19 = 190.
ANSWER:E
Answer: (E) 190
Question: If 13 = 13w/(1-w) ,then (w)2 =
(A) 1/4
(B) 1/2
(C) 1
(D) 2
(E) 3
Rationale: 13-13w=13w
26w=13
w=1/2
2w*2=1/2*2=1
ANSWER:C
Answer: (C) 1
Question: a^(-4x/3) = a^-4
What is the value of x ?
(A) 2
(B) 3
(C) -1
(D) -4
(E) -2/3
Rationale: -4x/3 = -4
-4x = -12; x= 3
Ans: B
Answer: (B) 3
Question: From a bunch of seven keys, three particular keys have to be used to open a combination lock, such that the second key can be used only after the first key and the third key can be used only after the second key. What are the chances of opening the lock in a random selection of three keys?
(A) 1/20
(B) 1/70
(C) 1/140
(D) 1/210
(E) 1/350
Rationale: The probability is 1/7*1/6*1/5 = 1/210.
The answer is D.
Answer: (D) 1/210
Question: If A:B = 2:3 and B:C = 4:5 then A:B:C is
(A) 2:3:5
(B) 5:4:6
(C) 8:12:15
(D) 6:4:5
(E) none
Rationale: Solution:
A/B = 2/3;
B/C = 4/5;
A:B:C = 2*4:3*4:3*5 = 8:12:15.
Answer: Option C
Answer: (C) 8:12:15
Question: One half of a two digit number exceeds its one fourth by 3. What is the sum of the digits of the number?
(A) 3
(B) 9
(C) 11
(D) 12
(E) 15
Rationale: Explanation:
x/2 – x/4 = 3 => x =12
1 + 2 = 3
A
Answer: (A) 3
Question: If a coin is flipped, the probability that the coin will land heads is 1/2. If the coin is flipped 5 times, what is the probability that it will land tails up on the first 4 flips and not on the last flip?
(A) 1/8
(B) 1/32
(C) 1/4
(D) 1/2
(E) 1/16
Rationale: (1/2) * (1/2) * (1/2) * (1/2) * (1/2) = 1/32 Answer: B
Answer: (B) 1/32
Question: A FIVE DIGIT NUMBER IS FORMED BY USING THE DIGITS 0,1,2,3,4 WITH OUT REPETITIONS . WHAT IS THE PROBABILITY THE NUMBER IS DIVISIBLE BY4?
(A) 1/5
(B) 5/6
(C) 2/5
(D) 7/3
(E) 2/7
Rationale: If a number is divisible by 4 the last 2 digits of the number has to be divisible by 4.
If the number ends with 10: Number of possibilities = 3 * 2 * 1 = 6
number ends with 20: Possibilities = 3 * 2 * 1 = 6
number ends with 30: Possibilities = 6
number ends with 12: Possibilities = 6
number ends with 14: Possibilities = 6
number ends with 32: Possibilities = 6
number ends with 34: Possibilities = 6
number ends with 24: Possibilities = 6
Total number of possibilities with restriction = 6*8 = 48
Total number of possibilities without restriction = 5! = 120
Probability = 48/120 = 2/5
Answer: C
Answer: (C) 2/5
Question: How many 4 digit numbers can be formed with the digits 0, 1, 2, 3, 4, 5, 6 and 2?
