mathewhe/aqua_rat huggingface dataset:
Question: If |x^2 − 42| = x, which of the following could be the value of x?
(A) –7
(B) –6
(C) 2
(D) 6
(E) 14
Rationale: The LHS is not negative, so the RHS is also not negative. Thus x >= 0.
First, let's assume that x^2-42 is negative.
-(x^2 - 42) = x
x^2 + x - 42 = 0
(x+7)(x-6) = 0
x = 6 or x = -7 (However, x can not be negative.)
Then x = 6 is a possible value for x.
The answer is D.
Answer: (D) 6
Question: If 4 (P's Capital ) = 6 ( Q's Capital ) = 10 ( R's Capital ) , then out of the total profit of Rs 4650 , R will receive
(A) 600
(B) 700
(C) 800
(D) 900
(E) None of these
Rationale: Explanation :
Let P's capital = p, Q's capital = q and R's capital = r
Then
4p = 6q = 10r
=> 2p = 3q = 5r
=>q = 2p/3
r = 2p/5
P : Q : R = p : 2p/3 : 2p/5
= 15 : 10 : 6
R's share = 4650 * (6/31) = 150*6 = 900. Answer : Option D
Answer: (D) 900
Question: What is the rate of simple interest?
I. The total interest earned was Rs. 4000.
II. The sum was invested for 4 years.
(A) I alone sufficient while II alone not sufficient to answer
(B) II alone sufficient while I alone not sufficient to answer
(C) Either I or II alone sufficient to answer
(D) Both I and II are not sufficient to answer
(E) Both I and II are necessary to answer
Rationale: Explanation:
We know that, R =( 100 xS. I / P x T )
Now, I gives, S.I. = Rs. 4000.
II gives, T = 4 years.
But, P is unknown. So, we cannot find R.
So, given data is insufficient to get R.
answer is (D).
Answer: (D) Both I and II are not sufficient to answer
Question: Solve This
6 + 7 = 12
8 + 9 = 16
5 + 6 = 10
7 + 8 = 14
Then, 9 + 9 = ??
(A) 11
(B) 12
(C) 17
(D) 14
(E) 18
Rationale: 17
ANSWER:C
Answer: (C) 17
Question: A box contains THIRTEEN bulbs out of which 6 are defective. If FIVE bulbs are chosen at random, find the probability that atleast one bulb is good
(A) 455/451
(B) 428/421
(C) 427/429
(D) 456/489
(E) 423/127
Rationale: Required probability = 1-6C5/13C5 = 1 - 2/429 = 427/429.Answer:C
Answer: (C) 427/429
Question: A is twice as good a workman as B and they took 11 days together to do the work B alone can do it in.
(A) 17 days
(B) 12 days
(C) 29 days
(D) 25 days
(E) 33 days
Rationale: WC = 2:1
2x + x = 1/11
x = 1/33 => 33 days
ANSWER:E
Answer: (E) 33 days
Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 1/7 hours to fill the tank. The leak can drain all the water of the tank in?
(A) 17 hr
(B) 19 hr
(C) 10 hr
(D) 24 hr
(E) 30 hr
Rationale: Work done by the tank in 1 hour
= (1/2 -2 1/7)
= 1/30 Leak will empty the tank in 30 hrs.
Answer:E
Answer: (E) 30 hr
Question: Two trains having equal lengths, take 10 seconds and 15 seconds respectively to cross a post. If the length of each train is 120 meters, in what time (in seconds) will they cross each other when traveling in opposite direction?
(A) 22
(B) 38
(C) 12
(D) 99
(E) 73
Rationale: Explanation:
Speed of train 1 = = 12 m/sec
Speed of train 2 = = 8 m/sec
if they travel in opposite direction, relative speed = 12 + 8 = 20 m/sec
distance covered = 120 + 120 = 240 m
time = distance/speed = 240/20 = 12 sec
Answer: C) 12
Answer: (C) 12
Question: An illiterate retailer marks all its goods at 50% above the cost price and thinking that he will still make 25% profit, offers a discount of 25% on the market price. What is the actual profit on the sales?
