divelab/Sys2Bench huggingface dataset:
Question: The measures of the 2 acute angles of a triangle are in the ratio of 3 : 6. What arethe measures of the 2 angles?
Options:
A)20°
B)70°
C)60°
D)120°
E)140°
Rationale: If the ratio of the two angles is 3:6, then the measures of two angles can be written as 3x and 6x. Also the two acute angles of a triangle is equal to 90°. Hence
3x + 6x = 90
9x = 90
x = 10
Measures of the two acute angles are
3x = 3 × 10 = 30°
6x = 6 × 10 = 60°
C
Answer: C
Question: A tradesman by means of his false balance defrauds to the extent of 20%? in buying goods as well as by selling the goods. What percent does he gain on his outlay?
Options:
A)37
B)27
C)44
D)26
E)27
Rationale: Explanation:
g% = 20 + 20 + (20*20)/100
= 44%
Answer: C
Answer: C
Question: 49 Ã— 49 Ã— 49 Ã— 49 x 49 Ã— 49 Ã— 49 Ã— 49= 7?
Options:
A)4
B)7
C)8
D)16
E)None of these
Rationale: 49 Ã— 49 Ã— 49 Ã— 49 x 49 Ã— 49 Ã— 49 Ã— 49 = 7?
or, 7(2) Ã— 7(2) Ã— 7(2) Ã— 7(2) x 7(2) Ã— 7(2) Ã— 7(2) Ã— 7(2)= 7^?
or 7(16) = 7? or, ? =16
Answer D
Answer: D
Question: 5/9= 25/45 . which method did you use to determine whether this proportion is true or false?
Options:
A)true
B)neutral
C)false
D)not sure
E)none
Rationale: 5/9= 25/45. cross multiplication: 5 * 45= 225, 25 * 9 = 225,
we see that 225 are not equal to 225. so there is proportion. corrcet answer: (A)
Answer: A
Question: The sum of the number of boys and girls in a school is 150. if the number of boys is x, then the number of girls becomes x% of the total number of students. The number of boys is ?
Options:
A)60
B)38
C)26
D)29
E)11
Rationale: Explanation:
We have : x + x% of 150 = 150
Answer: A) 60
Answer: A
Question: A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 86.49, the number of the member is the group is:
Options:
A)93
B)67
C)77
D)87
E)97
Rationale: Money collected =(86.49 x 100) paise = 8649 paise
numbers of members = 8649 squareroot = 93
Answer A
Answer: A
Question: 2. Abhishek started a business investing 50,000. After one year he invested another 30,000 and Sudin also joined him with a capital of 70,000. If the profit earned in three years from the starting of business was 87,500, then find the share of Sudin in the profit
Options:
A)37,500
B)32,500
C)38,281
D)52,500
E)None of these
Rationale: Ratio of Abhishek and Sudin for one month
= (50,000 × 36) + (30,000 × 24) : (70,000 × 24)
= (18,00,000 + 7,20,000) : 16,80,000 = 3 : 2
Hence share of Sudin in the profit earned from the business.
= 87,500/(3+2)×2 = 35,000
Answer E
Answer: E
Question: Which of the following is two more than the square of an odd integer?
Options:
A)14,173
B)14,361
C)14,643
D)14,737
E)14,981
Rationale: one of the given options should be a square if 2 is subtracted from it.
the options would be
(A) 14,171
(B) 14,359
(C) 14,641
(D) 14,735
(E) 14,979
We can solve this question with many approaches. Here are the 2 easiest methods.
Method 1:-
If a square has odd unit's digit, then it's ten's digit will always be even.
Only 14,641 satisfies this condition.
Method 2:-
If you know about palindromic numbers,
then you can clearly see that 14,641 is a palindromic square.
Answer:- C
Answer: C
Question: E and F have a data plan which gives them 200 GB every month. If E uses 7 GB every 9 days and F uses 5 GB every 4 days, how many GB will be unused after a 30 day month? Answer in fractions.
