divelab/Sys2Bench huggingface dataset:
Question: The rate of a certain chemical reaction is directly proportional to the square of the concentration of chemical A present and inversely proportional to the concentration of chemical B present. If the concentration of chemical B is increased by 30%, which of the following is closest to the percent change in the concentration of chemical A required to keep the reaction rate unchanged?
Options:
A)100% decrease
B)60% decrease
C)40% decrease
D)40% increase
E)50% increase
Rationale: The rate of reaction is invesrsly proportional to the concentration of chemical B present. It used to have B=1 . Now that B is increased by 30%. So the new equation would be 2B=(1/2). In order for the rate of reaction to still be 1, we need to change the concentration of A to yield a 2. It used to be A^2=1, now the new equation should be (sqrt(2)*A)^2=2. The change in the concentration of A can be calculated as (sqrt(2) -1)/1 or approximately 40% increase. Answer B.
Answer: B
Question: In a workshop there are 4 kinds of beds, 3 kinds of closets, 2 kinds of shelves and 5 kinds of chairs. In how many ways can a person decorate his room if he wants to buy in the workshop one shelf, one bed and one of the following: a chair or a closet?
Options:
A)168.
B)80.
C)56.
D)48.
E)64.
Rationale: Bed = Select 1 out of 4 = 4C1 = 4
Shelf = Select 1 out of 2 = 2C1= 2
Chair (5)+ Closet (3) = Total 8 = Select 1 out of 8 = 8C1
Possible combinations to chooseBED*SHELF*(CHAIR+CLOSET)=4*2*8=64 ways
ANSWER IS E
Answer: E
Question: For a,e,d are the positive integers, and d|a means that “a is divisible by d”, if d|ae, which of the following must be true?
Options:
A)d|a
B)d|e
C)d|2ae
D)d|(a+e)
E)d|(a-e)
Rationale: d/a means a is divisible by d
d/ae means ae divisible by d.
all are integers so ,
if ae is divisible by d,
1 a can be divisible by d
or
2 e can be divisble by d.
so the question stem asks must true.
so option a and b are could but not must.
option c is 2ae divisible by d. if ab is divisible by d then 2ae is divisible by d.
option d and e we can't predict.
so option C is correct.
Answer: C
Question: The owner of a furniture shop charges his customer 20% more than the cost price. If a customer paid Rs. 8600 for a computer table, then what was the cost price of the computer table?
Options:
A)Rs.6289
B)Rs.6298
C)Rs.6290
D)Rs.7166
E)Rs.7708
Rationale: CP = SP * (100/(100 + profit%))
= 8600(100/120) = Rs.7166.
Answer: D
Answer: D
Question: How many two-digit numbers yield a remainder of 2 when divided by both 5 and 16?
Options:
A)0
B)1
C)2
D)3
E)4
Rationale: Easier to start with numbers that are of the form 16p+2 ---> 18,34,50,66,82,96.
Out of these,there is only one number (82) is also of the form 5q+2. Thus 1 is the answer. B is the correct answer.
Answer: B
Question: A committee has 5 men and 6 boys. What are the number of ways of selecting 2 men and 3 boys from the given committee?
Options:
A)A)165
B)B)178
C)C)180
D)D)200
E)E)210
Rationale: Explanation:
The number of ways to select two men and three boys = âµCâ‚‚ * â¶Câ‚ƒ
= (5 *4 )/(2 * 1) * (6 * 5 * 4)/(3 * 2)
= 200
D)
Answer: D
Question: Two taps A and B can fill a cistern in 12 minutes and 18 minutes respectively. They are turned on at the same time. If the tap A is turned off after 4 minutes, how long will tap B take to fill the rest of the cistern ?
Options:
A)8 min.
B)9 min.
C)10 min.
D)7 min.
E)None of these
Rationale: In one min, (A + B) fill the cistern = 1⁄12 + 1⁄18 = 5⁄36th
In 4 min, (A + B) fill the cistern = 5⁄36 × 4 = 5⁄9th
Rest part = 1 - 5⁄9 = 4⁄9th
∵ 1⁄18th part is filled by B in one min.
