divelab/Sys2Bench huggingface dataset:
Question: The original price of a car was $25,000. Because the car owner thought he could get more money for the car, he set a new price by increasing the original price of the car by 5%. After a week, the car had not sold, so the owner discounted the new price by 5%, and the car was finally sold. What price was the car sold for?
Options:
A)$24,937.50
B)$24,948.50
C)$24,954.50
D)$24,958.50
E)$24,963.50
Rationale: The car was sold for (0.95)(1.05)($25000)=$24,937.50
The answer is A.
Answer: A
Question: The average of first seven prime numbers:
Options:
A)5.6
B)11.2
C)12.9
D)8.2
E)7.4
Rationale: Explanation:
The first seven prime numbers is 2, 3, 5, 7, 11, 13, 17
Average = 58/7 = 8.2
Answer: Option D
Answer: D
Question: A certain manufacturer produces items for which the production costs consist of annual fixed costs totaling $130,000 and variables costs averaging $8 per item. If the manufacturer’s selling price per item is $12, how many items the manufacturer produce and sell to earn an annual profit of $140,000?
Options:
A)2,858
B)8,667
C)21,429
D)35,000
E)67,500
Rationale: Let the items manufactured or sold bex
130000+8x = 12x-140000
4x = 270000
x = 67500
Ans:E
Answer: E
Question: Kanul spent $3000 in buying raw materials, $1000 in buying machinery and 30% of the total amount he had as cash with him. What was the total amount?
Options:
A)$5825.16
B)$5725.26
C)$5714.28
D)$5912.52
E)$5614.46
Rationale: Let the total amount be x
then, (100-30)% of x = 3000+1000
70% of x = 4000
70x/100 = 4000
x = $40000/7
x = $5714.28
Answer is C
Answer: C
Question: The parameter of a square is equal to the perimeter of a rectangle of length 16 cm and breadth 14 cm. Find the circumference of a semicircle whose diameter is equal to the side of the square. (Round off your answer to two decimal places)?
Options:
A)23.77 cm
B)23.47 cm
C)83.57 cm
D)23.57 cm
E)23.56 cm
Rationale: Let the side of the square be a cm.
Parameter of the rectangle = 2(16 + 14) = 60 cm Parameter of the square = 60 cm
i.e. 4a = 60
A = 15
Diameter of the semicircle = 15 cm
Circimference of the semicircle
= 1/2(∏)(15)
= 1/2(22/7)(15) = 330/14
= 23.57 cm to two decimal places
Answer:D
Answer: D
Question: If d is an even integer and d/18 is an odd integer, which of the following is NOT an even integer?
Options:
A)(d^2)/54
B)(d^2)/20
C)(d^2)/9
D)(d^2)/6
E)(d^2)/2
Rationale: since d is an even integer and d/18 is an odd integer. thus maximum power of 2 in a is one. why ?? because if the power of 2 in the expression has been 2 or greater, then the d/18 must have been an even integer. (18=2*3^2. as 18 contain only one 2 in the expression)
now, any expression in which we have 4 at the denominator will be odd. out of the given options only 12 is a multiple of 4. hence answer should be B
Answer: B
Question: The largest 4 digit number exactly divisible by 88 is:
Options:
A)3377
B)2255
C)7732
D)9944
E)9932
Rationale: D
9944
Divide largest four digit number 9999 by 88. You get 113.625.
Obviously 113 would be exactly divisible so we want to know what that number is.
We get this by multiplying 113 with 88 = 9944
Answer: D
Question: A chemist mixes one liter of pure water with x liters of a 60% salt solution, and the resulting mixture is a 10% salt solution. What is the value of x?
Options:
A)1/5
B)1/3
C)1/2
D)1
E)3
Rationale: Concentration of salt in pure solution = 0
Concentration of salt in salt solution = 60%
Concentration of salt in the mixed solution = 10%
The pure solution and the salt solution is mixed in the ratio of --> (60 - 10)/(10 - 0) = 5/1
1/x = 5/1
x = 1/5
Answer: A
Answer: A
Question: Which of the following data sets has the smallest standard deviation?
Options:
A) {3, 3, 3, 3, 3}
B) {2, 3, 3, 3, 4}
C) {2, 2, 2, 4, 5}
D) {0, 2, 3, 4, 6}
E) {-1, 1, 3, 5, 7}
Rationale: since we are asked to compare 'standard deviation', we should look out for similarity between all the sets..
The SIMILARITY is - the SUM of all sets is equal =15..
and hence average = 15/5 = 3...