Options:
A)365/6
B)73/6
C)35/6
D)835/6
E)200/6
Rationale: Number of GB that E uses every day: 7/9
Number of GB that F uses every day: 5/4
Number of GB that E and F use every day: 7/9+5/4=73/36
Number of GB that E and F use in 30 days: 30x(73/36)=365/6
Number of GB remaining: 200-365/6=835/6
Answer is D
Answer: D
Question: A person walking at 4 Kmph reaches his office 8 minutes late. If he walks at 6 Kmph, he reaches there 12 minutes earlier. How far is the office from his house?
Options:
A)4 1/5 Km
B)4 1/7 Km
C)3 1/5 Km
D)3 1/7 Km
E)4 Km
Rationale: Formula = S1*S2/S2-S1 * T1+T2/60
= 4*6/2 * 20/6
= 24/2 * 20/60
= 10 * 2/5
= 20/5 = 4 Km
E)
Answer: E
Question: If the average (arithmetic mean) of x and y is 80, and z – x = 100, what is the average of y and z?
Options:
A)140
B)100
C)110
D)120
E)130
Rationale: x+y/2 = 80
=> x+y = 160
x = z - 100...sub this value
z-100+y = 160
=>z+y = 260
=>z+y/2 = 130
Answer : E
Answer: E
Question: John has taken four (4) tests that have an average of 83. In order to bring his course grade up to a ‘B’, he will need to have a final average of 87. What will he need to average on his final two tests to achieve this grade?
Options:
A)87
B)90
C)92
D)95
E)97
Rationale: Traditional Method:
Total scored till now 83*4=332
Total score to avg 87 in 6 tests = 87*6=522
Total to be scored on 2 tests = 522-332=190
Avg on 2 tests = 190/2 = 95
Answer: D
Answer: D
Question: Bag A contains red, white and blue marbles such that the red to white marble ratio is 1:3 and the white to blue marble ratio is 2:3. Bag B contains red and white marbles in the ratio of 1:4. Together, the two bags contain 60 white marbles. How many red marbles could be in bag A?
Options:
A)1
B)3
C)4
D)12
E)8
Rationale: 6 is the answer.
Bag A-
R:W:B = 2:6:9
Let W in bag A be 6K
Bab B -
R:W = 1:4
Let W in bag B be 4k
W = 60 = 6K+4k
=> k =6
Total Red's in bag A will be 2K = 12
D
Answer: D
Question: Sam purchased 20 dozens of toys at the rate of Rs. 375 per dozen. He sold each one of them at the rate of Rs. 33. What was his percentage profit?
Options:
A)5.2%
B)5.4%
C)5.6%
D)6%
E)6.5%
Rationale: Cost Price of 1 toy = Rs. 375 = Rs. 31.25
12
Selling Price of 1 toy = Rs. 33
So, Gain = Rs. (33 - 31.25) = Rs. 1.75
Profit % = 1.75	x 100	%	=	28	% = 5.6%
C)
Answer: C
Question: Sachi invested amount of 8000 in a fixed deposit for 2 years at compound interest rate of 5 % per annum. How much Sachi will get on the maturity of the fixed deposit.
Options:
A)8000
B)8500
C)8820
D)8870
E)8900
Rationale: CI = (800*(1+5/100)^2
==> 8820
ANSWER C
Answer: C
Question: At a particular graduation party with 300 guests, 70% of the guests brought gifts, and 40% of the female guests brought gifts. If 15 males did not bring gifts to the party, how many females did bring gifts?
Options:
A)18
B)28
C)50
D)68
E)70
Rationale: the correct method
total = 300..
70% of 300 = 210 got gifts..
90 did not get gift, out of which 15 are males, so remaining 90-15=75 are females..
But 40% females brought gift, so 60% did not get it..
so 60% = 75, 100%= 75*100/60=125..
ans 40% of 125 =50
C
Answer: C
Question: If a is the sum of b and c, then which one of the following must equal b – c?
Options:
A)a+2c
B)a+c
C)a-c
D)a-2c
E)a+2c
Rationale: Given a= b+c if you subtracts both side with -2c
a-2c = b-c
Answer : D
Answer: D
Question: Husband has prepared for a candle light dinner on the honeymoon for his wife. While they were having the dinner, a strong breeze flew through the open window and four candles out of ten were extinguished. After that, the husband closed the window.
