divelab/Sys2Bench huggingface dataset:
Question: One fourth of a solution that was 10 percent salt by weight was replaced by a second solution resulting in a solution that was 16 percent salt by weight. The second solution was what percent salt by weight ?
Options:
A)34%
B)24%
C)22%
D)18%
E)8.5%
Rationale: EQ can be written as ...
let sol be s... so (3/4)s*(.1)+(1/4)s*t=s*(.16).... we get t(% of salt in 2nd sol)=34%=A
Answer: A
Question: Working alone at its constant rate, machine A produces x boxes in 10 minutes and working alone at its constant rate, machine B produces 2x boxes in 5 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce 5x boxes?
Options:
A)3 minutes
B)4 minutes
C)5 minutes
D)6 minutes
E)10 minutes
Rationale: Rate = Work / Time
Given Rate of Machine A = X / 10 min
Machine B Produces 2x boxes in 5 min hence , Machine B produces 4x boxes in 10 min .
Rate of Machine B = 4x / 10
we need tofind the combined time that machines A and B, working simultaneouslytakeat their respective constant rates
let's first find the combined Rate of Machine A and B
Rate of Machine A = X / 10 min + Rate of Machine B = 4x / 10 = 5X/10
Now combine Time = combine work needs to be done / Combine Rate = 5x/5x * 10 = 10 Min
Ans: E
Answer: E
Question: A and B together can do a work In 4 days. A alone can do it in 12 days. What time B will take to do the work alone?
Options:
A)6 days
B)8 days
C)12 days
D)10 days
E)5 days
Rationale: Explanation:
A and B 1day's work = 1/6
A alone can do 1day's work = 1/12
what time B will take to do the work alone?
B = (A+B) - A = (1/6) - (1/12) = 12 Days
Answer: Option C
Answer: C
Question: 28, 26, 21, 19, 14, 12, ?
Options:
A)3
B)2
C)8
D)7
E)5
Rationale: This is a simple alternating subtraction series, with a pattern -2, -5, -2, -5 ....
Answer : D.
Answer: D
Question: If money is invested at r percent interest, compounded annually, the amount of investment will double in approximately 70/r years. If Pat's parents invested $ 8000 in a long term bond that pays 4 percent interest, compounded annually, what will be the approximate total amount of investment 36 years later, when Pat is ready for college?
Options:
A)$20000
B)$15000
C)$32000
D)$10000
E)$9000
Rationale: Since investment doubles in 70/r years then for r=4 it'll double in 70/4=~18 years (we are not asked about the exact amount so such an approximation will do). Thus in 36 years investment will double twice and become ($8,000*2)*2=$32,000 (after 18 years investment will become $8,000*2=$16,000 and in another 18 years it'll become $16,000*2=$32,000).
Answer: C.
Answer: C
Question: An article is bought for Rs.400 and sold for Rs.360, find the loss percent?
Options:
A)18 2/3%
B)16 7/3%
C)16 2/8%
D)10%
E)76 2/3%
Rationale: 400 ---- 40
100 ---- ? => 10%
Answer:D
Answer: D
Question: If a committee of 3 people is to be selected from among 5 married couples so that the committee does not include two people who are married to each other, how many X such committees are possible?
Options:
A)X=20
B)X=40
C)X=50
D)X=80
E)120
Rationale: Each couple can send only onerepresentativeto the committee. Let's see in how many ways we can choose 3 couples (as there should be 3 members) each to send onerepresentativeto the committee: 5C3=10.
But these 3 chosen couples can send two persons (either husband or wife): 2*2*2=2^3=8.
Total # of ways: 5C3*2^3=80.
Answer: D.
Answer: D
Question: 3 buffaloes eat as much as 4 cows or 2 oxen. At a farm there are 15 buffaloes, 8 oxen and 24 cows. The fodder for these cattle is available for 24days. If 8 more cows & 9 more buffaloes are brought in, how long will the fodder last?