(A) a. 220
(B) b. 249
(C) c. 432
(D) d. 216
(E) e. 288
Rationale: Taking Question with it's same language as given
To make number divisible by 5, the unit digit should be either 0 or 5 only
Case 1: If unit digit is fixed as zero
With two6s The choice to fill the remaining three digits = 3C2 x 5 = 15
With all remaining 3 digits different, The choice to fill the remaining three digits = 6 x 5 x 4= 120
Total Such cases = 120+15 = 135
Case 2: If unit digit is fixed as Five
With two6s and one0The choice to fill the remaining three digits = 2 [6605 or 6065]
With two6s and without0The choice to fill the remaining three digits = 3C2 x 4 = 12
With all remaining 3 digits different, and one0The choice to fill the remaining three digits = 2 (ways to place zero) x 5 x 4= 40
With all remaining 3 digits different, and without0The choice to fill the remaining three digits = 3 x 5 x 4= 60
Total Such cases = 2+12+40+60 = 114
Total numbers = 135+114 = 288
ANSWER OPTION E
Answer: (E) e. 288
Question: Sum of two numbers prime to each other is 15 and their L.C.M. is 56. What are the numbers?
(A) 9 and 8
(B) 5 and 10
(C) 7 and 9
(D) 7 and 8
(E) 10 and 8
Rationale: As two numbers are prime, only options satisfy ie option A and D and C
but option D will make the product of numbers i.e 56
ANSWER:D
Answer: (D) 7 and 8
Question: If A speaks the truth 75% of the times, B speaks the truth 60% of the times. What is the probability that they tell the truth at the same time
(A) 0.49
(B) 0.48
(C) 0.45
(D) 0.482
(E) 0.411
Rationale: Explanation:
Probability that A speaks truth is 75/100 = 0.75
Probability that B speaks truth is 60/100 = 0.6
Since both A and B are independent of each other
So probability of A intersection B is P(A) × P(B) =0.75 × 0.6 = 0.45
Answer: C
Answer: (C) 0.45
Question: The salary of Mr. X is 30% more than that of Mr. Y . Find what percent of Mr. Y’s salary is less than Mr. X’s?
(A) 23 1/8%
(B) 23 7/3%
(C) 23 1/3%
(D) 23 1/3%
(E) 53 3/3%
Rationale: y=100	x=130
130---------30
100---------? => 23 1/3%
Answer:C
Answer: (C) 23 1/3%
Question: A bag of potatoes weighs 50 lbs divided by half of its weight. How much does the bag of potatoes weight?
(A) 20 lb
(B) 30 lb
(C) 10 lb
(D) 15 lb
(E) 5 lb
Rationale: Sol.
50÷5 = 10.
Answer : C
Answer: (C) 10 lb
Question: If xy > 0, which of the following must be negative?
(A) -x/y
(B) xy
(C) x/y
(D) 2xy
(E) 2x/y
Rationale: - / + = -
Answer : A
Answer: (A) -x/y
Question: The length of the bridge, which a train 140 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
(A) 200 m
(B) 235 m
(C) 245 m
(D) 250 m
(E) 270 m
Rationale: Let the length of the bridge:L
The equation now is L+140/12.5m/s(45km/hr or12.5m/s)=30
Solving, L =235m
ANSWER:B
Answer: (B) 235 m
Question: Which is a better investment 5% stock at 412 or 3 3/2 stock at 360?
(A) 5% stock at 412
(B) Both are equally good
(C) Cannot be compared, as the total amount of investment is not given
(D) None
(E) 3 3/2 stock at 360
Rationale: Let investment in each case be Rs. (412 x 360).
Income in 1st case = Rs.5 x 412 x 360/412	= Rs. 1800.
Income in 2nd case = Rs.9 x 412 x 360/(2*117)	= Rs. 5704.6
Clearly, 3 3/2 stock at 360 is better.
ANSWER:E
Answer: (E) 3 3/2 stock at 360
Question: A, B and C started a business with capitals of Rs. 8000, Rs. 10000 and Rs. 12000 respectively. At the end of the year, the profit share of B is Rs. 1900. The difference between the profit shares of A and C is?
