mathewhe/aqua_rat huggingface dataset:
Question: A man buys a field of agricultural land for Rs. 3,60,000. He sells one-third at a loss of 20% and two-fifths at a gain of 25%. At what price must he sell the remaining field so as to make an overall profit of 10%?
(A) Rs.1,00,000
(B) Rs. 1,15,000
(C) Rs. 1,20,000
(D) Rs. 1,25,000
(E) None of these
Rationale: Solution: First Method
CP = 3600000.
To gain 10% on whole land, SP = 360000 + 10% of 360000 = Rs. 396000.
1/3 of the land sold on 20% loss.
SP of 1/3 land = (360000/3) - 20% of (360000/3) = Rs. 96000.
SP of 2/5 of the land = (360000 * 2)/5 + 25% of (360000*2)/5 = Rs. 180000.
Thus, SP of the remaining land = 396000 - 96000 - 180000 = Rs. 120000.
Answer: Option C
Answer: (C) Rs. 1,20,000
Question: Two pens and three pencils cost $86. four Pens and a pencil cost $112. find the cost of a pen and that of a pencil.
(A) 25, 12
(B) 12, 30
(C) 30, 45
(D) 50, 48
(E) 15, 25
Rationale: Let the cost of a pen and a pencil be $ X and $ Y respectively.
Then, 2x + 3y = 86 ….(i) and 4x + y =112.
Solving (i) and (ii), we get: x = 25 and y = 12.
Cost of a pen =$ 25 and the cost of a pencil =$ 12.
Answer A.
Answer: (A) 25, 12
Question: Which interchange of signs will make the following equation correct ?
35 + 7 × 5 ÷ 5 – 6 = 24
(A) 24
(B) 23
(C) 22
(D) 26
(E) 28
Rationale: A
24
35 ÷ 7 × 5 +5 – 6 = 24
5 × 5 + 5 – 6 = 24
25 – 1 = 24
24 = 24
Answer: (A) 24
Question: Two students appeared at an examination. One of them secured 9 marks more than the other and his marks was 56% of the sum of their marks. What are the marks obtained by them?
(A) 42, 33
(B) 44, 36
(C) 44, 38
(D) 45, 40
(E) 44, 48
Rationale: Let the marks secured by them be x and (x + 9)
Then sum of their marks = x + (x + 9) = 2x + 9
Given that (x + 9) was 56% of the sum of their marks
=>(x+9) = 56/100(2x+9)
=>(x+9) = 14/25(2x+9)
=> 25x + 225 = 28x + 126
=> 3x = 99
=> x = 33
Then (x + 9) = 33 + 9 = 42
Hence their marks are 33 and 42
Option 'A'
Answer: (A) 42, 33
Question: At what price must an Book costing $47.50 be marked in order that after deducting 15% from the list price. It may be sold at a profit of 25% on the cost price?
(A) 72.85
(B) 69.85
(C) 62.85
(D) 82.85
(E) 60.85
Rationale: C
$62.50
CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(85/100) = 59.375
MP = 69.85
B
Answer: (B) 69.85
Question: The simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 85 and Rs. 80 respectively. The sum is:
(A) 1360
(B) 1450
(C) 1600
(D) 1800
(E) None
Rationale: Sol.
Sum = S.I. * T.D. / (S.I)-(T.D.) = 85 * 80 / (85 - 80) = Rs.1360.
Answer A
Answer: (A) 1360
Question: Louie takes out a three-month loan of $2000. The lender charges him 10% interest per month compounded monthly. The terms of the loan state that Louie must repay the loan in three equal monthly payments. To the nearest dollar, how much does Louie have to pay each month?
(A) A)333
(B) B)383
(C) C)402
(D) D)433
(E) E)804
Rationale: Here's the calculation for that case, assume monthly payment is X.
After 1st month: (2000)(1.1)-X = 2200-X
After 2nd month: (2200-X)(1.1)-X = 2420-2.21X
After 3rd month: (2420-2.21X)(1.1)-X = 2662-3.31X
Now, the amount after the last payment in 3rd month must bring the total to 0. Hence:
2662-3.31X = 0
X = 2662/3.31 = 804
Answer E
Answer: (E) E)804
Question: If r=1 and (r-b)/c = 1 which of the following is NOT a possible value of b?