Options:
A)10
B)15
C)21
D)18
E)29
Rationale: Sol. 2 oxen = 3 buffaloes = 4 cows 8 oxen = 16 cows and 15 buffaloes = 20 cows 16 cows + 20 cows + 24 cows = 60 cows Since fodder is available for 60 cows for 24 days
So fodder will be available for (60 + 8 + 12) = 80 cows c 24x60	.0 .
for-^—=18 days.
D
Answer: D
Question: 14, 18, x, 20
The median of the list of positive integers above is 16. Which of the following could be the average (arithmetic mean) of the list?
Options:
A)3
B)5.5
C)6.25
D)16
E)7.5
Rationale: GivenThe median of the list of positive integers above is 16
So arranging the numbers from lowest to highest, avg of 2 middle terms needs to be 16
so the sequence will be x 14 18 20
Lets say x = 12, which gives us mean = sum/4 = 16
D is correct
Answer: D
Question: The price of an article is reduced by 25% in order to
restore the must be increased by ?
Options:
A)3/100%
B)100/3%
C)6/25%
D)25/6%
E)4/75%
Rationale: [x/(100-x)]*100 =[25/(100-25)]*100
=(25/75)*100=100/3%
ANSWER B 100/3%
Answer: B
Question: With a uniform speed a car covers the distance in 8 hours. Had the speed been increased by 4 km/hr, the same distance could have been covered in 7 1/2 hours. What is the distance covered?
Options:
A)287 km
B)480 km
C)127 km
D)177 km
E)2698 km
Rationale: Let the distance be x km. Then,
x/(7 1/2) - x/8 = 4
2x/15 - x/8 = 4 => x
= 480 km
Answer: B
Answer: B
Question: The salary of a person was reduced by 15%. By what percent should his reduced salary be raised so as to bring it at par with his original salary?
Options:
A)10%
B)17.6%
C)13.7%
D)15.1%
E)12.3%
Rationale: Let the original salary be $100
New salary = $85
Increase on 85=15
Increase on 100 = 15/85* 100 = 17.6%
Answer is B
Answer: B
Question: On a certain road 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 30% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?
Options:
A)10.5%
B)12.5%
C)15%
D)22%
E)14.28%
Rationale: 0.1 M = 0.70 E
=> E/M = 1/7 * 100 = 14.28%
So answer is E.
M - # of Motorists
E - # of Motorists exceeding speed
Answer: E
Question: Two numbers are such that the ratio between them is 3:5 but if each is increased by 10, the ratio between them becomes 5 : 7, the numbers are
Options:
A)3, 5
B)7, 9
C)13, 22
D)15, 25
E)None
Rationale: Explanation:
Let the numbers be 3a and 5a
Then 3a+10/5a+10=5/7
⇒7(3a+10)=5(5a+10)⇒a=5
The numbers are 15 & 25
Correct Option: D
Answer: D
Question: A parallelogram has sides 12 cm and 9 cm. If the distance between its shorter sides is 8 cm, find the distance between its longer side.
Options:
A)2
B)4
C)6
D)8
E)9
Rationale: Adjacent sides of parallelogram = 2 cm and 9 cm
Distance between shorter sides = 8 cm
Area of parallelogram = b × h
= 9 × 8 cm²
= 72 cm²
Again, area of parallelogram = b × h
72 = 12 × h
h = 72/12
h = 6 cm
Therefore, the distance between its longer side = 6 cm.
ANSWER-OPTION C
Answer: C
Question: A person buys an article at Rs.550. At what price should he sell the article so as to make a profit of 30%?
Options:
A)600
B)715
C)772
D)662
E)521
Rationale: Cost price = Rs.550
profit = 30% of 550 = Rs.165
Selling price = Cost price + Profit
= 550 + 165 = 715
Answer: B
Answer: B
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 38 years now, the son's age five years back was:
Options:
A)12 years
B)14 years
C)15 years
D)20 years
E)11 years
Rationale: Let the son's present age be x years. Then, (38 - x) = x
2x = 38.
x = 19.