(A) 288
(B) 760
(C) 155
(D) 600
(E) 441
Rationale: Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6
And also given that, profit share of B is Rs. 1900
=> 5 parts out of 15 parts is Rs. 1900
Now, required difference is 6 - 4 = 2 parts
Required difference = 2/5 (1900) = Rs. 760
Answer:B
Answer: (B) 760
Question: 66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length if the wire in meters will be:
(A) 76 m
(B) 80 m
(C) 84 m
(D) 88 m
(E) 90 m
Rationale: Explanation:
Let the length of the wire be h
Radius=1/2mm=1/20cm
πr2h=66
(22/7)*(1/20)*(1/20)*h=66
=>h=(66∗20∗20∗7) / 22
=8400cm
=84m
ANSWER IS C
Answer: (C) 84 m
Question: 4 professors and 6 students are being considered for membership on a supervisory committee which must consist of 3 people. If the committee has to include at least 1 professor, how many ways can this committee be formed?
(A) 36
(B) 60
(C) 72
(D) 80
(E) 100
Rationale: combinations:
1 professor 2 students
students: 6 x 5 / 2 = 15
15*4 = 60
2 professors 1 student
4 x 3 / 2 = 6
6*6 = 36
3 professors
4/1 = 4
60 + 36 + 4 = 100
ANS:E
Answer: (E) 100
Question: A,B,C together can do a work in 8 days. A alone can do the work in 30 days and B alone can do the same work in 20 days. Find in what time C alone can do that work?
(A) 16days
(B) 20.8days
(C) 24days
(D) 28.5days
(E) 32.4days
Rationale: The required answer is = 8*30*20 / 30*20-8(30+20)
= 4800/200 = 24days
Answer is C
Answer: (C) 24days
Question: Find the value of 72519 x 9999 = m?
(A) 345466221
(B) 345455672
(C) 353456678
(D) 725117481
(E) 789545233
Rationale: 72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
D
Answer: (D) 725117481
Question: The compound interest on $ 30,000 at 7% per annum is $4347. The period (in years) is:
(A) 2
(B) 21/2
(C) 3
(D) 4
(E) 5
Rationale: Amt = $(30000+4347) = $34347
let the time be n yrs then 30000(1+7/100)^n=34347
(107/100)^n=34347/30000=(107/100)^2
n = 2 yrs
ANSWER A
Answer: (A) 2
Question: It is known that no more than 8 children will be attending a party. What is the smallest number of cookies that must be brought to the party so that each child receives the same number of cookies?
(A) 35
(B) 105
(C) 180
(D) 210
(E) 840
Rationale: The question states that there are no more than 8 children in the party. Thus, the possibility is that there could be 1, 2, 3, 4, 5, 6,7 or 8 children.
If you assume answer as 35 and there are 3 children, you may not distribute be able to distribute cookies equally.
similarly if there were 105 cookies, and 2 children, cookies cannot be distributed equally.
or if there were 210 cookies, and 4 children, cookies cannot be distributed equally.
Thus, the question asks for a number of cookies which can be distributed to any number of children (from 1 to 8).
And therefore the smallest number of cookies would be lcm of (1, 2, 3, 4, 5, 6, 7,8), i.e., 840.
Answer (E)
Answer: (E) 840
Question: A, B and C rents a pasture for Rs.435. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
(A) 120
(B) 227
(C) 268
(D) 198
(E) 176
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
8/29 * 435 = 120
Answer:A
Answer: (A) 120
Question: Of all the students in a certain dormitory, 1/2 are first-year students and the rest are second-year students. If 4/5 of the first-year students have not declared a major and if the fraction of second-year students who have declared a major is 1 times the fraction of first-year students who have declared a major, what fraction of all the students in the dormitory are second-year students who have not declared a major?
(A) 1/15
(B) 1/5
(C) 4/15
(D) 1/3
(E) 2/5
Rationale: tot students=x
1st year student=x/2----> non majaor=4/5(x/2)-----> maj=1/5(x/2)
2nd year student=x/2---->maj=1(1/5(x/2))=1/10(x)--->non major=x/2-1/10(x)=2/5(x)
hence 2/5
E
Answer: (E) 2/5
Question: Mother is aged thrice than her daughter Silvia. After 8 years, he would be 2(1/2) times of Silvia’s age. After 8 years, how many times would she be of Silvia’s age?