(A) -2
(B) -1
(C) 0
(D) 1
(E) 2
Rationale: Equation is:
(r-b)/c = 1 where r = 1
so plug in 1 for r and look at it again
(1-b)/c = 1
now C can be anything we want, so if b = -2 we can plug it in and make it work
(1-(-2))/c = 1
3/c = 1
c = 3 and it works
HOWEVER, if we have a 0 in the numerator there isn't a number on earth that makes 0/C = 1
(1-1)/c = 1
0/c = 1
there aren't any matches for C to make this true
B cannot be 1.
Answer is D
Answer: (D) 1
Question: A bag consists of 1 rupee, 50 paise and 25p coins and their total value in rupees is Rs 1120 .These three types of coins are in the ratio 3:20:4. How may 25 paisa coins are there?
(A) 30 coins
(B) 330 coins
(C) 320 coins
(D) 32 coins
(E) 10 coins
Rationale: The ratio is 100p: 50 p : 25 p =4 : 2: 1
The coins are in the ratio = 3 :20: 4
The ratio of their values in rupees=> 12 :40 :4
The value of 25 p coins in total Rs 1120 = 1120 x 4/56= 80 rupees
Number of 25 p coins are = 80x4 = 320 coins
Answer:C
Answer: (C) 320 coins
Question: Anintegratedteam consists of 2 members from the engineering team and 2 members from the design team. If the engineering team has 8 members and the design team has 6 members, how manyintegratedteam formations are possible?
(A)  36
(B)  54
(C)  176
(D)  220
(E)  360
Rationale: 2 out of 8 times 2 out of 6 => 8*7/2*1 * 6*5/2*1 = 360
E
Answer: (E)  360
Question: In a certain store, the profit is 320% of the cost. If the cost increases by 25% but the selling price remains constant, approximately what percentage of the selling price is the profit?
(A) 30%
(B) 70%
(C) 100%
(D) 250%
(E) 300%
Rationale: cp = 100
profit = 320 ans SP = 420
new CP = 125% of RS 100 = Rs 125
New SP = 420
profit = (420-125) = 295
req % (295/420*100)% = 1475/21% = 70%
ANSWER B
Answer: (B) 70%
Question: Tn = 2Tn-1 + 4 and Qn = 4Qn-1 + 8 for all n > 1. If T5 = Q4 and T7 = 316, what is the first value of n for which Qn is an integer?
(A)  1
(B)  2
(C)  3
(D)  4
(E)  5
Rationale: Assuming I have understood the symbols used correctly answer is C- 3
T7 = 2S6 +4 = 316
T6 = 312/2 = 156 = 2T5 + 4
T5 = 152/2 = 76 = Q4
Q4 = 4Q3 + 8 = 76
Q3 = 68/4 = 17
Q3 = 4Q2 + 8 = 17
Q2 = 9/4 = 2.25
Q2 = 4Q1 + 8
Q1 will not be integer
Answer: (C)  3
Question: A train 55 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) 4 sec
(D) 6 sec
(E) 3 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
= [55 * 3/55] sec
= 3 sec
Answer:E
Answer: (E) 3 sec
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that exactly three bulbs are good?
(A) 20/69
(B) 20/63
(C) 20/62
(D) 20/29
(E) 20/61
Rationale: Required probability
= (⁵C₃ . ⁴C₁)/⁹C₄
= (10 * 4)/126
= 20/63
Answer: B
Answer: (B) 20/63
Question: In how many ways the letters of the word RAM be arranged?
(A) 8
(B) 12
(C) 10
(D) 6
(E) 120
Rationale: Total ways of arranging the letters = 3! = 6 ways.
D)
Answer: (D) 6
Question: Country X imported approximately $1.44 billion of goods in 1996. If Country X imported $388 million of goods in the first two months of 1997 and continued to import goods at the same rate for the rest of the year, by how much would Country Xs 1997 imports exceed those of 1996?