(A) 0.125
(B) 26.5%
(C) 27.8%
(D) None of the above
(E) Cannot be determined
Rationale: Explanation :
Let C.P =Rs 100.then, marked price =Rs100
S.P=75% of Rs 150= Rs 112.50
Hence, gain%=12.50%
Answer : A
Answer: (A) 0.125
Question: If the perimeter of a rectangular garden is 680 m, its length when its breadth is 82 m is?
(A) 286 m
(B) 899 m
(C) 200 m
(D) 166 m
(E) 258 m
Rationale: 2(l + 82) = 680 => l
= 258 m
Answer: E
Answer: (E) 258 m
Question: A number when divided by 5, gives 45 as quotient and 0 as remainder. What will be the remainder when dividing the same number by 10
(A) A)5
(B) B)3
(C) C)4
(D) D)6
(E) E)7
Rationale: Explanation:
P ÷ 5 = 45
=> P = 45 * 5 = 225
P / 10 =225 / 10 = 22, remainder = 5
Answer: Option A
Answer: (A) A)5
Question: The toll T, in dollars, for a truck using a certain bridge is given by the formula T = 0.50 + 0.50( x − 2), where x is the number of axles on the truck. What is the toll for an 18-wheel truck that has 2 wheels on its front axle and 4 wheels on each of its other axles?
(A)  $ 2.00
(B)  $ 3.00
(C)  $ 3.50
(D)  $ 4.00
(E)  $ 5.00
Rationale: Number of wheels in truck = 18
Number of wheels on its front axle =2
number of wheels remaining = 16
number of axles remaining axles = 16/4 = 4
Total number of axles = 5
T = 0.50 + 0.50( x − 2)
= 0.50 + .5*3
= 0.5 +1.5 = 2 $
Answer A
Answer: (A)  $ 2.00
Question: The circumference of the front wheel of a cart is 40 ft long and that of the back wheel is 48 ft long. What is the distance travelled by the cart, when the front wheel has done five more revolutions than the rear wheel?
(A) 1200 ft
(B) 800 ft
(C) 900 ft
(D) 1000 ft
(E) 1500 ft
Rationale: total distance - x
x/40 - x/48 = 5
x = 1200 ft
ANSWER A
Answer: (A) 1200 ft
Question: The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 11 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
(A) 23 years
(B) 24 years
(C) 25 years
(D) 26 years
(E) 27 years
Rationale: EXPLANATION
Let the average age of the whole team by x years.
11x â€“ (26 + 40) = 9(x -1)
11x â€“ 9x = 54
2x = 54
x = 27.
So, average age of the team is 27 years.
Answer E
Answer: (E) 27 years
Question: Difference between a two-digit number and the number obtained by interchanging the two digits is 36, what is the difference between two numbers
(A) 2
(B) 4
(C) 8
(D) 12
(E) 14
Rationale: Explanation:
Let the ten digit be x, unit digit is y.
Then (10x + y) - (10y + x) = 36
=> 9x - 9y = 36
=> x - y = 4.
Option B
Answer: (B) 4
Question: By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent?
(A) 42 6/8%
(B) 42 6/7%
(C) 42 4/7%
(D) 42 9/7%
(E) 42 6/7%
Rationale: SP = CP + g
50 SP = 50 CP + 15 SP
35 SP = 50 CP
35 --- 15 CP gain
100 --- ? => 42 6/7%
Answer: B
Answer: (B) 42 6/7%
Question: In a BCCI meeting there are 14 people. All shake hands with each other once. How many handshakes will be there altogether?
(A) 28
(B) 13
(C) 14
(D) 19
(E) 18
Rationale: There will be n-1 handshakes as A person will shake hands with all the other members.
=14-1=13
Answer:B
Answer: (B) 13
Question: 40% of Ram's marks is equal to 20% of Rahim's marks which percent is equal to 30% of Robert's marks. If Robert's marks is 80, then find the average marks of Ram and Rahim?
(A) 93
(B) 77
(C) 68
(D) 90
(E) 62
Rationale: Given, 40% of Ram's marks = 20% of Rahim's marks = 30% of Robert's marks.
Given, marks of Robert = 80
30% of 80 = 30/100 * 8 = 24
Given, 40% of Ram's marks = 24.