∴ 4⁄9th part is filled by B in 18 × 4⁄9 = 8 min
Answer A
Answer: A
Question: Two trains 160 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. The time which they take to cross each other is?
Options:
A)10.52 sec
B)18.8 sec
C)14.52 sec
D)10.8 sec
E)11.52 sec
Rationale: Relative speed = 60 + 40 = 100 km/hr.
= 100 * 5/18 = 250/9 m/sec.
Distance covered in crossing each other = 160 + 160 = 320 m.
Required time = 320 * 9/250 = 288/25 = 11.52 sec.
Answer: E
Answer: E
Question: What is the maximum number of points that 10 circles of different radii intersect?
Options:
A)24
B)26
C)33
D)90
E)100
Rationale: the maximum number of points that two circles intersect is two.
therefore, each of these 10 circles intersect two point with each of the other 9 circles.
as a consequence, the number of these points is equal to two times the number of combination of the 10 circles.
2∗(10!)/(2!∗10!)=90
Answer: D
Answer: D
Question: A “palindromic integer” is an integer that remains the same when its digits are reversed. So, for example, 43334 and 516615 are both examples of palindromic integers. How many 6-digit palindromic integers are both even and greater than 700,000?
Options:
A)60
B)100
C)180
D)240
E)300
Rationale: The first digit and last digit are the same so the only possibility is 8.
The second and third digits can be any number from 0 to 9.
The total number of palindromic integers is 1*10*10 = 100
The answer is B.
Answer: B
Question: Which of the following is the full form of the term SLR as used in the banking sector?
Options:
A)Social Lending Ratio
B)Statutory Liquidity Ratio
C)Scheduled Liquidity Rate
D)Separate Lending Rate
E)None of these
Rationale: Answer:B
Answer: B
Question: Two taps can separately fill a cistern 10 minutes and 15 minutes respectively and when the waste pipe is open, they can together fill it in 36 minutes. The waste pipe can empty the full cistern in?
Options:
A)8.2
B)7.2
C)6.2
D)9.2
E)5.2
Rationale: 1/10 + 1/15 - 1/x = 1/36
x = 7.2
Answer:B
Answer: B
Question: A 300 meter long train crosses a platform in 39 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
Options:
A)300
B)340
C)350
D)320
E)310
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 39 = 50/3
3(x + 300) = 1950 è x = 350m.
Answer: Option C
Answer: C
Question: If 11.25 m of a uniform steel rod weighs 42.75 kg. what will be the weight of 5 m of the same rod?
Options:
A)22.8 kg
B)25.6 kg
C)19 kg
D)26.5 kg
E)None of these
Rationale: Explanation :
Let the required weight be x kg. Then, Less length, Less weight (Direct Proportion)
=> 11.25 : 5 :: 42.75 : x
=> 11.25 x x = 5 x 42.75
=> x = (5 x 42.75) / 11.25
=> x = 19
Answer : C
Answer: C
Question: It takes 80 identical printing machines 5 hours to print 200,000 posters. How long would it take 50 of these machines to print the same total?
Options:
A)6 hr, 40 min
B)7 hr
C)7 hr, 30 min
D)8 hr
E)10 hr
Rationale: 50% of 80 = 40% or 0.40
5 hr x 60 min = 300 min
300 min x 0.40 = 120 min
120 min + 5 hr = 2 hr + 5 hr = 7 hr total
It will take 50 machines 7 hours to print the same amount of posters.
Answer is B
Answer: B
Question: How many words with or without meaning, can be formed by using all the letters of the word, â€˜MOUSEâ€™, using each letter exactly once?
Options:
A)120
B)140
C)160
D)720
E)820
Rationale: The word â€˜MOUSEâ€™ contains 5 different letters.
Therefore, Required number of words= Number of arrangement of 5 letters, taken all at a time
=5P5
= 5!
= 5*4*3*2*1
= 120
ANSWER:A
Answer: A
Question: Find the angle between the hour hand and the minute hand of a clock when
3.25.
Options:
A)47.5
B)46.5
C)45.5
D)48.5
E)44.5
Rationale: angle=30(hours)-(11/2)(minutes)
=30*3-(5.5*25) (hour=3 and minutes=25)
=90-137.5
=47.5
ANSWER:A
Answer: A
Question: x, y, and z are three positive integers whose average is 10. If x≤y≤z and z-x=3, which of the following could be the median Q of x, y, and z?