Now we have 5 different sets which have AVG as 3, so we will look for the spread of the other elements of set around the AVERAGE..
clearly E has a range of 7-(-1) or 8, and has the highest standard deviation..
Next is D, which has a range of 6-0 or 6..
and (A) {3, 3, 3, 3, 3} has smallest standard of deviation.
ans A
Answer: A
Question: A cow is tethered in the middle of a field with a 14 feet long rope. If the cow grazes 100 sq.ft. per day, then approximately what time will be taken by the cow to graze the whole field?
Options:
A)5 days
B)6 days
C)7 days
D)8 days
E)9 days
Rationale: Area of the field grazed = [22/7*14*14]sq.ft. = 616 sq.ft.
Number of days taken to graze the field = 616/100 days
=> 6 days
ANSWER:B
Answer: B
Question: The digit in the unit’s place of a number is equal to the digit in the ten’s place of half of that number and the digit in the ten’s place of that number is less than the digit in unit’s place of half of the number by 1. If the sum of the digits of number is 7, then what is the number
Options:
A)34
B)49
C)162
D)52
E)79
Rationale: Let the ten’s digit be x and unit’s digit be y
Then, (10x+y)/2=10y+(x+1)
8x-19y=2
And x+y=7
X=5 and y=2
Then reqired number is 52
Option D
Answer: D
Question: A local bank that has 14 branches uses a two-digit code to represent each of its branches. The same integer can be used for both digits of a code, and a pair of two-digit numbers that are the reverse of each other (such as 17 and 71) are considered as two separate codes. What is the fewest number of different integers required for the 14 codes?
Options:
A)3
B)4
C)5
D)14( ( 2 integers 4 codes)
E)7
Rationale: Pick any two integer.
Integers: 12
Code: 11, 12, 21, 22 = 4 Codes
Add one more integer: 3
13, 31, 33, 23, 32 = 5 Codes
Add one more integer: 4
44, 14, 41, 24, 42, 34, 43 = 7 Codes
Total = 16 Codes. Enough. Answer: D
4 integers create 14 codes.
Answer: D
Question: Marie's seafood restaurant gets a delivery of fresh seafood every day, 7 days per week, and her delivery company charges herddollars per delivery plusccents per item delivered. If lst week Sarah's seafood restaurant had an average ofxitems per day delivered, then which of the following is the total cost, in dollars, of last week's deliveries ?
Options:
A)7cdx/100
B)d + 7cx/100
C)7d + 7xc/100
D)7d + xc/100
E)7cdx
Rationale: Answer is C. Straightforward question.
Answer: C
Question: A merchant has 1000 kg of sugar part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The Quantity sold at 18% profit is?
Options:
A)700 kg
B)500 kg
C)600 kg
D)800 kg
E)900 kg
Rationale: By the rule of alligation:
Profit of first part Profit of second part
So, ratio of 1st and 2nd parts = 4 : 6 = 2 : 3.
Quantity of 2nd kind = (3/5 x 1000)kg = 600 kg
Answer: C
Answer: C
Question: A motorcyclist goes from Bombay to Pune, a distance of 256 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?
Options:
A)1:2
B)1:5
C)1:4
D)1:1
E)5:8
Rationale: T = 256/32 = 8 h
T = 8 - 3 = 5
Time Ratio = 8:5
Speed Ratio = 5:8
Answer: E
Answer: E
Question: A clothing store originally bought 100 jackets at a total cost of j dollars. If each jacket was sold for 20 percent more than its original cost, what was the individual price, in terms of j, of each jacket sold?
Options:
A)j/83
B)7j/500
C)140j
D)j/100+40
E)140j/100
Rationale: lets take j=1000, as decided by you..
now 20% increase makes it 1200..
this is the price for 100 jackets, so selling price for each jacket=1200/100=$12..
=j/83
so ans is correct as A..
Answer: A
Question: If R is an integer greater than 6, which of the following must be divisible by 3?
Options:
A)R(R+1)(R-4)
B)N(N+2)(N-1)
C)N(N+3)(N-5)
D)N(N+4)(N-2)
E)N(N+5)(N-6)
Rationale: Now take R = 3k , R = 3k+1 R = 3k+2..put in all the choices. If by putting all the values of R we get it is divisible by 3, then it is correct answer choice.
A is correct. It will hardy take 10 sec per choice as we have to consider only 3k+1 and 3k+2.
Answer: A
Question: The C.P of 10 pens is equal to the S.P of 12 pens. Find his gain % or loss%?