=> Ram's marks = (24 * 100)/40 = 60
Also, 20% of Rahim's marks = 24
=> Rahim's marks = (24 * 100)/20 = 120
Average marks of Ram and Rahim = (60 + 120)/2 = 90.
Answer:D
Answer: (D) 90
Question: In a shower, 4 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:
(A) 75 cu. m
(B) 600 cu. m
(C) 750 cu. m
(D) 6000 cu. m
(E) 7.50 cu. m
Rationale: 1 hectare = 10000 sq mtr
The volume of water that falls on 1.5 hectares of ground = 0.04*1.5*10000 = 600 cub mtr .
ANSWER:B
Answer: (B) 600 cu. m
Question: One fourth of a solution that was 10 percent sugar by weight was replaced by a second solution resulting in a solution that was 16 percent sugar by weight. The second solution was what percent sugar by weight ?
(A) 34%
(B) 24%
(C) 22%
(D) 18%
(E) 8.5%
Rationale: Let the original solution be 100 ml
It had 10ml of sugar
1/4 of this solution is removed
sugar remaining = 7.5 ML
25 ml of x% solution is added.
New volume of sugar = 7.5+25*x/100
Since resulting solution is 16% sugar by weight, volume of sugar = 16ml
equating the 2
x=(16-7.5)*4
=34
ANSWER:A
Answer: (A) 34%
Question: What do you get if you add 5 to 500 five times?
(A) 305
(B) 510
(C) 320
(D) 505
(E) 509
Rationale: D
505 , 505 , 505 , 505 , 505
Answer: (D) 505
Question: A man spends 10% of his income in house rent, 20% of the rest on his childrenâ€™s education, 25% of the rest miscellaneous causes. If he now posses Rs. 1944 then his income is?
(A) 3600
(B) 5500
(C) 5000
(D) 4000
(E) 2000
Rationale: X * (90/100) * (80/100) * (75/100) = 1944
X * 0.9 * 0.8 * 0.75
X = 1944/0.54
X = 3600
ANSWER A
Answer: (A) 3600
Question: A sum of Rs.4800 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
(A) Rs.3128
(B) Rs.3120
(C) Rs.3122
(D) Rs.3121
(E) Rs.3122
Rationale: Explanation:
Let A be the amount received at the end of the three years.
A = 4800[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4800 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.7920
So the interest = 7920 - 4800 = Rs.3120
Answer: B
Answer: (B) Rs.3120
Question: P and Q began business with Rs.6000 and Rs.9000 after 4 months, P withdraws Rs.2000 and B advances Rs.3000 more.
At the end of the year, their profits amounted to Rs.1175 find the share of Q.
(A) 800
(B) 625
(C) 825
(D) 725
(E) 850
Rationale: (6*4 + 4*8):(9*4 + 12*8)
14 : 33
33/47 * 1175 = 825.Answer:C
Answer: (C) 825
Question: If C is the temperature in degrees Celsins and F is the temperature in degrees Fahrenheit, then the relationship between temperatures on the two scales is expressed by the equation 9C=5(F-32). On a day when the temperature extremes recorded at two different cities differed by 55 degrees on the Fahrenheit scale, by how many degrees did the temperature extremes differ on the Celsius scale?
(A) a) 65/9
(B) b) 13
(C) c) 28
(D) d) 45
(E) e) 81
Rationale: The relationship is 9/5 - 32, so approximately half of difference in Celsius (the -32 part won't be used in this case).
Just looking at the answer choices you can pick C which is the only number near half of 55. The other answer choices are too far apart so no need to calculate.
Answer: (C) c) 28
Question: If 20 ounces of a strong vinegar solution are diluted with 40 ounces of water to form a five-percent vinegar solution, what was the concentration of the original solution?
(A) 8%
(B) 10%
(C) 12%
(D) 15%
(E) 18%
Rationale: Let x be the concentration of the original solution.
20x = 0.05(60)
x = 0.15
The answer is D.
Answer: (D) 15%
Question: A basket has 6 apples and 4 oranges. Three fruits are picked at random. What is the probability that at least 2 apples are picked?