(A)  $24 million
(B)  $120 million
(C)  $144 million
(D)  $240 million
(E)  $888 million
Rationale: Convert units to millions as answer is in millions
1996 Imports = $1.44 bill = $1440 mill
i.e. 1440/12 = $120 mill/month
1997 Imports = $388 mill/2 month
i.e. $194 mill/month
Difference/month = 194-120 = 74
Difference/year = $74 mill * 12 = $988 mill
ANSWER: E
Answer: (E)  $888 million
Question: A train 360 m long runs with a speed of 45 km/hr. What time will it take to pass a platform of 140 m long?
(A) 38 sec
(B) 35 sec
(C) 44 sec
(D) 40 sec
(E) 50 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 + 140 = 500 meter
Time taken to cross the platform = 500/(25/2) = 500×2/25 = 40 seconds
Answer: Option D
Answer: (D) 40 sec
Question: In a student's election between two candidates, 75% of the voters cast thierthier votes, out of which 2% of the votes were declared invalid. A candidate got 9261 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election.
(A) 16800
(B) 1600
(C) 1680
(D) 1700
(E) 17500
Rationale: Let the number of votes enrolled be x. Then ,
Number of votes cast =75% of x. Valid votes = 98% of (75% of x).
75% of (98% of (75%of x)) =9261.
[(75/100)*(98/100)*(75/100)*x] =9261.
X = [(9261*100*100*100)/(75*98*75)] =16800.
ANSWER A
Answer: (A) 16800
Question: A certain manufacturer of cake, muffin, and bread mixes has 80 buyers, of whom 50 purchases cake mix, 40 purchase muffin mix, and 20 purchase both cake mix and muffin mix. If a buyer is to be selected at random from the 100 buyers, what is the probability that the buyer selected will be one who purchases neither cake mix nor muffin mix?
(A) a. 1/10
(B) b. 3/8
(C) c. 1/2
(D) d. 7/10
(E) e. 9/10
Rationale: C+M+B-CM-MB-CB-2CMB = 80
C - cake buyers, M - muffin and B - Bread buyers. CM,MB,CB and CMB are intersecting regions.
the question asks for people who have bought only bread mixes = B-CB-MB-2CMB has to be found out.
50 + 40 + B-CB-MB-20-2CMB = 80
B-CB-MB-2CMB = 30
hence the probability = 30/80 = 3/8.
B
Answer: (B) b. 3/8
Question: A man cycling along the road noticed that every 10 minutes a bus overtakes him and every 4 minutes he meets an oncoming bus. If all buses and the cyclist move at a constant speed, what is the time interval between consecutive buses?
(A) 5 minutes
(B) 6 minutes
(C) 8 minutes
(D) 9 minutes
(E) 48/7 minutes
Rationale: Let's say the distance between the buses is d. We want to determine Interval=\frac{d}{b}, where b is the speed of bus.
Let the speed of cyclist be c.
Every 10 minutes a bus overtakes cyclist: \frac{d}{b-c}=10, d=10b-10c;
Every 4 minutes cyclist meets an oncoming bus: \frac{d}{b+c}=4, d=4b+4c;
d=10b-10c=4b+4c, --> b=7c/3, --> d=12b-12b*3/7=48/7b.
Interval=\frac{d}{b}=\frac{48/7b}{b}=48/7
Answer: E (48/7 minutes).
Answer: (E) 48/7 minutes
Question: The H.C.F of two numbers is 8. Which of the following can never be their L.C.M?
(A) 55
(B) 44
(C) 66
(D) sixty (60)
(E) 12
Rationale: H.C.F of two numbers divides their L.C.M exactly. Clearly, 8 is not a factor of 60.
Answer:D
Answer: (D) sixty (60)
Question: A lockbox has a 4 digit number passcode. How many different passwords are possible if repetition of numbers is allowed?
(A) 40
(B) 10000
(C) 1000
(D) 100
(E) 10
Rationale: 10 x 10 x 10 x 10 = 10,000
Answer: B
Answer: (B) 10000
Question: A man on tour travels first 160 km at 64 km/hr and the next 160 km at 80 km/hr. Find the average speed for first 320 km of tour.
(A) 70.11 km/hr
(B) 71.11 km/hr
(C) 72.11 km/hr
(D) 73.11 km/hr
(E) None of these
Rationale: Explanation:
We know Time = Distance/speed
So total time taken =
(160/64+160/80)=9/2hours
Time taken for 320 Km = 320∗2/9=71.11km/hr
Option B
Answer: (B) 71.11 km/hr
Question: A man saves Rs 300 at the end of each year and lends the money at 5% compound interest. How
much will it become at the end of 3 years.