How many candles were left in the end?
Options:
A)2
B)3
C)4
D)5
E)6
Rationale: Solution:
Four
As the window was closed it is obvious that the six candles that were not extinguished were lit till they melted away entirely. Thus only four candles that were extinguished remain at the end.
Answer C
Answer: C
Question: Mr. Jones is the Chairman of a committee. In how many ways can a committee of 5 be chosen from 10 people given that Mr. Jones must be one of them?
Options:
A)126
B)252
C)459
D)3024
E)4126
Rationale: Total Ways of choosing the committee = Total Ways of choosing 4 out of 9 candidates leaving Mr.Jones as one of the selected candidate in advance
Total Ways of choosing 4 out of 9 candidates = 9C4 = 9!/(5!*4!) = 126
Answer: option A
Answer: A
Question: There are cats got together and decided to kill the mice of 999975. Each cat kills equal number of mice and each cat kills more number of mice than cats there were. Then what are the number of cats?
Options:
A)941,1009
B)991,1001
C)995,1005
D)791,1009
E)931,1009
Rationale: 999975 can be written as 1000000 â€“ 25
= 10002 â€“ 52 ie of the form a2-b2=(a+b)(a-b)
=(1000+5)*(1000-5)
= (1005)*(995)
Given that number of cats is less than number if mice.
So number of cats is 995 and number of mice were 1005
Answer C
Answer: C
Question: The average of six numbers is 3.95. The average of two of them is 3.2, while the average of the other two is 3.85. What is the average of the remaining two numbers?
Options:
A)4.5
B)4.6
C)4.7
D)4.8
E)4.9
Rationale: Sum of the remaining two numbers
= (3.95 × 6) – [(3.2 × 2) + (3.85 × 2)]
= 23.70 – (6.4 + 7.7)
= 23.70 – 14.1 = 9.60
∴ Required average = (9.6⁄2) = 4.8
Answer D
Answer: D
Question: How many shots of 1cm radius can be prepared from a sphere of 3cm radius?
Options:
A)33
B)77
C)27
D)88
E)121
Rationale: 4/3 π * 3 * 3 * 3 = 4/3 π * 1 * 1 * 1 * x
x = 27
Answer: C
Answer: C
Question: A club wants to mix 30 pounds of candy worth $8.00 per pound with candy worth $5.00 per pound to reduce the cost of the mixture to $6.00 per pound. How many pounds of the $5.00 per pound candy should be used?
Options:
A)30
B)40
C)50
D)60
E)70
Rationale: Let number of pounds of 5$ candy to be used be w
6 = (30*8 + 5*w)/(30 +w)
=>180 + 6w = 240 + 5w
=> w = 60
Answer D
Answer: D
Question: How many even multiples of 25 are there between 249 and 501?
Options:
A)5
B)6
C)9
D)10
E)11
Rationale: 250 = 10*25
500 = 20*25
The even multiples are 25 multiplied by 10, 12, 14, 16, 18, and 20 for a total of 6.
The answer is B.
Answer: B
Question: How many two letter words are formed using the letters of the word RAM?
Options:
A)8
B)1
C)6
D)4
E)9
Rationale: The number of letters in the given word is four.
The number of three letter words that can be formed using these four letters is 3P2
= 3 * 2 = 6.
Answer: C
Answer: C
Question: Jim is able to sell a hand-carved statue for $550 which was a 35% profit over his cost. How much did the statue originally cost him?
Options:
A)$407.41
B)$412.40
C)$455.40
D)$474.90
E)$488.20
Rationale: 550 = 1.35*X
X = 550/1.35 = 407.407407...
which rounds to $407.41, which is (A).
Answer: A
Question: Can you deduce the pattern and find the next number in the series?
2,6, 12, 20, 30, __?
Options:
A)41
B)45
C)56
D)49
E)42
Rationale: Solution:
42
Explanation:
2=1*1+1
6=2*2+2
12=3*3+3
20=4*4+4
30=5*5+5
Thus the next number will be
6*6+6=42
Answer E
Answer: E
Question: A train passes a station platform in 36 seconds and a man standing on the platform in 20 seconds. If the speed of the train is 54 km/hr, what is the length of the platform?