Options:
A)16 2/6%
B)16 9/3%
C)16 2/3%
D)16 3/3%
E)12 2/3%
Rationale: 10 CP = 12 SP
12 --- 2 CP loss
100 --- ? => 16 2/3%
Answer:C
Answer: C
Question: If two numbers x, a perfect square and y, a perfect cube are added results a two digit number, whose digits if reversed, difference is 72, Find x and y ?
Options:
A)x=4,y=8
B)x=4,y=9
C)x=16,y=64
D)x=4,y=9
E)x=5,y=8
Rationale: 16+64=80
when reversed 08
80-8=72
x=16,y=64
ANSWER:C
Answer: C
Question: A box contains nine bulbs out of which 4 are defective. If four bulbs are chosen at random, find the probability that atleast one bulb is good?
Options:
A)125/129
B)125/122
C)125/126
D)125/121
E)125/125
Rationale: Required probability
= 1 - 1/126
= 125/126
Answer: C
Answer: C
Question: Concentrated grapes juice comes inside a cylinder tube with a radius of 2.5 inches and a height of 15 inches. The tubes are packed into wooden boxes, each with dimensions of 11 inches by 10 inches by 31 inches. How many tubes of concentrated grapes juice, at the most, can fit into 3 wooden boxes?
Options:
A)24.
B)28.
C)36.
D)42.
E)48.
Rationale: Concentrated grapes juice comes inside a cylinder tube since height of a tube is 15 inches , the tubes can fit only in one way .
now, diameter of each tube = 5 inches
therefore, 4*2 can be put in each wooden box
in 3 boxes 3*4*2 can be accommodated
= 24=A
Answer: A
Question: If x dollars is invested at 10 percent for one year and y dollars is invested at 8 percent for one year, the annual income from the 10 percent investment will exceed the annual income from the 8 percent investment by $74. If $2,000 is the total amount invested, how much is invested at 8 percent?
Options:
A)$600
B)$700
C)$800
D)$900
E)$1000
Rationale: 0.1x = 0.08(2000-x)+74
0.18x = 234
x = 1300
Then the amount invested at 8% is $2000 - $1300 = $700
The answer is B.
Answer: B
Question: Find the value of (2 − 1/3) (1 − 1/4)(1 − 1/5)……… (1 − 1/99)(1 − 1/100)
Options:
A)1/13
B)1/19
C)1/20
D)1/21
E)1/31
Rationale: (2 − 1/3) (1 − 1/4)(1 − 1/5)..... (1 − 1/99)(1 − 1/100)
5/3 × 3/4 × 4/5 × ....... 98/99 × 99/100 = 5/100 = 1/20
C)
Answer: C
Question: At McDonalds you can order Chicken McNuggets in boxes of 6, 9, and 20. What is the largest number such that you can not order any combination of the above to achieve exactly the number you want?
Options:
A)43
B)53
C)63
D)73
E)83
Rationale: The answer is 43.
For any desired number if it is divisible by 3 it can easily be made with 6 and 9 packs, except if the number is 3 itself. If you can't use all six packs then use one 9 pack and you can do the rest with six packs.
If the number is not divisible by 3 then use one 20 pack. If the remaining number is divisible by 3 then use the above method for the rest.
If the number still isn't divisible by 3 use a second 20 pack. The remainder must be divisible by 3, in which case use the 6 and 9 packs as above.
The largest impossible number would be such that you would have to subtract 20 twice to get a remainder divisible by 3. However, you can't make 3 itself with 6 and 9 packs. So the largest impossible number is 2*20+3=43.
correct answer A
Answer: A
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)120 m
B)240 m
C)300 m
D)200 m
E)None of these
Rationale: Explanation:
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 IS B
Answer: B
Question: By how much is three-fifth of 620 greater than four- seventh of 210 ?
Options:
A)520
B)215
C)252
D)None of these
E)Cannot be determined
Rationale: Solution
3/5 of 620 - 4/7 of 210 = 252.
Answer C
Answer: C
Question: A man is walking at the rate of 9 km/hr crosses a bridge in 15 minutes. The length of the bridge is
Options:
A)1000 meters
B)1050 meters
C)2200 meters
D)2250 meters
E)None of these
Rationale: Explanation:
We need to get the answer in meters. So we will first of change distance from km/hour to meter/sec by multiplying it with 5/18 and also change 15 minutes to seconds by multiplying it with 60.