I. 9
II. 10
III. 11
Options:
A)I only
B)II only
C)III only
D)I and II only
E)I and III only
Rationale: Average gives us an idea that 3 nos. are close to 10.
so 10, 10, 10 is an unacceptable option because (z-x =3), but it helps in getting other combinations.
Let us see options.
If 9 has to be median.
1st term has to less than 9 or equal to 9. (also maintain z-x = 3)
9 9 12 --> satisfies all conditions so 9 can be a median value.
If 11 has to be a median
3rd term has to be 11 or more than 11. (also maintain z-x = 3)
8 11 11 -->satisfies all conditions so 9 can be a median value.
Now for 10 to be median Q.
z+ x = 20 and z-x = 3, we wont have integer values of z.
10 cannot be a median
E is the answer.
Answer: E
Question: The price of a laptop . set worth Rs. 20000 is to be paid in 20 installments of Rs. 1000 each. If the rate of interest be 6% per annum, and the first installment be paid at the time of purchase, then the value of the last installment covering the interest as well will be?
Options:
A)A)19009
B)B)19074
C)C)19008
D)D)19000
E)E)19002
Rationale: Explanation:
Money paid in cash = R . 1000
Balance payment = (20000 - 1000) = Rs. 19000
Answer: Option D
Answer: D
Question: Point X is located on line segment AB and point Y is located on line segment CD. If AB = CD and AX < CY, then
Options:
A)XB < YD
B)XB < YD
C)AX > XB
D)AX < XB
E)CY < AB
Rationale: A------X--B
C--Y------D
CY < AB.
Answer: E.
Answer: E
Question: In a joint business, the capital of A, B and C were Rs. 45000, Rs. 30000 and Rs. 22500 respectively. A withdrew half of his capital after 4 months. After 9 months of this withdrawal, there was a total profit of Rs. 28400. Find the each share of profit?
Options:
A)7800
B)8000
C)8200
D)8400
E)8600
Rationale: Given A=45000 B=30000 C=22500
A:B:C= 450:300:225
As A withdrew its half of capital after 4 months,it can withdraw 22500 rupees
But before 4 months, it is 45000 only and the profit is calculated after withdrwal it is almost 9+4=13 months.For that 9 months, the capital for A is half of its original capital,
So A= 450*4+ 225*9= 1800+2025= 3825
Similarly, B= 300*13=3900
Similarly,C= 225*13= 2925
Therefore, ratio of A:B:C= 3825: 3900 : 2925= 51:52:39
C's share=39/142(28400)=7800
ANSWER:A
Answer: A
Question: A, B and C rents a pasture for Rs.638. A put in 12 horses for 8 months, B 16 horses for 9 months and 18 horses for 6 months. How much should C pay?
Options:
A)270
B)198
C)676
D)156
E)122
Rationale: 12*8 :16*9 = 18*6
8: 12: 9
9/29 * 638= 198
Answer: B
Answer: B
Question: If the simple interest on a sum of money for 2 years at 5% per annum is Rs. 55, what is the compound interest on the same sum at the rate and for the same time?
Options:
A)s. 56.37
B)s. 53.22
C)s. 56.219
D)s. 51.18
E)s. 51.11
Rationale: Explanation:
Sum = (55 * 100) / (2 * 5) = Rs. 550
Amount = [550 * (1 + 5/100)2] = Rs. 606.375
C.I. = (606.375 - 550) = Rs. 56.37
Answer:A
Answer: A
Question: If an amount of Rs 41,800 is distributed equally
amongst 22 persons, how much amount would each
person get?
Options:
A)Rs 1900
B)Rs 2000
C)Rs 745
D)Rs 765
E)None
Rationale: Required amount =41800/22 = Rs 1900
Answer A
Answer: A
Question: The simple interest on a sum of money will be Rs.800 after 10 years. If the principal is trebled after 5 years what will be the total interest at the end of the tenth year?