(A) Rs 662
(B) Rs 333.01
(C) Rs 663.02
(D) Rs 993.03
(E) None of these
Rationale: Explanation:
=[300(21/20×21/20×21/20)+300(21/20×21/20)+300(21/20)]=993.03
Answer: D
Answer: (D) Rs 993.03
Question: The prime factorization of integer N is A x A x B x C, where A, B and C are all distinct prime integers. How many factors does N have?
(A) 11
(B) 12
(C) 14
(D) 16
(E) 18
Rationale: if N=ap+br+cr
then prime factor of N will be: (p+1)(q+1)(r+!)
here
p=2,q=1,r=1
(2+1)(1+1)(1+1)
3*2*2
ANSWER:B
Answer: (B) 12
Question: By weight, liquid X makes up 0.8 percent of solution A and 1.8 percent of solution B. If 400 grams of solution A are mixed with 700 grams of solution B, then liquid X accounts for what percent of the weight of the resulting solution?
(A) 1.58%
(B) 1.98%
(C) 10%
(D) 15%
(E) 19%
Rationale: I think there is a typo in question.
It should have been "By weight Liquid 'X ' makes up..... "
Weight of Liquid X = 0.8 % of Weight of A + 1.8% of Weight of B
When 400gms of A and 700gms of B is mixed :
Weight of Liquid X = (0.8 * 400)/100 + (1.8* 700)/100 = 15.8gms
% of Liquid X in resultant mixture = (15.8/1000) *100 = 1.58%
A
Answer: (A) 1.58%
Question: 2 cow’s and 8 goats are brought for Rs.1400. If the average price of a goat be Rs.60. What is the average price of a cow.
(A) Rs. 480
(B) Rs.960
(C) Rs.960
(D) Rs. 460
(E) Rs. 560
Rationale: Explanation:
Average price of a goat = Rs.60
total price of 8 goats = 8*60 = Rs.480
But total price of 2 cows and 8 goats = Rs. 1400
Total price of 2 cows is = 1400 - 480
= 980
Average price of a cow = 980/2
= Rs. 460
Answer: Option D
Answer: (D) Rs. 460
Question: A courtyard is 30 meter long and 16 meter board is to be paved with bricks of dimensions 20 cm by 10 cm. The total number of bricks required is?
(A) 22877
(B) 24000
(C) 20000
(D) 27999
(E) 17799
Rationale: Number of bricks =Courtyard area/1 brick area
=(3000×1600/20×10)=24000
Answer: B
Answer: (B) 24000
Question: Length of train is 130 meters and speed of train is 45 km/hour. This train can pass a bridge in 30
seconds, then find the length of the bridge.
(A) 230 meters
(B) 235 meters
(C) 240 meters
(D) 245 meters
(E) None of these
Rationale: ExplanaƟon:
Let the length of bridge is X [as always we do :)]
Speed of train is = 45*(5/18) m/sec = 25/2 m/sec
Time = 30 seconds
Total distance = 130+x
We know Speed = distance/Ɵme
so,
130+x30=252=>2(130+x)=750x=245 meters
So length of the bridge is 245 meters
Answer:D
Answer: (D) 245 meters
Question: 7.515/10.02 =
(A)  0.35
(B)  0.3505
(C)  0.3509
(D)  0.351
(E)  0.75
Rationale: 7.515 / 10.02
7.515 / 1002 = 7.5
move the comma two places to the left as we have 2 decimal places from the divisor: 0.75. Answer: E
Answer: (E)  0.75
Question: If p/7 = r/2 and r = 0.75s, what is the ratio of p to r to s?
(A) 2 : 3 : 4
(B) 8 : 12 : 9
(C) 21 : 6 : 8
(D) 6 : 4 : 3
(E) 12 : 8 : 3
Rationale: p/7=r/2, r=0.75s, what is p:r:s?
we get p/r=7/2 and r/s=3/4, so
7/3*3/2 and 2/2*3/4
21/6 and 6/8
C
Answer: (C) 21 : 6 : 8
Question: A man sells a horse for Rs.200 and loses something, if he had sold it for Rs.620, his gain would have been double the former loss. Find the cost price of the horse?