(A) 1/2
(B) 1/3
(C) 2/3
(D) 2/5
(E) 3/5
Rationale: The total possible choices are 10C3 = 120
The ways to choose 3 apples: 6C3 = 20
The ways to choose 2 apples: 6C2 * 4C1 = 60
P(at least 2 apples) = 80/120 = 2/3
The answer is C.
Answer: (C) 2/3
Question: In a ratio which is equal to 3:4, if the antecedent is 12, then the consequent is?
(A) 12
(B) 16
(C) 20
(D) 22
(E) 25
Rationale: We have 3/4 = 12/x
3x = 48
x = 16
consequent = 16
Answer is B
Answer: (B) 16
Question: There are two positive numbers in the ratio 5:8. If the larger number exceeds the smaller by 27, then find the smaller number?
(A) 25
(B) 66
(C) 45
(D) 88
(E) 44
Rationale: Let the two positive numbers be 5x and 8x respectively.
8x - 5x = 27
3x = 27 => x = 9
=> Smaller number = 5x = 45.
Answer: C
Answer: (C) 45
Question: Gordon buys 5 dolls for his 5 nieces. The gifts include two identical S beach dolls, one E, one G, one T doll. If the youngest niece doesn't want the G doll, in how many different ways can he give the gifts
(A) 24
(B) 48
(C) 72
(D) 96
(E) 120
Rationale: Total # of ways to distribute SSEGT among 5 sisters (without restriction) is 5!2!=605!2!=60;
The # of ways when the youngest niece gets G is: 4!2!=124!2!=12 (give G to youngest and then distribute SSET among 4 sisters).
So, # of ways when youngest niece doesn't get G is: 60−12=4860−12=48.
Answer: 48.
ANSWER:B
Answer: (B) 48
Question: There are two tanks a and b. A drains water with 6L/m and b drains water with 8L/m. A starts drain water at 9:00 and after 2 minute, b starts draining of water. At what time, both with have same level.
(A) 9:12
(B) 9:10
(C) 9:08
(D) 9:04
(E) 9:06
Rationale: 9:01 --- 6 L
9:02 --- 12 L
from 9:03 onwards --------18,24,30,36,42,48,54,60
B =>
from 9:03 onwards -------- 8,16,24,32,40,48,56,64
at 9:08 both A & B have same level (48 L)
ANSWER:C
Answer: (C) 9:08
Question: Q is the set of the first n positive odd numbers, where n is a positive integer. Given that n > k, where k is also a positive integer, x is the maximum value of the sum of k distinct members of Q, and y is the minimum value of the sum of k distinct members of Q, what is x + y?
(A)  kn
(B)  kn + k^2
(C)  kn + 2k^2
(D)  2kn – k^2
(E)  2kn
Rationale: Probably the easiest way to solve this question would be to assume some values for n and k.
Say n=3, so Q, the set of the first n positive odd numbers would be: Q={1, 3, 5};
Say k=1, so X, the maximum value of the sum of K distinct members of Q would simply be 5. Similarly, Y, the minimum value of the sum of K distinct members of Q would simply be 1.
X+Y=5+1=6.
Now, substitute n=3 and k=1 in the options provided to see which one yields 6. Only asnwer choice E fits: 2kn=2*3*1=6.
Answer: E.
Answer: (E)  2kn
Question: In an examination 35% of the students passed and 481 failed. How many students appeared for the examination?
(A) A)540
(B) B)400
(C) C)700
(D) D)740
(E) E)840
Rationale: Let the number of students appeared be x
then, 65% of x = 481
65x/100 = 481
x = 481*100/65 = 740
Answer is D
Answer: (D) D)740
Question: In right triangle ABC, AC is the hypotenuse. If AC is 35 and AB + BC = 55, what is the area of the triangle ABC?
(A) 225
(B) 450
(C) 25√2
(D) 200
(E) 200√2
Rationale: Square AB + BC = 55:
(AB)^2 + 2*AB*BC + (BC)^2 = 3025. Since (AC)^2 = (AB)^2 + (BC)^2 = 35^2 = 1225, then (AB)^2 + 2*AB*BC + (BC)^2 = 1225 + 2*AB*BC = 3025.
1225 + 2*AB*BC = 3025.
AB*BC = 900.
The area = 1/2*AB*BC = 450.
Answer: B.