Son's age 5 years back (19 - 5) = 14 years.
ANSWER B
Answer: B
Question: If x represents the sum of all the positive three-digit numbers that can be constructed using each of the distinct nonzero digits a, b, and c exactly once, what is the largest integer by which x must be divisible?
Options:
A)3
B)6
C)11
D)22
E)222
Rationale: Maybe there is a faster way to do it but I did it like this:
How many ways can you arrange abc?
abc
acb
bac
bca
cab
cba
which are equivalent to:
100a + 10b + c
100a + 10c + b
100b + 10a + c
100b + 10c + a
100c + 10a + b
100c + 10b + a
if you add them all together you get 222a + 222b + 222c
ANSWER:E
Answer: E
Question: On Thursday, the original price of a shirt was discounted by 20%. On Monday, the price of the shirt was marked up C percent so that the new price on Monday was 20% more than the original price before the discount. What is the value of C?
Options:
A)20%
B)30%
C)33 1⁄3%
D)40%
E)50%
Rationale: Let the original price be 100
discounted Price = 80
New Price = 20 +100 =120
C=(40/80)*100
Ans:E
Answer: E
Question: In a group of cows and chickens, the number of legs was 18 more than twice the number of heads. The number of cows was:
Options:
A)5
B)7
C)9
D)12
E)14
Rationale: Let the number of cows be x and their legs be 4x.
Let the number of chicken be y and their legs be 2x.
Total number of legs = 4x + 2y.
Total number of heads = x + y.
The number of legs was 18 more than twice the number of heads.
Therefore, 2 × (x + y) + 18 = 4x + 2y.
or, 2x + 2y + 18 = 4x + 2y.
or, 2x + 18 = 4x [subtracting 2y from both sides].
or, 18 = 4x – 2x [subtracting 2x from both sides].
or, 18 = 2x.
or, x = 9 [dividing by 2 on both sides].
Therefore, the number of cows = 9.
Correct Answer:C)9
Answer: C
Question: If the L.C.M of two numbers is 750 and their product is 18750, find the H.C.F of the numbers.
Options:
A)50
B)30
C)125
D)25
E)None of these
Rationale: H.C.F = (Product of the numbers) / (Their L.C.M) = 18750/750 = 25.
ANSWER:D
Answer: D
Question: 3 men and 7 women can complete a work in 10 days . But 4 men and 6 women need 8 days to complete the same work . In how many days will 10 women complete the same work?
Options:
A)40
B)45
C)50
D)35
E)30
Rationale: Work done by 4 men and 6 women in 1 day = 1/8
Work done by 3 men and 7 women in 1 day = 1/10
Let 1 man does m work in 1 day and 1 woman does w work in 1 day. The above equations can be written as
4m + 6w = 1/8 ---(1)
3m + 7w = 1/10 ---(2)
Solving equation (1) and (2) , we get m=11/400 and w=1/400
Amount of work 10 women can do in a day = 10 × (1/400) = 1/40
Ie, 10 women can complete the work in 40 days
Answer is A.
Answer: A
Question: The ‘moving walkway’ is a 300-foot long walkway consisting of a conveyor belt that moves continuously at 3 feet per second. When Bill steps on the walkway, a group of people that are also on the walkway stands 120 feet in front of him. He walks toward the group at a rate of 3 feet per second. Once Bill reaches the group of people, he stops walking and stands with them until the walkway ends. What is Bill’s average rate Y of movement for his trip along the moving walkway?
Options:
A)2 feet per second
B)2.5 feet per second
C)3 feet per second
D)4 feet per second
E)5 feet per second
Rationale: A, B, and C don't make ANY sense! we know for some time...(a majority of the 300ft) Bill will walk at a pace of 6ft per second...and then at some later time he will stop and move at 3 ft per second... The average Y MUST bebetween3-6 ft per second or the Earth is FLAT!!!.