(A) 140
(B) 162
(C) 160
(D) 150
(E) 71
Rationale: CP = SP + 1CP = SP - g
200 + x = 620 - 2x
3x = 420 => x = 140
Answer:A
Answer: (A) 140
Question: (4300331)-?=2535618
(A) 1865113
(B) 1775123
(C) 1764713
(D) 1675123
(E) None of them
Rationale: Let 4300331-x=2535618
then x=4300331-2535618
=1764713
Answer is C
Answer: (C) 1764713
Question: (2+0.0001)/(0.04+20)
The value of the expression above is closet to which of the following?
(A) 0.0001
(B) 0.001
(C) 0.1
(D) 1
(E) 10
Rationale: Notice that we need approximate value of the fraction.
Now, the nominator is very close to 2 and the denominator is very close to 20, hence the value of the fraction is very close to 2/20=0.1.
Answer: C.
Answer: (C) 0.1
Question: The cost price of 16 articles is the same as the selling price of 12 articles. Find the loss/profit percentages.
(A) 30%
(B) 32.50%
(C) 33 1/3%
(D) 40%
(E) 50%
Rationale: Explanation:
The gain is 4 out of 12 articles.
Therefore, gain percentage = 4x100/12 = 100/3 = 33 1/3%
Answer: Option C
Answer: (C) 33 1/3%
Question: A borrowed some money at the rate of 5% p.a. for the first four years, 8% p.a.for the next 8 years and 10% p.a.for the period beyond 12 years If the total interest paid by him at the end of 14 years is 41600, how much money did he borrow?
(A) 40,000
(B) 50,000
(C) 62,000
(D) 45,000
(E) None of these
Rationale: Let the sum be x. Then,
(x×4×5/100)+(x×8×8/100)+(x×2x10/100)=41600
⇒ 20x + 64x + 20x = (41600 × 100)
⇒ 104x = 4160000
⇒ x = 40000.
Answer A
Answer: (A) 40,000
Question: A batsman makes a score of 85 runs in the 11th inning and thus increases his average by 5. Find his average after 11th inning.
(A) 40
(B) 50
(C) 62
(D) 45
(E) 35
Rationale: Let the average after 11th inning = x
Then, average after 10th inning = x-5
10(x-5)+85 = 11x
x = 85-50 = 35
Answer is E
Answer: (E) 35
Question: At a loading dock, each worker on the night crew loaded 3/4 as many boxes as each worker on the day crew. If the night crew has 1/2 as many workers as the day crew, what fraction of all the boxes loaded by the two crews did the day crew load?
(A) 4/7
(B) 5/7
(C) 8/11
(D) 7/12
(E) 11/15
Rationale: Let x be the number of workers on the day crew.
Let y be the number of boxes loaded by each member of the day crew.
Then the number of boxes loaded by the day crew is xy.
The number of boxes loaded by the night crew is (x/2)(3y/4) = 3xy/8
The total number of boxes is xy + 3xy/8 = 11xy/8
The fraction loaded by the day crew is xy / (11xy/8) = 8/11
The answer is C.
Answer: (C) 8/11
Question: There are 10 red balls, 10 blue balls, 15 green balls and 9 black balls in a bag. What is the minimum number of balls to be taken out of the bag to assure that you have all the balls of one color?
(A) 10
(B) 23
(C) 43
(D) 41
(E) 16
Rationale: The worst case scenario would be if we pick 9 red balls, 9 blue balls, 14 (?) balls and 8 black balls. In this case we'll have 11+9+14+8=40 balls and still won't have all the balls of one color. The next 41rd ball we pick, no matter which color it'll be, will guarantee that we have all the balls of one color.
Answer: D.
Answer: (D) 41
Question: If 25% of x is 30 less than 15% of 1500, then x is?
(A) 872
(B) 738
(C) 837
(D) 780
(E) 83
Rationale: 25% of x = x/4 ; 15% of 1500
= 15/100 * 1500 = 225
Given that, x/4 = 225 - 30
=> x/4 = 195 => x = 780.