(A) 2 years
(B) 4 years
(C) 3 years
(D) 5 years
(E) 6 years
Rationale: A
2 years
Let Silvia’s current age is A years.
Then, mom’s current age = (A + 3A) years = 4A years.
(4A + 8) = (5/2) (A + 8)
=> 8A + 16 = 5A + 40
=> 3A = 24
A = 8
Needed ratio = { (4A + 16)/(A+16) }
= 48/24
= 2
Answer: (A) 2 years
Question: One fish tank is half full. After adding 10 gallons the tank is 7/8 of the tank. Calculate the capacity of the fish tank.
(A) 80/3 gallons
(B) 90/3 gallons
(C) 70/3 gallons
(D) 60/3 gallons
(E) 50/3 gallons
Rationale: If x is capacity of full tank, then
x*(7/8-1/2) =10
x*3/8=10
x= 80/3 gallons
ANSWER:A
Answer: (A) 80/3 gallons
Question: Raji,Lakshmi and Priya enter into partnership. Raji invests some money at the beginning, Lakshmi invests double the amount after 6 months, and Priya invests thrice the amount after 8 months. If the annual gain be Rs.12000. Priya's share is?
(A) 2500
(B) 3500
(C) 4500
(D) 2800
(E) 4000
Rationale: x* 12 : 2x* 6: 3x* 4
1:1:1
1/3 * 12000 = 4000
Answer: E
Answer: (E) 4000
Question: Present ages of X and Y are in the ratio 5:6 respectively. Seven years hence this ratio will become 6:7 respectively. What is X's present age in years?
(A) 35 years
(B) 77 years
(C) 55 years
(D) 44 years
(E) 33 years
Rationale: Let the present ages of X and Y be 5x and 6x years respectively.
Then, (5x + 7)/(6x + 7) = 6/7
7(5x + 7) = 6(6x + 7) => x = 7
X's present age = 5x = 35 years.Answer: A
Answer: (A) 35 years
Question: In how many different number of ways a Committee of 3person of can be selected from 4boys and 3girls such that at least 1 girl is included in the committe
(A) 30
(B) 29
(C) 31
(D) 17
(E) 85
Rationale: 1G 2B 2G 1B 3G
=(3C1*4C2)+(3C2*4C1)+3C3
=(3*6)+(3*4)+1
=18+12+1=31
Total 4M 3W
7C3=35
4C3=4
At least one girl = total - with out girl
At least one girl =35-4=31
C)
Answer: (C) 31
Question: The area of a parallelogram is 1764sq m and its base is nine times size of the corresponding altitude. Then the length of the base is?
(A) 21
(B) 9
(C) 11
(D) 14
(E) 7
Rationale: 9x * x = 1764 => x
= 14
Answer: D
Answer: (D) 14
Question: In order to fence a square Manish fixed 48 poles. If the distance between two poles, is 3 metres then what will be the area of the square so formed?
(A) Cannot be determined
(B) 2600 cm2
(C) 2500 cm2
(D) 1296 cm2
(E) None of these
Rationale: Let the side of the square be x m.
∴ Perimeter of the square = 48 × 3 = 4x ∴ x = 36 m
∴ Area = (36)2 = 1296 m2
Answer D
Answer: (D) 1296 cm2
Question: After decreasing 20% in the price of an article costs Rs.200. Find the actual cost of an article?
(A) 280
(B) 250
(C) 260
(D) 270
(E) 300
Rationale: CP* (80/100) = 200
CP= 2.5* 100 => CP = 250
Answer: B
Answer: (B) 250
Question: During a certain two-week period, 76 percent of the movies rented from a video store were comedies, and of the remaining movies rented, there were 5 times as many dramas as action movies. If no other movies were rented during that two-week period and there were A action movies rented, then how many comedies, in terms of A, were rented during that two-week period?