Speed=9âˆ—5/18=5/2m/sec
Time=15âˆ—60seconds=900seconds
Distance=Timeâˆ—Speed/Distance=5/2âˆ—900=2250meter
Option D
Answer: D
Question: which one is odd?
4377
3954
9863
8454
9831
Options:
A)4377
B)3954
C)9863
D)8454
E)None
Rationale: Correct Answer : C
sum of digit of all other number is 21, but sum of digit of 9863 is 26
Answer: C
Question: It takes Beth 9 minutes to do one oil change, and it takes Logan 12 minutes. At 4:56 pm, they both finish an oil change simultaneously. If Beth and Logan both began doing oil changes at exactly the same time and worked without pausing, when did they both start doing oil changes?
Options:
A)4:11 pm
B)4:20 pm
C)4:29 pm
D)4:38 pm
E)4:47 pm
Rationale: Since Beth finishes s oil changes after s × 9 minutes and Logan finishes c oil changes after c × 12 minutes, they both finished doing an oil change at the same time when s × 9 = c × 12. Since s and c must be integers (they represent the number of oil changes finished) this question is asking you to find a common multiple of 9 and 12. The question asks for the first time they began a car simultaneously, so you must find the least common multiple and subtract. The least common multiple of 9 and 12 is 36, so in the context of the question, this would be 36 minutes. Therefore, they began changing the oil of a car at the same time at 4:56 - 36 minutes, or 4:20 p.m. The answer is (B).
Answer: B
Question: A man can row with a speed of 30 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
Options:
A)A)63kmph
B)B)63kmph
C)C)35kmph
D)D)62kmph
E)E)74kmph
Rationale: Explanation:
M = 30
S = 5
DS = 30 + 5 = 35
Answer: Option C
Answer: C
Question: Every Sunday, Giri jogs 3 miles. For the rest of the week, each day he jogs 1 mile more than the previous day. How many miles does giri jog in 2 weeks ?
Options:
A)42
B)63
C)84
D)98
E)108
Rationale: In one week, Giri jogs 3 + 4 + 5 + 6 + 7 + 8 + 9 = 42 miles
In two weeks, Giri jogs 84 miles.
ANSWER:C
Answer: C
Question: Rs.1500 is divided into two parts such that if one part is invested at 6% and the other at 5% the whole annual interest from both the sum is Rs.83. How much was lent at 5%?
Options:
A)700
B)299
C)266
D)500
E)188
Rationale: (x*5*1)/100 + [(1500 - x)*6*1]/100 = 83
5x/100 + 90 â€“ 6x/100 = 83
x/100 = 7
=> x = 700
Answer:A
Answer: A
Question: Sam and Nik start from A and B respectively at the same time and travel towards each other at constant speeds along the same route. After meeting at a point between A and B, Sam and Nik proceed to their destinations of B and A respectively. Sam reaches B 60 minutes after the two meet and Nik reaches A 90 minutes after their meeting. How long did Sam take to cover the distance between A and B?
Options:
A)60 minutes
B)120 minutes
C)200 minutes
D)225 minutes
E)none of the above
Rationale: t-time taken for AB to meet
(Vs+Vn)t=Vs*60+Vn*90;
Vs(t-60)=Vn(90-t)
This means 60<t<90
so ans will be 60+t
Only B fits this eqn
Answer: B
Question: If log 27 = 1.431, then the value of log 9 is:
Options:
A)0.934
B)0.954
C)0.955
D)0.945
E)0.96
Rationale: log 27 = 1.431
Log 3^3 = 1.431
log 3 = 0.477
log 9 = log(3^2) = 2 log 3 = (2*0.477) = 0.954
ANSWER D
Answer: D
Question: What do you get if you add 7 to 290 three times?
Options:
A)305
B)296
C)289
D)297
E)309
Rationale: D
297 , 297 , 297
Answer: D
Question: On taking delivery of a consignment of eggs the market stall owner was furious to find that several were cracked. In fact, on counting them up in order to assess the damage he found that 72 were cracked, which was 12 per cent of the total consignment. How many eggs in total were in the consignment?
Options:
A)700
B)350
C)500
D)600
E)850
Rationale: D
600
= 72 ÷ 12 × 100
= 600.
Answer: D
Question: A train 275 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
Options:
A)5
B)6
C)7
D)15
E)9
Rationale: Speed of train relative to man = (60 + 6) km/hr = 66 km/hr
[66 * 5/18] m/sec = [55/3] m/sec.
Time taken to pass the man = [275 * 3/55] sec
= 15 sec
Answer: D
Answer: D
Question: A rectangular circuit board is designed to have width w inches, perimeter p inches, and area q square inches. Which of the following equations must be true?