Answer:D
Answer: (D) 780
Question: If Jesse flips a coin five times in a row, what is the probability that the result will be heads at least 3 times?
(A) 21/128
(B) 29/128
(C) 35/128
(D) 1/16
(E) 1/2
Rationale: Question : Atleast 3 heads in 5 flip.
The total outcome of flip is = 2^5 = 32
For any Coins problem write the ask in the shown format.
HHHTT
HHHHT
HHHHH
Once you have written in the above mentioned format the answer is pretty straight.
HHHTT = [5!]/3!*2! = 10
HHHHT = [5!]/4! = 5
HHHHH = [5!]/[5!] = 1
Sum = 10+5+1 = 16/32 = 1/2
Answer - E
Answer: (E) 1/2
Question: How many 3 digits number are there which sum of digits is equal to 16.
(A) 63
(B) 64
(C) 65
(D) 66
(E) 67
Rationale: 100-200=4;
200-300=5;
---------
---------
700-800=10;
800-900=9;
900-999=8;
Total= 66
ANSWER:D
Answer: (D) 66
Question: The cost price of a radio is Rs.1500 and it was sold for Rs.1230, find the loss %?
(A) 18%
(B) 12%
(C) 22%
(D) 24%
(E) 21
Rationale: 1500 ---- 270
100 ---- ? => 18%
Answer:A
Answer: (A) 18%
Question: Two trains running in opposite directions cross a man standing on the platform in 47 seconds and 38 seconds respectively and they cross each other in 40 seconds. The ratio of their speeds is:
(A) 3 : 1
(B) 3 : 2
(C) 2 : 7
(D) 3 : 25
(E) 3 : 4
Rationale: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 47 x meters, and length of the second train = 38 y meters. (47 x + 37 y) / (x + y) = 40 ==>
47 x + 38 y = 40x + 40 y ==> 7x = 2 y ==> x/y = 2/7
Answer: Option C
Answer: (C) 2 : 7
Question: In 1998 the profits of company N were 10 percent of revenues. In 1999, the revenues of company N fell by 20 percent, but profits were 14 percent of revenues. The profits in 1999 were what percent of the profits in 1998?
(A) 80%
(B) 105%
(C) 120%
(D) 112%
(E) 138%
Rationale: 0,112R = x/100*0.1R
Answer D
Answer: (D) 112%
Question: What is the largest integer n such that
n2- 38/n + 1
is an integer?
(A) 36
(B) 38
(C) 72
(D) 76
(E) None of these
Rationale: Doing the long division algebraically, we get a quotient of n-1 with a remainder of
-37. In order for the division to give an integer, n+1 must divide -37 evenly. So n+1 = 37,
and n = 36.
correct answer A
Answer: (A) 36
Question: If 135*s is a perfect square then s can be which of the following numbers?
(A) 15
(B) 35
(C) 54
(D) 105
(E) 150
Rationale: My solution:
For a number to be a perfect square all the prime factors must be in pairs. So,
Prime factors of 135 are 3 *3 *3 *5
1)15 = 3 * 5
2) 35 = 5 * 7
3) 54 = 2 * 3 * 3 * 3
4) 105 = 3 * 5 * 7
5) 150 = 2 * 3 * 5 * 5
So only answer choice A completes the pairing of 3, 5 . It adds a3, a5, and a7to the prime factors of 135 (3*3*3*5) and makes it a perfect square. A
Answer: (A) 15
Question: Solution X is 30% chemical A and 70% chemical B by volume. Solution Y is 40% chemical A and 60% chemical B by volume. If a mixture of X and Y is 36% chemical A, what percent of the mixture is Solution X?
(A) 30%
(B) 35%
(C) 40%
(D) 45%
(E) 50%
Rationale: The volume of the mixture be X+Y.
0.3X +0.4Y=0.36(X+Y)
X=2Y/3
X/(X+Y)=(2Y/3) / (5Y/3)=2/5=40%.
The answer is C.
Answer: (C) 40%
Question: Grace has 18 jellybeans in her pocket. She has 10 red ones, 4 green ones, and 4 blue ones. What is the minimum number of jellybeans she must take out of her pocket to ensure that she has one of each color?