(A) 16A
(B) 19A
(C) 17A
(D) 18A
(E) 20A
Rationale: Total movies = 100.
Comedies = 76.
Action + Drama = 24. Since there were 5 times as many dramas as action movies, then Action + 5*Action = 24 --> Action = A = 4.
Comedies = 76 = 19A.
Answer: B.
Answer: (B) 19A
Question: A store sells branded shirts for $20 each and unbranded shirts $16 each. On every branded shirt, the store makes a profit of $6 while on every unbranded shirt it makes a profit of $4. If on a given day the store's sales amounted to $960, which of the following cannot be the profit made on that day?
(A) $264
(B) $268
(C) $270
(D) $272
(E) $276
Rationale: $270 is the only option that does not satisfy a combination of integer number sales of branded and unbranded shirts sales. Answer: C
Answer: (C) $270
Question: A fruitseller sells mangoes at the rate of Rs.9 per kg and thereby loses 20%.At what price per kg,he should have sold them to make a profit of 5% ?
(A) Rs.11.81
(B) Rs.12
(C) Rs.12.25
(D) Rs.12.31
(E) None
Rationale: Solution
80 : 9 = 105 : x or x =(9x105/80) = 11.81.
Hence, S.P. per kg. = Rs.11.81.
Answer A
Answer: (A) Rs.11.81
Question: A motorcyclist goes from Bombay to Pune, a distance of 192 kms at an average of 32 kmph speed. Another man starts from Bombay by car 2 ½ hours after the first, and reaches Pune ½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
(A) 3:5
(B) 4:5
(C) 2:5
(D) 2:4
(E) 2:7
Rationale: T = 160/32 = 5 h
T = 5 - 3 = 2
Time Ratio = 5:2
Speed Ratio = 2:5
ANSWER:C
Answer: (C) 2:5
Question: A shipment of 1500 heads of cabbage, each of which was approximately the same size was purchased for $600.The day the shipment arrived 2/3 of the heads were sold, each at 25% above the cost per head.The following day the rest were sold at a price per head equal to 10% less than the price each head sold for the day before.what was the gross profit E on this shipment?
(A) a) $100
(B) b) $115
(C) c) $125
(D) d) $130
(E) e) $135
Rationale: I recommend one should use fractions to solve this one rather than converting it into decimals
Sol:
1500 heads -> $600
1 head -> $600/1500
1 head -> $(2/5)
25% more of (2/5) -> 125/100 * 2/5 = $(1/2)
He sold 2/3*1500 = 1000 heads for $(1/2) per head
Total revenue by selling 1000 heads = 1000 * 1/2 = $500
Heads left: 500
Cost per head: 90% of the previous price: 90/100 * 1/2 = $(9/20)
Total revenue by selling 500 heads = 9/20 * 500 = 225
Total revenue after selling 1500 cabbage heads - 225+500 = $725
Money spent on the purchase: $600
Profit E= 725-600 = $125
Ans:C
Answer: (C) c) $125
Question: The sum of first five prime numbers is:
(A) 28
(B) 72
(C) 55
(D) 33
(E) 58
Rationale: A
Required sum = (2 + 3 + 5 + 7 + 11) = 28.
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.
Answer: (A) 28
Question: The circumference of a circle is equal to 72 pi. Find the radius of this circle.
(A) 35
(B) 36
(C) 37
(D) 38
(E) 39
Rationale: The circumference of a circle is given by
C = 2 pi r, where r is the radius of the circle.
Substitute C by 72 pi to obtain the equation
72 pi = 2 pi r
Simplify and solve for r to obtain
r = 36
Answer B
Answer: (B) 36
Question: There are three numbers. 5/7th of the first number is equal to 48% of the second number. The second number is 1/9th of the third number. If the third number is 1125, then find 25% of the first number?