So we are down to DE, D doesn't make sense on a weighted averages level because we know when Bill gets on the walkway the patrons are already 40% of the way down the 300ft walkway AND they are still moving at half the rate of Bill!! So for Bill to average 4 ft per second he would have had to spend a majority of the 300 ft at 3ft per second because 4 is much closer (when you factor in the size of the values we're dealing with 2 is double 1) to 3 than to 6. We know from the information that isn't possible. Billmust havespent the majority of his time at 6 ft per second before he stopped walking. That leaves only answer E as plausible.
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)180 m
B)240 m
C)260 m
D)280 m
E)380 m
Rationale: Speed = 54 x 5/18 = 15 m/s
Length of the train = (15 x 20)m = 300 m.
Let the length of the platform be x metres.
Then, (x + 300)/36 = 15
--> x + 300 = 540
x = 240m.
Answer : B.
Answer: B
Question: Three 6 faced dice are thrown together. The probability that exactly two dice show the same number on them is ?
Options:
A)5/ 19
B)5/ 12
C)5/ 27
D)5/ 18
E)5/ 11
Rationale: Using question number 11 and 12, we get the probability as
1 - (1/36 + 5/9)
=5/ 12
Answer: B
Answer: B
Question: 21 buses are running between two places P and Q. In how many ways can a person go from P to Q and return by a different bus?
Options:
A)625
B)600
C)576
D)676
E)420
Rationale: we can go in any bus out of the 21 buses.
Hence He can go in 21 ways.
Since we can not come back in the same bus that he used for travelling,
we can return in 24 ways.
Total number of ways = 21 x 20 = 420
ANSWER:E
Answer: E
Question: Private Benjamin is a member of a squad of 10 soldiers, which must volunteer 4 of its members for latrine duty. If the members of the latrine patrol are chosen randomly, what is the probability W that private Benjamin will be chosen for latrine duty?
Options:
A)1/10
B)1/5
C)2/5
D)3/5
E)4/5
Rationale: Easier way : Desired probability = 1- 'excluded' probability
In this case, Excluded probability = probability of Benjamin not being a part of the 4 volunteers. We can choose 4 out of 9 remaining soldiers in 9C4 ways. total ways possible = 10C4.
Thus excluded probability = 9C4/10C4 = 3/5
Thus, the desired probability W= 1- 3/5 = 2/5. Thus C is the correct answer.
Answer: C
Question: Donovan took a math test and got 35 correct and 10 incorrect answers.
What was the percentage of correct answers? (Round to the nearest
hundredth)
Options:
A)57.78%
B)67.78%
C)77.78%
D)47.78%
E)97.78%
Rationale: 35 correct answers+10 incorrect answers=45 total answers
Multiple the opposites
100 x 35 = 3500
77.777/3500
77.78% (rounded to hundredth)
correct answer C
Answer: C
Question: If a choir consists of 2 boys and 4 girls, in how many ways can the singers be arranged in a row, so that all the boys are together? Do not differentiate between arrangements that are obtained by swapping two boys or two girls.
Options:
A)120
B)30
C)24
D)11
E)5
Rationale: There are 5 possibilities:
bbgggg
gbbggg
ggbbgg
gggbbg
ggggbb
Think of all 2 boys as a single unit. Together with 4 girls it makes a total of 5 units. The difference between the arrangements is the position of the boys (as a single unit). So the problem reduces to finding the number of unique patterns generated by changing the position of the boys who can occupy 1 of 5 available positions. If the number of available unique positions is 5, then the number of unique patterns equals 5 as well.
Answer: E.
Answer: E
Question: If the product of two positive integers is 144, which of the following could be the LCM and HCF of the two numbers?
I. LCM : 24; HCF : 6
II. LCM : 18; HCF : 8
III. LCM : 16; HCF : 9
Options:
A)I only
B)II and III only
C)I and II only
D)I and III only
E)I, II and III
Rationale: We need to keep two things in mind here:
1. Product of two numbers = LCM*HCF
2. LCM should be a multiple of HCF
Only Statement I follows these two rules.