Answer: (B) 450
Question: Due to construction, the speed limit along an 6-mile section of highway is reduced from 55 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ?
(A)  4
(B)  8
(C)  10
(D)  15
(E)  24
Rationale: 6/35 - 6/55 = 6/5 * ( 11 - 7)/77
= 6/5 * 4/77 * 60 min
= 6 * 12 * 4/77
= 288/77 ~ 3.7
Answer - A
Answer: (A)  4
Question: In how many different orders can the people Alice, Benjamin, Charlene, David, Elaine, Frederick, Gale, and Harold be standing on line if each of Alice, Benjamin, Charlene must be on the line before each of Elaine, Gale, and Harold?
(A) 1,008
(B) 2016
(C) 1,512
(D) 2,018
(E) 2,268
Rationale: Place D and F first: 8 options for D, 7 options for F
We are left with 6 empty places. A, B and C must take first 3 places and F, G, H must take the remaining three. A, B and C can be arranged in their places in 3! ways. The same for E, G, and H.
Total = 8*7*3!*3! = 2,016.
Answer: B
Answer: (B) 2016
Question: A room is 30 m long and 24 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:
(A) 9.6 m3
(B) 96 m3
(C) 960 m3
(D) 9600 m3
(E) 96000 m3
Rationale: Let the height be H
2(30+24) x H – 2(30-24)
H=(2(30x24))/(2(30+24)) = (30x24)/54 = 40/3 m
Volume = 30x24x40/3 = 9600 m3
answer :D
Answer: (D) 9600 m3
Question: If the cost price of 60 articles is equal to the selling price of 40 articles, then what is the percent profit?
(A) 30%
(B) 40%
(C) 50%
(D) 60%
(E) 70%
Rationale: Let x be the cost price of one article.
Let y be the selling price of one article.
40y = 60x
y = 1.5x
The answer is C.
Answer: (C) 50%
Question: The average of 50 numbers is 30. If two numbers, 35 and 40 are discarded, then the average of the remaining numbers is nearly
(A) 28.32
(B) 28.78
(C) 29.27
(D) 29.68
(E) None
Rationale: Solution
Sum of 50 numbers	= 30 x 50
= 1500.
Sum of remaining 48 numbers	= 1500 - (35+40)
= 1425.
∴ Required average	= (1425 / 48)
= 475 / 16.
= 29.68.
Answer D
Answer: (D) 29.68
Question: In a partnership between A, B and C. A's capital is Rs.5000. If his share of a profit of Rs.900 is Rs.200 and C's share is Rs.130, what is B's capital?
(A) 19878
(B) 14250
(C) 26908
(D) 11750
(E) 22073
Rationale: 200 + 130 = 330
900 - 330 = 570
200 ---- 5000
570 ---- ? => 14250
Answer: B
Answer: (B) 14250
Question: The value of 5 in the number 357.21 is
(A) 5 ones
(B) 5 twenty
(C) 5 tens
(D) 5 hundreds
(E) none of the above
Rationale: Ans is C
The number 357.21 consists of: 3 hundreds, 5 tens, 7 ones, 2 tenths and 1 hundredth =>the value of 5 in 357.21	is 5 tens
Answer: (C) 5 tens
Question: A WORKS TWICE AS FAST AS B. IF B CAN COMPLETE A WORK IN 6 DAYS INDEPENDENTLY, THE NUMBER OF DAYS IN WHICH A AND B CAN TOGETHER FINISH THE WORK IS:
(A) 3/4 DAYS
(B) 2/1 DAYS
(C) 4/3 DAYS
(D) 3/2 DAYS
(E) 1/2 DAYS
Rationale: RATIO OF RATES OF WORKING OF A AND B = 2:1. SO, RATIO OF TIME TAKEN = 1:2
A'S 1 DAY'S WORK = 1/3, B'S 1 DAY'S WORK = 1/6
(A+B)'S 1 DAY'S WORK = (1/3+1/6)=1/2=1/2
SO, A AND B TOGETHER CAN FINISH THE WORK IN 1/2 DAYS.
CORRECT OPTION: E
Answer: (E) 1/2 DAYS
Question: 325,244,180,131 ?