Options:
A)w^2 + pw + q = 0
B)w^2 - pw + 2q = 0
C)2w^2 + pw + 2q = 0
D)2w^2 - pw - 2q = 0
E)2w^2 - pw + 2q = 0
Rationale: Notice that we can discard options A, and C right away. The sum of 3 positive values Cannot be 0.
Now, assume:
Width =w = 1 inchand length = 1 inch;
Perimeter =p = 4 inches;
Area =q = 1 square inches.
Plug the values of w, p, and q into the answer choices: only for E 2w^2 - pw + 2q = 2 - 4 + 2 = 0.
Answer: E.
Answer: E
Question: If neha is 10
Both Sonali and priyanka is 15
Both sadaf and tanu is 10.
how much is prinka by the same system ?
Options:
A)8
B)9
C)10
D)11
E)12
Rationale: Solution:
prinka is 10, in a system that awards five for each vowel.
Answer C
Answer: C
Question: 15 people can write 90 book in 20 days working 7 hour a day.then in how many day 240 can be written by 72 people?
Options:
A)240/9
B)309/28
C)100/9
D)200/9
E)339/26
Rationale: work per day epr hour per person= 90/(20*7*15) // eq-1
people= 72; let suppose day=p; per day work for 8 hours
acc. to condition
work per day epr hour per person= 240/(p*7*72) // eq-2
eq-1==eq-2;
p= 100/9
ANSWER:C
Answer: C
Question: A rectangular-shaped carpet remnant that measures x feet by y feet is priced at $80. What is the cost of the carpet, in dollars per square yard? (9 square feet = 1 square yard)
Options:
A)80xy
B)720xy
C)xy/9
D)xy/80
E)720/(xy)
Rationale: xy sq ft = $80
1 sq ft = $80/xy
multiplying by 9 on both side
9 sq ft = $720/xy
or 1 sq yard = $720/xy
Hence E.
Answer: E
Question: A 12 month project had a total budget of $24,000. After seven months, the project had spent $12,500. At this point, how much was the project under budget?
Options:
A)$1500
B)$1600
C)$1700
D)$1800
E)$1900
Rationale: Each month, the project should spend $24,000 / 12 = $2000.
In 7 months, the project should spend 7*$2000=$14,000.
The project is under budget by $14,000 - $12,500 = $1500.
The answer is A.
Answer: A
Question: A cube has two of its faces painted half red and half white. The other faces are completely painted white. What is the ratio between the red painted areas and the white painted areas of the cube?
Options:
A)1:5
B)3:6
C)1:2
D)2:9
E)1:3
Rationale: Let x be the area of each face of the cube.
The area painted red is 2(x/2) = x
The area painted white is 2(x/2) + 4x = 5x
The ratio of red to white is x:5x which is 1:5.
The answer is A.
Answer: A
Question: In a hostel there were 100 students. To accommodate 20 more students the average is decreased by rupees 5. But total expenditure increased by Rs.400. Find the total expenditure of the hostel now?
Options:
A)5402
B)542
C)5400
D)5429
E)5421
Rationale: 100x + 400 = 12(x – 5)
x = 50
100 * 50 + 400 = 5400
Answer:C
Answer: C
Question: In a bank investment compounds annually at an interest rate of 34.1% What is the smallest investment period by which time the investment will more than triple in value?
Options:
A)1.2
B)1
C)4
D)2
E)3
Rationale: Assume initial amount is x
Annual Interest is 34.1% so after 1 year the amount will become x * (100+34.1)/100 => x*4/3
now we need to find n for x * (4/3)^n = 3x
or in other words n = 4
C
Answer: C
Question: What is the tens digit of 6^18?
Options:
A)1
B)3
C)5
D)7
E)9
Rationale: The tens digit of 6 in integer power starting from 2 (6^1 has no tens digit) repeats in a pattern of 5: {3, 1, 9, 7, 5}:
The tens digit of 6^2=36 is 3.
The tens digit of 6^3=216 is 1.
The tens digit of 6^4=...96 is 9.
The tens digit of 6^5=...76 is 7.
The tens digit of 6^6=...56 is 5.
The tens digit of 6^7=...36 is 3 again.
etc...
18 has the form 5n+3, so the tens digit of 6^18 is 1.
The answer is A.