Options:
A)8981
B)3799
C)1200
D)1600
E)1732
Rationale: P --- 10 ---- 800
P --- 5 ----- 400
3P --- 5 ----- 1200
------
=> 1600
Answer: D
Answer: D
Question: Find the simple interest on Rs.620 for 10 months at 10 paisa per month?
Options:
A)277
B)620
C)640
D)678
E)121
Rationale: I = (620*10*10)/100 = 620
Answer: B
Answer: B
Question: You collect coins. Suppose you start out with 18. Since you're nice, you give Sharon 3 coins. Since you're nice, you give Steven 4 coins. How many coins do you have at the end?
Options:
A)2
B)3
C)4
D)5
E)11
Rationale: Solution
Start with 18 coins.
Sharon takes 3 coins from you: 18 - 3 = 15 coins.
Steven takes 4 coins from you: 15 - 4 = 11 coins.
So you have 11 at the end.
Correct answer : E
Answer: E
Question: A 300 m long train crosses a platform in 39 sec while it crosses a signal pole in 8 sec. What is the length of the platform?
Options:
A)287 m
B)350 m
C)1267 m
D)1287 m
E)1162.5 m
Rationale: Speed = 300/8 = 75/2 m/sec.
Let the length of the platform be x meters.
Then, (x + 300)/39 = 75/2
=> x = 1162.5 m.
Answer:E
Answer: E
Question: A shopkeeper sells one transistor for Rs. 840 at a gain of 20% and another for Rs. 960 at a loss of 4%. His total gain or loss percent is:
Options:
A)100/17% loss
B)100/17% gain
C)20/3% loss
D)None of these
E)Cannot be determined
Rationale: Explanation :
Let the cost price of 1st transistor be Rs. x and the cost price of 2nd transistor be Rs. y
S.P. of 1st transistor at 20% profit = Rs. 840
=> (x + 20% of x) = 840
=> x*(120/100) = 840
=> x = 700
S.P. of 2nd transistor at 4% loss = Rs. 960
=> (y - 4% of y) = 960
=> y*(96/100) = 960
=> y = 1000
So, total C.P. = (x + y) = Rs. 1700
Total S.P. = 840 + 960 = 1800
Profit = (S.P. - C.P.) = (1800 - 1700) = Rs. 100
% Profit = (100/1700∗100)% = 100/17 %
Answer : B
Answer: B
Question: If the simple interest on $1500 increase by $20,when the time increase by 2 years. Find the rate percent per annum.
Options:
A)0.6%
B)0.5%
C)0.1%
D)0.2%
E)0.7%
Rationale: Applying the above formula, we have
20=1500*r*2/100
r=20*100/1500*2=0.7%.
Answer is E
Answer: E
Question: A train 175 m long, running with a speed of 63 km/hr will pass a tree in?
Options:
A)22 sec
B)16 sec
C)17 sec
D)88 sec
E)10 sec
Rationale: Speed = 63 * 5/18 = 35/2 m/sec
Time taken = 175 * 2/35 = 10 sec
Answer:E
Answer: E
Question: A sum of Rs. 1870 has been divided among A, B and C such that A gets of what B gets and B gets of what C gets. B’s share is:
Options:
A)Rs. 120
B)Rs. 160
C)Rs. 240
D)Rs. 330
E)None
Rationale: EXPLANATION
Let C’s share = Rs. x
Then, B’s share = Rs. x/4 , A’s share = Rs. (2/3 x x/4 ) = Rs. x/6
=x/6 + x/4 + x = 1870
=> 17x/12 = 1870
=> 1870 x 12/ 17 = Rs.1320
Hence, B’s share = Rs. (1320/4) = Rs. 330.
Answer D
Answer: D
Question: A parking space have 8 different slots. 8 cars has to arrange in 8 slots. But there are exactly 4 cars between 3 specified cars. In how many ways cars can be arranged?
Options:
A)720
B)650
C)1500
D)1640
E)1440
Rationale: we arranged 3 specified cars in 3 slots = 3!
remaining 5 cars in 5 slots = 5!
number of ways = 3!*5! = 720
correct option is A
Answer: A
Question: 3/4 of 1/2 of 2/5 of 5060 = ?