(A) 42
(B) 43
(C) 44
(D) 40
(E) 95
Rationale: 325 - 244 = 81 = 9^2
244 - 180 = 64 = 8^2
180 - 131 = 49 = 7^2
so we can write
131 - x = 36 = 6^2 , where x is the next number
x = 131 - 36 = 95
so the next number will be 95
ANSWER:E
Answer: (E) 95
Question: Balloons are bought at 8 for Rs.10/- and sold at 10 for Rs.8/-. Find the gain or loss percentage?
(A) 36% Loss
(B) 36% Gain
(C) 18% Loss
(D) 18% Gain
(E) 19% Loss
Rationale: Explanation:
8 Balloons -----> Rs.10/-
10 Balloons ----> Rs.8/-
Note: In every time same in the cost price articles and selling price articles.
10(8 10) ==> 80 100 = Cost price
8(10 8) ==> 80 64 = Selling price
Then, 36/100 × 100 = 36 % Loss
Answer: Option A
Answer: (A) 36% Loss
Question: Y and Z walk around a circular track. They start at 5 a.m from the same point in the opposite directions. Y and Z walk at a speed of 3 rounds per hour and 4 rounds per hour respectively. How many times shall they cross each other before 7 a.m
(A) 14
(B) 15
(C) 16
(D) 17
(E) 18
Rationale: Explanation:
Relative speed = (3+4) =9 rounds per hour
So, they cross each other 9 times in an hour hence, they cross 18 times before 7 a.m
Answer: Option E
Answer: (E) 18
Question: If p is a positive integer and 10p/96 is an integer, then the minimum number of unique prime factors p could have is Q:
(A) Q=1
(B) Q=2
(C) Q=3
(D) Q=4
(E) Q=5
Rationale: 10p/96 should resolve to a integer => 5p/48 should resolve to an integer.
Hence p/48 should resolve to a integer.
48 -- > 2^4 * 3.
Hence p should have atleast 2^4*3 for p/48 to resolve to a int.
The unique prime factors in 2^4 * 3 is 2, 3 and hence the answer is B(2).
Answer: (B) Q=2
Question: The boat moves downside 50km and upside 10km in 2 hours each. Then find the boat speed in still water?
(A) 10km/hr
(B) 15km/hr
(C) 20km/hr
(D) 25km/hr
(E) 30km/hr
Rationale: Down stream = 50/2 = 25km/hr
Up stream = 10/2 = 5km/hr
speed of boat in still water = 30/2 = 15km/hr
Answer is B
Answer: (B) 15km/hr
Question: A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by:
(A) 12
(B) 27
(C) 26
(D) 11
(E) 99
Rationale: Explanation:
Let the ten's digit be x and unit's digit be y.
Then, number 10x + y.
Number obtained by interchanging the digits = 10y + x.
(10x + y) + (10y + x) = 11(x + y)
which is divisible by 11.
Answer: D
Answer: (D) 11
Question: if q=0 and k = qr/2 -s, then what is r in terms of k,q,s?
(A) 2k+s/q
(B) 2sk/q
(C) 2(k-s)/q
(D) 2k+sq/q
(E) 2(k+s)/q
Rationale: k+s=qr/2
2(k+s)=qr
r=2(k+s)/q
ANSWER:E
Answer: (E) 2(k+s)/q
Question: If k, (k+200), (k+350), and 15*K are all multiples of F, then F could equal which of the following ?
(A) 20
(B) F=25
(C) 75
(D) 100
(E) 150
Rationale: {Multiple of F} - {Multiple of F} = {Multiple of F}.
(K+200) - k = 200 = {Multiple of F}.
(K+350) - k = 350 = {Multiple of F}.
Both 200 and 350 are multiples of only option B.
Answer: B.
Answer: (B) F=25
Question: A sum of money is to be distributed among P, Q, and R in the ratio 6:19:7. If R gives Rs. 200 from his share to Q, the ratio of P, Q and R becomes 3:10:3, what is the total sum?
(A) Rs. 4800
(B) Rs. 12800
(C) Rs. 3200
(D) Rs. 7200
(E) data inadequate
Rationale: Explanation:
Let the shares of P, Q and R be 6x, 19x and 7x.