Answer: A
Question: A and B together invested Rs. 15,000 in a business. At the end of the year, out of total profit is Rs. 2,000 B's share was Rs. 600. A's investment was
Options:
A)Rs. 4,500
B)Rs. 8,250
C)Rs. 10,500
D)Rs. 11,250
E)Rs. 12,250
Rationale: A+B=15000
total profit=2000
2000-600=1400
1400;600=7:3
then 7*15000/10=10500
ANSWER:C
Answer: C
Question: By selling 50 meters of cloth. I gain the selling price of 15 meters. Find the gain percent?
Options:
A)42 6/5
B)42 6/0
C)42 6/3
D)42 6/7
E)42 6/2
Rationale: SP = CP + g
50 SP = 50 CP + 15 SP
35 SP = 50 CP
35 --- 15 CP gain
100 --- ? => 42 6/7%
Answer:D
Answer: D
Question: The average age of a committee of 8 members is 36 years. A member aged 55 years
retired and his place was taken by another member aged 39 years . The average age of
present committee is;
Options:
A)39 years
B)34 years
C)36 years
D)35 years
E)31 years
Rationale: Exp. Total age of the committee = 36*8 = 288,
Total age when a member is retired
and a new one was joined = 288-55 +39, =272
Average age of present committee = 272/8 = 34.
Answer: B
Answer: B
Question: Set S contains exactly 10 numbers and has an average (arithmetic mean) of 6.2. If one of the numbers in Set S is increased by 6, while all other numbers remain the same, what is the new average of Set S?
Options:
A)6.6
B)6.7
C)6.8
D)6.85
E)6.9
Rationale: Old set S - Total is avg * no of elements = 6.2*10 = 62
If one number is increased by 6 then total increased to 62+6=68
New avg - 68/10 = 6.8.
Hence answer is C.
Answer: C
Question: Car A is 10 miles behind car B, which is traveling in the same direction along the same route as Car A.Car A is traveling at a constant speed of 58 miles per hour and Car Bis traveling at a constant speed of 50miles per hour.How many hours will it take for Car A to overtake and drive 8 miles ahead of Car B?
Options:
A)1.5
B)2.25
C)2.75
D)2.5
E)3.5
Rationale: Relative speed of car A is 58-50=8 miles per hour, to catch up 10 miles and drive 8 miles ahead so to drive 18 miles it'll need 18/8=2.25 hours.
Answer: B
Answer: B
Question: If a/b = 4/3, Then (3a + 2b) / (3a - 2b) = ?
Options:
A)6
B)3
C)5
D)-1
E)None
Rationale: Answer
Dividing numerator as well as denominator by b, we get
Given Exp. = (3a + 2b) / (3a - 2b) = (3a/b + 2) / (3a/b - 2)
= [ (3 x 4) / 3 + 2 ] / [ (3 x 4)/3 - 2 ]
= (4 + 2) / (4 - 2)
= 3
Option: B
Answer: B
Question: The positive two-digit integers p and q have the same digits, but in reverse order. Which of the following must be a factor of p + q?
Options:
A)66
B)9
C)10
D)12
E)14
Rationale: Remember: When you take the difference between the two, it will always be 9. e.g 23-32=9, 89-98=9
and when you add both integers, the sum will always be a multiple of 11 e.g 23+32=55, 89+98= 187
66 is multiple of 11
Answer : A
Answer: A
Question: P runs 20% faster than Q so P gives Q a 50 meter head start. If the race ends in a tie, how far (in meters) did P run in the race?
Options:
A)250
B)300
C)350
D)400
E)450
Rationale: Let D be the race distance that P ran.
Let T be the time it took to complete the race.
Let V be Q's speed.
T = D/1.2V = (D-50) / V
D=1.2D-60
0.2D=60
D=300 meters.
The answer is B.
Answer: B
Question: A Cricketer makes a score of 134 runs in the 22nd inning and thus increases his average by 3.5. Find his average after 22nd inning.
Options:
A)40
B)60.5
C)52
D)55
E)36
Rationale: Explanation :
Let the average after 22nd innings = x
Then average after 21th innings = (x-3.5)
Therefore 21(x-3.5) + 134 = 22x
Therefore x = 60.5
Answer : B
Answer: B
Question: Reena took a loan of Rs. 1200 with simple interest for as many years as the rate of interest. If she paid Rs. 432 as interest at the end of the loan period, what was the rate of interest?
Options:
A)7
B)6
C)5
D)4
E)3
Rationale: Let rate = R% and time = R years.
Then, (1200 * R * R) / 100 = 432
12R2 = 432
R2 = 36 => R = 6.
Answer: B
Answer: B