(A) 4
(B) 8
(C) 12
(D) 13
(E) 15
Rationale: The worst scenario is when she takes 10 red and 4 green, total of 14 jellybeans, and still doesn't have 3 distinct colors. But the next draw (15th) will surely be the third color jellybean (blue) as there is no other color jellybeans left in pocket.
Answer: E.
Answer: (E) 15
Question: The chance of rain on any given day in Tel-Aviv is 50%. What is the probability Q that it rained in Tel-Aviv on exactly 4 out of 6 randomly chosen days?
(A) 15/64
(B) 30/64
(C) 1/2
(D) 1/4
(E) 52/64
Rationale: chances of rain on exactly 4 days and not rain on 2 days = (1/2)^4* (1/2)^2 = 1/64
Chosing 4 days out of 6 = 6!/(4!*2!) = 15
chances of rain on exactly 4 days out of 6 days Q= 15/64
Ans A it is.
Answer: (A) 15/64
Question: Of the 15 employees of a certain company, twice as many are in the sales department as are in all of the other departments combined. What is the number of employees in the sales department?
(A) 10
(B) 20
(C) 30
(D) 40
(E) 45
Rationale: This is ratio problem solving question.
I will prefer to use RMV box.
R M V
Sales 2 5 10
Other 1 5 5
Total 3 5 15
Answer is 10. i.e A
Answer: (A) 10
Question: In how many ways can five boys, three girls and a teacher sit in a row such that all boys sit together?
(A) A)10000
(B) B)12100
(C) C)14400
(D) D)1097
(E) E)2781
Rationale: Treat all boys as one unit. Now there are four students and a teacher and they can be arranged in 5! ways. Again five boys can be arranged among themselves in 5! ways.
Required number of arrangements
= 5! * 5! = 120 * 120
= 14400.
Answer:C
Answer: (C) C)14400
Question: A motorcyclist goes from Nagpur to Delhi, a distance of 600 kms at an average of 60 kmph speed. Another man starts from Nagpur by car 5 Â½ hours after the first, and reaches Delhi Â½ hour earlier. What is the ratio of the speed of the motorcycle and the car?
(A) 1:2
(B) 1:7
(C) 1:9
(D) 1:5
(E) 2:5
Rationale: T = 600/60 =10 h
T = 10 - 6 = 4
Time Ratio = 10:4= 5:2
Speed Ratio = 2:5
Answer: E
Answer: (E) 2:5
Question: A boatman can row 3 km against the stream in 20 minutes and return in 9 minutes. Find the rate of current ?
(A) 7/2 kmph
(B) 8/2 kmph
(C) 5.5 kmph
(D) 1/2 kmph
(E) 2/2 kmph
Rationale: Explanation:
Speed in upstream = Distance / Time = 3 x 60/20 = 9 km/hr.
Speed in downstream = 3 x 60/9 = 20 km/hr
Rate of current = (20-9)/2 = 5.5 km/hr.
Answer: C
Answer: (C) 5.5 kmph
Question: Find the value of * in the following
(1 5/3) ÷ 3/11 × */11 = (2 2/3 × 7/5 × 6/7)
(A) 3.2
(B) 3.4
(C) 3.6
(D) 3.8
(E) 4
Rationale: 3.6
Option 'C'
Answer: (C) 3.6
Question: A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 25%. The percentage of water in the mixture is:
(A) 4%
(B) 61/4%
(C) 20%
(D) 25%
(E) 30%
Rationale: Let C.P. of 1 litre milk be Re. 1
Then, S.P. of 1 litre of mixture = Re. 1, Gain = 25%.
CP of 1 lr = 100/125*1 = 4/5
Ratio of milk to water = 4/5:1/5 = 4:1
=20%
ANSWER C
Answer: (C) 20%
Question: What is the least integer that is a sum of four different primes each greater than 20?
(A) 79
(B) 83
(C) 120
(D) 133
(E) 169
Rationale: Given integer must be a sum of 4 primes each greater than 20. Thus each prime must be odd.
Therefore sum of Odd + Odd + Odd + Odd = Even
Only Even option is 120
Therefore Ans: C
To verify
120 = 23 + 29 +31 +37
Answer: (C) 120