Options:
A)392
B)759
C)753
D)493
E)540
Rationale: B
759
? = 5060 * (2/5) * (1/2) * (3/4) = 759
Answer: B
Question: A rectangular grass field is 85 m * 55 m, it has a path of 2.5 m wide all round it on the outside. Find the area of the path and the cost of constructing it at Rs.2 per sq m?
Options:
A)1450
B)1971
C)9676
D)1679
E)2691
Rationale: Area = (l + b +2d) 2d
= (85 + 55 +2.5 * 2) 2*2.5 => 725
725 * 2 = Rs.1450
Answer:A
Answer: A
Question: At a certain conference, 42% of the attendees registered at least two weeks in advance and paid their conference fee in full. If 40% of the attendees who paid their conference fee in full did not register at least two weeks in advance, what percent of conference attendees registered at least two weeks in advance?
Options:
A) 18.0%
B) 62.0%
C) 79.2%
D) 70.0%
E) 82.0%
Rationale: Refer to the table in the attachment:
Let x= No. of members who have paid in Full
40 % members paid in full and did not register in advance = 0.4x
42 % registerd in advance and paid in full.
So if total No. of members = 100, then 42 members paid Full and registered in advance.
Hence total members who paid full amount = 0.4x + 42 =x
0.6x =42
Hence x = 70
i.e. 80 out of 100 or 70 %
Ans. D
Answer: D
Question: 2 pipes function simultaneously the reservoir will be filled in 12 hrs. One pipe fills reservoir 10 hrs faster thanthe other. How many hours does the faster pipe take to fill the reservoir?
Options:
A)10
B)20
C)30
D)34
E)36
Rationale: 1/x + 1/(x + 10) = 1/12
x = 20
B
Answer: B
Question: The percentage profit earned by selling an article for Rs. 1820 is equal to the percentage loss incurred by selling the same article for Rs. 1280. At what price should the article be sold to make 25% profit?
Options:
A)3000
B)1230
C)2000
D)5600
E)1937.5
Rationale: C.P. be Rs. x.
Then, (1820 - x)/x * 100 = (x - 1280)/x * 100
1820 - x = x - 1280
2x = 3100 => x = 1550
Required S.P. = 125 % of Rs. 1550 = 125/100 * 1550 = Rs. 1937.5.
ANSWER E
Answer: E
Question: If x - 8 = |x - 9|, then x=?
Options:
A)8.5
B)8
C)9
D)6
E)4
Rationale: x - 8 = |x - 9| ...(given)
x^2 - 16x + 64 = x^2 - 18 x + 81
0*x^2 + 2*x - 17 = 0 ....(by solving above eq. we get) , x = 8.5 ===> Ans - A
Answer: A
Question: If a*b*c=130, b*c*d = 65, c*d*e=500 and d*e*f=250 the (a*f)/(c*d) = ?
Options:
A)1/2
B)1/4
C)3/4
D)2/3
E)1
Rationale: Explanation :
aâˆ—bâˆ—c/bâˆ—câˆ—d= 130/65 => a/d = 2
dâˆ—eâˆ—f/câˆ—dâˆ—e= 250/500 => f/c = 1/2
a/d* f/c = 2 * 1/2 = 1
Answer : E
Answer: E
Question: Average weight of 10 people increased by 0.5 kg when one person of 45 kg is replaced by a new
man. Then weight of the new man is
Options:
A)50
B)55
C)60
D)65
E)70
Rationale: Explanation:
Total weight increased is 0.5 * 10 =5.
So weight of new person is 45+5 = 50
Answer: Option A
Answer: A
Question: A coin is tossed 4 times. What is the probability of getting exactly 3 heads?
Options:
A)1/2
B)1/4
C)1/8
D)1/16
E)3/16
Rationale: The number of possible outcomes is 2^4 = 16
There are 4 ways to get exactly 3 heads.
P(exactly 3 heads) = 4/16 = 1/4
The answer is B.
Answer: B
Question: Dan has a membership at a local gym that also gives classes three nights a week. On any given class night, Dan has the option of taking yoga, weight training, or kickboxing classes. If Dan decides to go to either one or two classes per week, how many different combinations Y of classes are available?