Options:
A)37
B)240
C)288
D)267
E)211
Rationale: Speed = (54 * 5/18) m/sec = 15 m/sec. Length of the train = (15 x 20)m = 300 m. Let the length of the platform be x meters. Then, (x + 300)/36 = 15 ==> x + 300 = 540 ==> x = 240 m.Answer: B
Answer: B
Question: Anand and Deepak started a business investing Rs. 22,500 and Rs. 35,000 respectively. Out of a total profit of Rs. 13,800, Deepak’s share is :
Options:
A)Rs. 5400
B)Rs.7200
C)Rs. 8400
D)Rs. 9600
E)Rs. 8600
Rationale: Ratio of their shares = 22500 : 35000 = 9 : 14.
Deepak’s share = Rs. 13800 * 14/23
= Rs. 8400
ANSWER:C
Answer: C
Question: A man walking at a rate of 10km/hr crosses a bridge in 3 minutes. The length of the bridge is?
Options:
A)500
B)650
C)250
D)111
E)236
Rationale: Speed = 10*5/18 = 50/18 m/sec
Distance covered in 5 minutes = 50/18 * 5 *60 = 500 m
Answer is A
Answer: A
Question: Jill works as a waitress at the local diner where she earns an hourly wage of $6.00 per hour and a standard tip rate of 35% of the cost of the orders she serves. If she worked four 10-hour shifts this week and averaged $40 in orders per hour, how much did Jill earn this week?
Options:
A)280
B)300
C)320
D)350
E)1120
Rationale: Jill earns 6 dollars/hour and the hourly tip is (7/20)*40.
Jill thus earns 6*10+10*14 per day(or 6(10)+14(10)=20(14)=280).
Jill has worked for 4 days ->280*4=1120.
This matches answer choice E.
Answer: E
Question: A BAG CONTAINS 6 WHITE AND 4 BLACK BALLS .2 BALLS ARE DRAWN AT RANDOM. FIND THE PROBABILITY THAT THEY ARE OF SAME COLOUR.
Options:
A)7/15
B)4/8
C)15/7
D)6/7
E)9/5
Rationale: LET S BE THE SAMPLE SPACE
THEN N(S)=NO OF WAYS OF DRAWING 2 BALLS OUT OF (6+4)=10C2=(10*9)/(2*1)=45
LET E=EVENT OF GETTING BOTH BALLS OF SAME COLOUR
THEN N(E)=NO OF WAYS(2 BALLS OUT OF SIX) OR(2 BALLS OUT OF 4)
=(6C2+4C2)=(6*5)/(2*1)+(4*3)/(2*1)=15+6=21
P(E)=N(E)/N(S)=21/45=7/15
Ans: A
Answer: A
Question: A team bought a total of 355 balls. If each player on the team bought at least 16 balls, then what is the greatest possible number of players on the team?
Options:
A)21
B)22
C)23
D)24
E)25
Rationale: 355/16=22 plus remainder.
The answer is B.
Answer: B
Question: A, B, and C were to be paid in proportion to the part of work they did while working on the same piece of work. A and B individually can finish the piece of work in 12 days and 10 days respectively. They worked together for five days and then C completed the remaining work all alone. If $720 was the net sum to be paid for the entire work, what was the average daily wage of B?
Options:
A)$144
B)$90
C)$72
D)$54
E)$48
Rationale: The correct answer is C.
Answer: C
Question: John takes 18 hours to complete a certain job, while Bill takes only 6 hours to complete the same job. If Steve is faster than John but slower than Bill at completing the same job, then which of the following could be the time it takes the three men together, working at their constant, individual rates, to complete the job?
Options:
A)2 hours, 10 minutes
B)2 hours, 30 minutes
C)3 hours, 10 minutes
D)3 hours, 45 minutes
E)4 hours, 10 minutes
Rationale: The rate of John plus Bill is 1/18 + 1/6 = 4/18 of the job completed per hour.
If Steve worked at the same rate as John, the rate would be 4/18 + 1/18 = 5/18
The slowest possible time would be 18/5 hours = 3 hours, 36 minutes.