(A) 16
(B) 18
(C) 12
(D) 21
(E) 10
Rationale: Let the first number and the second number be F and S respectively.
5/2 F = 48/100 S ----> (1)
S = 1/9 * 1125 = 125
(1) => 5/7 F = 48/100 * 125
=> F = 84
25% of F = 1/4 * 84 = 21.
Answer: D
Answer: (D) 21
Question: A rectangular field has to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?
(A) 80
(B) 82
(C) 84
(D) 88
(E) 86
Rationale: Area of the field =680 sq. feet.
Length of the adjacent sides are
20 feet and 68020=34 feet.
Required length of the fencing
=20+34+34=88 feet
Answer is D.
Answer: (D) 88
Question: Anil purchases two books for Rs.100. He sells first at loss of 5% and second al 20% profit. If he gets Overall profit of 5% then what is cost of first book?
(A) Rs.45
(B) Rs.60
(C) Rs.55
(D) Rs.58
(E) Rs.56
Rationale: If cost of first book=x then second book=100-x
According to given condition x*(95/100) + (100-x)*(120/100) =100*(105/100) or
0.95x +120 -1.2x=105
x=60
ANSWER:B
Answer: (B) Rs.60
Question: A group of boy scouts and girls scouts is going on a rafting trip. 80% of the scouts arrived with signed permission slips. If 40% of the scouts were boy scouts and 75% of the boy scouts arrived with signed permission slips, then what percentage of the girl scouts arrived with signed permission slips? Round to the nearest percent.
(A) 79
(B) 81
(C) 82
(D) 83
(E) 85
Rationale: 40% were boy scouts so 60% (100-40=60) were girl scouts.
# of boy scouts with permission slips signed + # of girl scouts with permission slips signed = total # with permission slip signed
(75% of 40% of the total going) + (?% of 60% of the total going) = 80% of the total going
We can let the "total going" = 100 arbitrarily since we only care about the percent (of girl scouts w/ permission signed)
.75*.40*100 + x*.60*100 = .80*100
30 + x*60 = 80
60x=50
x=50/60
x=.833333
converting this to a percent, we have 83%
D
Answer: (D) 83
Question: Ifaequals the sum of the even integers from 2 to 20, inclusive, andbequals the sum of the odd integers from 1 to 19, inclusive, what is the value of a + b ?
(A) 110
(B) 100
(C) 190
(D) 200
(E) 210
Rationale: Answer is 10
Yes! there is really a faster way to solve it.
Sum of consecutive odd or even integers = (no. of odd or even ints) * (first int + last int) / 2
Here A = sum of even ints from 2 to 20, inclusive
number of even ints = 10,
first int + last int = 2+20 = 22
A = 10*22 / 2 = 110
B = sum of odd ints from 1 to 19, inclusive
number of odd ints = 10,
first int + last int = 1+19 = 20
A = 10*20 / 2 = 100
A+B = 110 + 100 = 210
Ans :E
Answer: (E) 210
Question: We bought 85 hats at the store. Blue hats cost $6 and green hats cost $7. The total price was $540. How many green hats did we buy?
(A) A)36
(B) B)30
(C) C)40
(D) D)42
(E) E)44
Rationale: Let B be the number of blue hats and let G be the number of green hats.
B+G=85.
B=85-G.
6B+7G=540.
6(85-G)+7G=540.
510-6G+7G=540.
G=540-510=30.
The answer is B.
Answer: (B) B)30
Question: If a man can cover 12 metres in one second, how many kilometres can he cover in 3 hours 45 minutes?
(A) 157
(B) 162
(C) 882
(D) 155
(E) 101
Rationale: 12 m/s = 12 * 18/5 kmph
3 hours 45 minutes = 3 3/4 hours = 15/4 hours
Distance = speed * time = 12 * 18/5 * 15/4 km
= 162 km.
Answer: B
Answer: (B) 162