Options:
A)3
B)6
C)Y=7
D)Y=9
E)Y=12
Rationale: I think it should be E only.
No where it is given that he attends different classes on each day.
Experts please provide your views.
--- EDITED my Response. It was a typo. I meant 12 is the answer.
If only Day 1 : 3 options
If Day 1 and Day 2 : 3*3 = 9 Options
So, Total = 3+9= 12.
Answer: D
Question: If 20 men can build a water fountain 56 metres long in 3 days, what length of a similar water fountain can be built by 35 men in 3 days?
Options:
A)40 m
B)64 m
C)77 m
D)89 m
E)98 m
Rationale: Explanation :
Let the required length be x metres
More men, More length built (Direct Proportion)
Less days, Less length built (Direct Proportion)
Men 20: 35
Days 3: 3 : : 56 : x
Therefore (20 x 3 x x)=(35 x 3 x 56)
x=(35 x 3 x 56)/60=98
Hence, the required length is 98 m.
Answer : E
Answer: E
Question: What is the sum of all possible solutions to |x - 5|^2 + |x - 5| = 20 ?
Options:
A)-1
B)6
C)7
D)10
E)14
Rationale: Denote |x - 5| as y: y^2 + y = 20 --> y = -5 or y = 4. Discard the first solution since y = |x - 5|, so it's an absolute value and thus cannot be negative.
y = |x - 5| = 4 --> x = 9 or x = -1. The sum =10
Answer: D.
Answer: D
Question: Approximately how many revolutions will be made by a car tire with a 10-inch diameter if the car travels 1⁄2 mile?
Options:
A)120
B)180
C)1003
D)1000
E)1,440
Rationale: Diameter of car tire = 10 inches
Radius of car tire = 5 inches = 5*2.54 cm = 12.7 cm
Circumference of the car tire = 2*pi * 12.7 = 2 *3.14 *12.7= 79.76 cm
Distance traveled by car = .5 mile = .5 *1.6 km = .8 km = 800 m = 8 * 10^4 cm
Number of revolutions =Distance traveled / Circumference of tire = 8 * 10^4 / 79.76 = 1003
Since the answer choices are far apart we should use estimation in this question .
Ideally ,in the GMAT the conversion between units would be provided .
Answer C
Answer: C
Question: Robin mixes two liquids, one blue in coloUr and other red in colour in the ratio 2:3 and sells the mixture at the rate of $20 per liter, thereby making a 25% profit on his outlay. The blue liquid costs Robin $5 per litre lesser than the red liquid. How much does a liter of red liquid cost?
Options:
A)12
B)13
C)14
D)15
E)16
Rationale: Let x be the required cost per litre of red paint.
Take 5 litres of this mixture.
Sold at 100 with a profit of 1/4th of total cost. So, total cost will be 1/5th less than 100; total cost = 80.
2(x-5) + 3(x) = 80
x = 14
Answer is C
Answer: C
Question: A cricketer scored 136 runs which included 12 boundaries and 2 sixes. What percent of his total score did he make by running between the wickets.
Options:
A)46.2%
B)54.54 %
C)55.88%
D)70%
E)None of these
Rationale: Explanation :
Number of runs made by running = 136 - (12 x 4 + 2 x 6)
= 136 - (60)
= 76
Now, we need to calculate 72 is what percent of 136.
=> 76/136 * 100 = 55.88 %
Answer : C
Answer: C
Question: A set of numbers has the property that for any number t in the set, 2t + 2 is in the set. If -1 is in the set, which of the following must also be in the set?
I. -3
II. 1
III. 6
Options:
A) I only
B) II only
C) I and II only
D) II and III only
E) I, II, and III
Rationale: The question is which of the followingmustbe in the set, notcouldbe in the set.
If -1 is in the set so must be 2*-1+2=0, as 0 is in the set so must be 0+2=2, as 2 is in the set so must be 4+2=6 and so on.
Answer: A.
Answer: A
Question: John has on his shelf four books of poetry, three novels, and two reference works. Suppose from these ten books, we were to pick two books at random. What is the probability that we pick one novel and one reference work?