If Steve worked at the same rate as Bill, the rate would be 4/18 + 1/6 = 7/18
The fastest possible time would be 18/7 hours = 2 hours + 4/7 hours.
The actual time is somewhere between these two extreme points.
The answer is C.
Answer: C
Question: If the speed of Y meters per minute is equivalent to the speed of X kilometers per hour, what is X in terms of Y? (1 kilometer=1000 meters)
Options:
A)15y/18
B)6y/5
C)18y/5
D)6y/100
E)3600000y
Rationale: If the speed of Y meters per second is equivalent to the speed of X kilometers per hour, what is X in terms of Y? (1 kilometer=1000 meters)
We need to find an equation with y in the answer...
convert all measurements so they are alike (i.e. convert km to m, minutes to hours, etc)
Speed = y/t
y meters/second
(60) x meters/hour
Speed = x/t
x KM/hour
Speed = x(1000m)/hour
x(1000meters)/hour = (60) x meters/hour
x(1000)/1hour = y(60) / 1 hour
x(1000) = y(60)
x = 0.06y
Answer: D. 6y/100
Answer: D
Question: An item is being sold for $10 each. However, if a customer will “buy at least 3” they have a promo discount of 17%. Also, if a customer will “buy at least 10” items they will deduct an additional 8% to their “buy at least 3” promo price. If Sam buys 10 pcs of that item how much should he pay?
Options:
A)$92.00
B)$88.00
C)$87.04
D)$80.96
E)$75.00
Rationale: Without any discount Sam should pay 10*10=$100. Now, the overall discount would be slightly less than 27%, thus he must pay slightly more than $73. Only answer choice E fits.
Answer: E
Answer: E
Question: A string of 15 light bulbs is wired in such a way that if any individual light bulb fails, the entire string fails. If for each individual light bulb the probability of failing during time period T is 0.06, what is the probability that the string of light bulbs will fail during the time period T?
Options:
A)1 - (0.94)^15
B)(0.06)^15
C)1 - (0.06)^15
D)(0.94)^15
E)0.06^150
Rationale: The string of light bulbs will fail if at least one light bulb fails. So, let's find the probability of the opposite event and subtract that value from 1.
The opposite event is when none of the 15 light bulbs fails, since the probability of each light bulb not to fail is 1-0.06=0.94 the probability that none of the 15 light bulbs fails is 0.94^15.
Hence, the probability that at least one light bulb fails is 1-0.94^15.
Answer: A.
Now, you should have spotted that your reasoning was not right because of one simple thing, consider the case when we have 100 light bulbs instead of 15, then according to your logic the probability that the string of light bulbs will fail would be 100*0.06=6, which is not possible since the probability of an event cannot be more than 1 (100%).
Answer: A
Question: A train moves fast a telegraph post and a bridge 264 m long in 8 sec and 20 sec respectively. What is the speed of the train?
Options:
A)28.9 km/hr
B)89.9 km/hr
C)28.9 km/hr
D)79.2 km/hr
E)19.9 km/hr
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 264)/20 = y
y = 22
Speed = 22 m/sec = 22 * 18/5 = 79.2 km/hr.
Answer:D
Answer: D
Question: Andrew purchased 7kg of grapes at the rate of 68 per kg and 9 kg of mangoes at the rate of 48 per kg. How much amount did he pay to the shopkeeper?
Options:
A)1000
B)908
C)930
D)1075
E)1080
Rationale: Cost of 7 kg grapes = 68 × 7 = 476.
Cost of 9 kg of mangoes = 48 × 9 = 432.
Total cost he has to pay = 476 + 432 = 908
B
Answer: B
Question: If x and y are different integers and x^2 = xy, which of the following must be true ?
I. y = 0
II. x = 0
III. x = y
Options:
A)I only
B)II only
C)III only
D)I and III only
E)II, and III
Rationale: Answer choice A is correct.
The question gives you x^2=xy
you can simplify that as x^2-xy=0
x(x-y)=0 the solution will be either x=0 or x=y, since x and y are different integers x cannot equal y, that leaves you x=0 to be the only answer.