By given condition, R’s new share = 7x – 200
Q’s new share = 19x + 200
New ratio = 6x :19x +200:7x-200=3:10:3
P : R = 6x :7x -200=3 :3
6x=7x-200
x=200
Total sum 6x + 19x + 7x = 32x = Rs. 4800
Answer: A
Answer: (A) Rs. 4800
Question: The average weight of 25 persons sitting in a boat had some value. A new person added to them whose weight was 46 kg only. Due to his arrival, the average weight of all the persons decreased by 5 kg. Find the average weight of first 25 persons?
(A) 288
(B) 278
(C) 297
(D) 176
(E) 267
Rationale: 25x + 46 = 26(x – 5)
x = 176
Answer: D
Answer: (D) 176
Question: An army’s recruitment process included N rounds of selection tasks. For the first A rounds, the rejection percentage was 60 percent per round. For the next B rounds, the rejection percentage was 50 percent per round and for the remaining rounds, the selection percentage was 70 percent per round. If there were 100000 people who applied for the army and 1400 were finally selected, what was the value of N?
(A) 4
(B) 5
(C) 6
(D) 8
(E) 10
Rationale: Since 70% is accepted and figure will be 1400 therefore in last stage tested/interviewed no. candidates should be 2000
So from here i will work for those two steps of decrements of 100000 candidates.
fastly i reduce 60% till it gets closer to our required 2000 candidates
step(1) 40000 accepted.
step(2) another 40%of 40000=16000 accepted.
here it is quiet observable that if we further deduct candidate by 60% it would change our probablity of easy going 2000 candidate.
so i would get to second stage of recruitment where 50 % is accepted
step(3) 50% of 16000=8000
step(4) 50% of 8000=4000
Step(5) 50% of 4000=2000...here we are done with total 5 steps
and last step of accepting 70% of 2000=1400(our target)
total 6 steps required.
Answer: C
Answer: (C) 6
Question: If x=-3, which of the following is(are) true? I. x^2=-|x| II |x|=-x III x/-3 = -1
(A) II, III only
(B) II only
(C) I,II only
(D) I only
(E) III only
Rationale: I. x^2=-|x| -3^2 = - |-3| Not true
II |x|=-x |-3| =-( -3 ) true
III x/-3 = -1 Not true
Answer : B
Answer: (B) II only
Question: A bag contains 4 black, 5 yellow and 6 green balls. Three balls are drawn at random from the bag. What is the probability that all of them are yellow?
(A) 2/81
(B) 2/91
(C) 1/81
(D) 1/91
(E) 1/51
Rationale: Total number of balls = 4 + 5 + 6 = 15
n(S) = tot no of ways of drawing 3 balls out of 15 =15c3
let E = event of drawing 3 balls
n(E) = no of ways of drawing 3 balls
= no of ways of drawing 3 balls from the total 5 = 5c3
=>(5*4/2*1)/(15*14*13/3*2*1)=2/91
ANSWER B
Answer: (B) 2/91
Question: A trucking company plans to gradually replace their older fleet of trucks with newer more energy efficient ones. Every year it plans to retire 6 trucks and buy 8 newer ones. How many years starting from 2005 will it take to reduce its fleet of 40 old trucks to less than half its fleet?
(A) 8
(B) 2
(C) 5
(D) 6
(E) 3
Rationale: Total fleet--40
End of year 2005 -- (retires 6 and buys 8) total fleet--42(34 old 8 new).
End of year 2006 -- (retires 6 and buys 8) total fleet--44(28 old 16 new).
End of year 2007 -- (retires 6 and buys 8) total fleet--46(22 old 24 new).
Answer is E--after 3 years the company has a total of 56 taxis (20 old 36 new), the old taxis are already less than 50% of its fleet.
Answer: (E) 3
Question: A pack of baseball cards consists of 12 outfielder cards and 8 infielder cards. What is the lowest number of outfielder cards that would have to be removed from the pack so that no more than 35 percent of the pack would be outfielder cards?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 8
Rationale: let the number of O card to be removed=X
then remaning cards=12-X
now this 12-X cards should count less than 35% of toatal Ocards
12-X<.35*12
X>12-4.2
X>7.8
X=8
Ans E
Answer: (E) 8