Options:
A)1/6
B)2/5
C)3/10
D)7/20
E)8/45
Rationale: When we are picking two books, one novel and one reference work, we could either pick a novel first and then a reference book or pick a reference book and then a novel. Therefore the answer is 3/9*2/8 + 2/9*3/8 = 1/6.
Answer: A.
Answer: A
Question: The distance light travels in one year is approximately 5,870,000,000,000 miles. The distance light travels in 100 years is
Options:
A) 587 × 108 miles
B) 587 × 1010 miles
C) 587 × 10-10 miles
D) 587 × 1012 miles
E) 587 × 10-12 miles
Rationale: The distance of the light travels in 100 years is:
5,870,000,000,000 × 100 miles.
= 587,000,000,000,000 miles.
= 587 × 1012 miles.
The answer is (D)
Answer: D
Question: 3 building 3 floors how many floors are in the 3 buildings?
Options:
A)1
B)6
C)3
D)9
E)10
Rationale: C
Answer: C
Question: Three investors, A, B, and C, divide the profits from a business enterprise in the ratio of 5 : 7 : 8, respectively. If investor A earned $ 3,000, how much money did investors B and C earn in total?
Options:
A)$4,000
B)$4,900
C)$5,600
D)$9,000
E)$10,500
Rationale: Let profit for A = 5x
profit for B = 7x
profit for C = 8x
Investor A earned = 3000
5x = 3000=>x=600
Total profit for B and C = 7x+ 8x = 15x
Therefore , 15x = 15*600 = 9,000
Answer D
Answer: D
Question: If (x-11)(x-3) < 0, which of the following must be true?
Options:
A)x^2 + 5x + 6 < 0
B)x^2 + 5x + 6 > 0
C)5 - x < 0
D)x - 5 < 0
E)11 - x > 0
Rationale: (x-11)(x-3) < 0; 3<x<11 --> Given condition
If we review options, E is always true.
Let us review others:
x^2 + 5x + 6 = (x+3)(x+2)
(x+3)(x+2)<0, then -3<x<-2 --> This will not be true with the given conditions (3<x<11). A is out
x^2 + 5x + 6 = (x+3)(x+2)
(x+3)(x+2)>0, then x> -2 and x < -3 --> This will not be true with the given conditions (3<x<11). B is out
(C)
5 - x < 0; 5<x; x> 5. But if x = 12 , then given condition is not satisfied. So C is also out.
D. x - 5 < 0
x<5
But if x = 1, (which is less than 3) then given condition is not satisfied.
E is the answer.
Answer: E
Question: What is the ratio G of the surface area of a cube to the surface area of a rectangular solid identical to the cube in all ways except that its length has been doubled?
Options:
A)1/4
B)3/8
C)1/2
D)3/5
E)2
Rationale: One side surface area of a cube = x*x = x^2
Total 6 sides = 6x^2
As for the rectangular, Height (H) and Width (W) are same as Cube, x. Only Length = 2x.
L x H = 2x * x = 2x^2 ----> 4 sides = 2x^2 * 4 = 8x^2
W * H = x * x = x^2 ------> 2 sides = x^2 * 2 = 2x^2
Total 6 sides = 8x^2 + 2x^2 = 10x^2
Ratio of cube area to rectangular area G= 6x^2 / 10x^2 ----> 6/10 ----> 3/5 (D)
Answer: D
Question: A, B, C rent a pasture. A puts 10 oxen for 7 months, B puts 12 oxen for 5 months and C puts 15 oxen for 3 months for grazing. If the rent of the pasture is Rs. 175, how much must C pay as his share of rent?
Options:
A)Rs.45
B)Rs.45
C)Rs.55
D)Rs.60
E)None
Rationale: Solution
A : B : C	=(10×7):(12×5):(15×3)
= 70 :60 :45
= 14 :12 :9
c's rent	=Rs.(175×9/35)
= Rs.45.
Answer A
Answer: A
Question: The sum of three consecutive even numbers is 42. Find the middle number of the three?
Options:
A)14
B)15
C)52
D)25
E)32
Rationale: Answer: Option A
Three consecutive even numbers (2P - 2), 2P, (2P + 2).
(2P - 2) + 2P + (2P + 2) = 42
6P = 42 => P = 7.
The middle number is: 2P = 14.
Answer: A