Answer E
Answer: E
Question: If f(x) = -*5 (x^4 - 1)/(x^2), what is f(1/x) in terms of f(x)?
Options:
A)f(x)
B)-f(x)
C)1/f(x)
D)5f(x)
E)2*f(x)
Rationale: -5*f(1/x) =-5* ((1/x)^4 - 1) / ((1/x)^2)
= -5*((1/x^4) - 1) / (1/x^2)
= -5*((1-x^4)/(x^4)) / (1/x^2)
= -5* (1-x^4)/(x^2)
= -5* ( (x^4) -1) / (x^2)
= 5f(x)
Answer is D.
Answer: D
Question: 4, 10, (?), 82, 244, 730
Options:
A)26
B)24
C)40
D)48
E)28
Rationale: 4 × 3 - 2 = 10
10 × 3 - 2 = 28
28 × 3 - 2 = 82
82 × 3 - 2 = 244
244 × 3 - 2 = 730
Answer is E.
Answer: E
Question: The cost of fencing a square field @ Rs. 20 per metre is Rs.10.080.How much will it cost to lay a three meter wide pavement along the fencing inside the field @ Rs. 50 per sq m
Options:
A)73828
B)73829
C)73811
D)73800
E)73129
Rationale: perimeter = total cost / cost per m = 10080 /20 = 504m
side of the square = 504/4 = 126m
breadth of the pavement = 3m
side of inner square = 126 - 6 = 120m
area of the pavement = (126 x126) - (120 x 120) = 246 x 6 sq m
cost of pavement = 246*6*50 = Rs. 73800
Answer: D
Answer: D
Question: In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 50 questions and secures 130 marks, the no of questions he attempts correctly is :
Options:
A)A)36
B)B)38
C)C)90
D)D)88
E)E)37
Rationale: Let the number of correct answers be X.
Number of incorrect answers = (60 – X).
4x – (50 – x) = 130
=> 5x = 180
=> x = 36
Answer:A
Answer: A
Question: How many cones of radius 4 m, height 2 m can be formed from a cylinder of 12 m radius, 10 m height:
Options:
A)135
B)125
C)145
D)115
E)155
Rationale: (Cylinder volume)/(Cone volume)
(πr(power2)h)/(1/3 πr(power2)h)
= (π × 12 × 12 × 10)/(1/3 π × 4 × 4 × 2) = 135
Answer is A.
Answer: A
Question: A sum at simple interests at 13 ½ % per annum amounts to Rs.2502.50 after 4 years find the sum.
Options:
A)Rs.1645.
B)Rs.1675.
C)Rs.1625.
D)Rs.1635.
E)Rs.1655.
Rationale: Let sum be Rs. x then , S.I.=Rs.(x*(27/2) *4*(1/100) ) = Rs.27x/50
amount = (Rs. x+(27x/50)) = Rs.77x/50
77x/50 = 2502.50  x = (2502.50 * 50)/77 = 1625
Hence , sum = Rs.1625.
Answer is C.
Answer: C
Question: Frank is 14 years younger then John. In 5 years John will be twice as old as Frank. How old will Frank be in four years?
Options:
A)8
B)10
C)13
D)14
E)16
Rationale: Frank is 15 years younger then John --> F+14=J;
In 5 years John will be twice as old as Frank (in 5 year John will be J+5 years old and Frank will be F+5 years old) --> J+5=2*(F+5) --> (F+14)+5=2*(F+5) --> F=9;
In 4 years Frank will be 9+4=13 years old.
Answer: C.
Answer: C
Question: A room contains 160 people, 20 percent of whom are women. A group of people, 30 percent of whom are women, leaves the room. Of the people remaining in the room, 10 percent are women. How many people left the room?
Options:
A)10
B)20
C)40
D)60
E)80
Rationale: Say group of x people left the room.
# of women in the room was 0.2*160=32;
# of women in the group that left 0.3x;
# of women in the room after the group left it is 0.1(160-x);
So, 32-0.3x= 0.1(160-x) --> x=80.
Answer: E.
Answer: E
Question: A 250 m long train is running at a speed of 55 Km/hr. It crossed a platform of length 520 m in ?
Options:
A)41.1 sec
B)20.2 sec
C)31.8 sec
D)50.4 sec
E)none of the above
Rationale: Speed = 55 Km/hr
(to convert km/hr in to M/s)
= 55 x 5/18 M/s
Distance = 250 m + 520 m ( If questions is about train crossing a post you need to consider only the length of Train, )
= 770 m
Time = Distance / Speed
= 770 x 18 / (5 x 55)
= 50.4 sec
Ans is :D
Answer: D
Question: The age of father 10 years ago was thrice the age of his son. Ten years hence, father's age will be twice that of his son. The ratio of their present ages is:
Options:
A)5:2
B)7:3
C)9:2
D)10:4
E)13:4
Rationale: Let the ages of father and son 10 years ago be 3x and x years respectively.
Then, (3x + 10) + 10 = 2[(x + 10) + 10]
3x + 20 = 2x + 40
x = 20.
Required ratio = (3x + 10):(x + 10) = 70:30 = 7:3.
Answer: Option B
Answer: B
Question: In Arun’s opinion, his weight is greater than 65 kg but less than 72 kg. His brother doest not agree with Arun and he thinks that Arun’s weight is greater than 60 kg but less than 70 kg. His mother’s view is that his weight cannot be greater than 68 kg. If all are them are correct in their estimation, what is the average of different probable weights of Arun?
Options:
A)67 kg.
B)68 kg.
C)69 kg.
D)Data inadequate
E)None of these
Rationale: EXPLANATION
Let Arun’s weight by X kg.
According to Arun, 65 < X < 72
According to Arun’s brother, 60 < X < 70.
According to Arun’s mother, X <= 68
The values satisfying all the above conditions are 66, 67 and 68.
Required Average =( 66 + 67 + 68 /3 )= (201/3) = 67 kg
Answer A
Answer: A
Question: A crate of apples contains 1 bruised apple for every 30 apples in the crate. Two out of every 4 bruised apples are considered not fit to sell, and every apple that is not fit to sell is bruised. If there are 12 apples not fit to sell in the crate, how many apples are there in the crate?
Options:
A)720
B)360
C)480
D)600
E)840
Rationale: as given 2 out of every 4 bruised apple is not fit to sell
or, 50% of the bruised apples are not fit to sell.
as per the question 12 are not fit to sell
or,
0.0.5x=12
x=1200/50=24
thus total number of bruised apples =24
total number of apples =30*24=720
Answer:A
Answer: A
Question: A library has an average of 510 visitors on Sundays and 240 on other day. The average number of visitors in a month of 5 days starting with sunday is
Options:
A)1215
B)1314
C)2900
D)1710
E)2750
Rationale: Explanation:
As the month begin with sunday, so there will be five sundays in the month. So result will be:
=(510×5+240×25/30)=(8550/5)=1710
Answer: Option D
Answer: D
Question: If 2n+4 - 2n+2 = 3, then n is equal to :
Options:
A)2
B)-2
C)1
D)-1
E)None
Rationale: Sol.
2n+4 - 2n+2 = 3 ⇔ 2n+2 (22 - 1) = 3 ⇔ 2n+2 = 1 = 20
⇔ n+2 = 0 ⇔ n= -2.
Answer B
Answer: B
Question: (935421 x 625) = ?
Options:
A)584625125
B)584626125
C)584629125
D)584637125
E)584638125
Rationale: 935421 x 625 = 935421 x 54 = 935421 x 10 4
2
=	935421 x 104	=	9354210000
24	16
= 584638125
E)
Answer: E
Question: Which of the following is true about 0<|x|-x/2<5?
Options:
A)-1<x<0
B)0<x<1
C)1<x<2
D)2<x<3
E)3<x<4
Rationale: when can be |x|-4x be greater than 0..
NEVER when x is positive..
ONLY A is left..
you can also substitute any value within the given range to check for answer
Example - put x as -0.5 for A. -1<x<0..
so |x|-x/2 = |-0.5|- (-0.5)/2 = 0.75 and it satisfies 0<|x|-4x<5
A
Answer: A