Correct Option A
Answer: A
Question: Ramu rides his bike at an average speed of 45 km/hr and reaches his desitination in four hours. Somu covers the same distance in six hours. If Ramu covered his journey at an average speed which was 9 km/hr less and Somu covered his journey at an average speed which was 10 km/hr more, then the difference in their times taken to reach the destination would be (in minutes).
Options:
A)23 minutes
B)30 minutes
C)87 minutes
D)16 minutes
E)19 minutes
Rationale: Distance travelled by Ramu = 45 * 4 = 180 km
Somu travelled the same distance in 6 hours.
His speed = 180/6 = 30 km/hr
Hence in the conditional case, Ramu's speed = 45 - 9 = 36 km/hr and Somu's speed = 30 + 10 = 40km/hr.
Therefore travel time of Ramu and Somu would be 5 hours and 4.5 hours respectively. Hence difference in the time taken = 0.5 hours = 30 minutes.
Answer: B
Answer: B
Question: A father said to his son, "I was as old as you are at present at the time of your birth." If the father's age is 52 years now, the son's age five years back was?
Options:
A)16 years
B)14 years
C)18 years
D)21 years
E)15 years
Rationale: Let the son's present age be x years.
Then, (52 - x) = x
2x = 52 => x = 26
Son's age 5 years back = (26 - 5)
= 21 years.
Answer: D
Answer: D
Question: A car takes 6 hours to cover a distance of 540 Km. how much should the speed in Kmph be maintained to cover the same direction in 3/2th of the previous time?
Options:
A)50 Kmph
B)60 Kmph
C)65 Kmph
D)70 Kmph
E)None
Rationale: Time = 6
Distence = 540
3/2 of 6 hours = 6 * 3/2 = 9 Hours
Required speed = 540/9 = 60 Kmph
B)
Answer: B
Question: Increasing the original price of a certain item by 25 percent and then increasing the new price by 25 percent is equivalent to increasing the original price by what percent?
Options:
A)31.25
B)37.5
C)50.0
D)52.5
E)56.25
Rationale: Soln:-
X*1.25*1.25 = 1.5625 X
so there is a net increase of 56.25% .
Answer E.
Answer: E
Question: A train 300m long takes 9 sec to cross a man walking at 3kmph in a direction opposite to that of the train. Find the speed of the train?
Options:
A)100kmph
B)90kmph
C)120kmph
D)117kmph
E)125kmph
Rationale: Let the speed of the train be x kmph
Speed of the train relative to man = x+3 = (x+3)*5/18 m/sec
300/[(x+3)*5/18] = 9
9(x+3) = 1080
x = 117kmph
Answer is D
Answer: D
Question: If a^x = b^y, then
Options:
A)log a/b= x/y
B)log a/ log b = x/y
C)log a/ log b = y/x
D)log b/a = x/y
E)log b/a = y/x
Rationale: a^x = b^y => log a^x = log b^y => x log a = y log b
=> log a/ log b = y/x
ANSWER:C
Answer: C
Question: On dividing 23 by a number, the quotient is 7 and the remainder is 2. Find the divisor.
Options:
A)1
B)2
C)3
D)6
E)7
Rationale: d = (D-R)/Q
= (23 - 2)/7
= 21/7 = 3
C
Answer: C
Question: Nitin borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by him at the end of eleven years is Rs. 8160, how much money did he borrow?
Options:
A)8000
B)9289
C)2689
D)2769
E)2992
Rationale: Let the sum be Rs. x. Then,
[(x * 6 * 3)/100] + [(x * 9 * 5)/100] + [(x * 13 * 3)/100] = 8160
18x + 45x + 39x = (8160 * 100)
102x = 816000 => x = 8000.
Answer:A
Answer: A
Question: What least number should be subtracted from 13600 such that the remainder is divisible by 87 ?
Options:
A)27
B)29
C)28
D)30
E)31
Rationale: 13600 ÷ 87 = 156, remainder = 28
Hence 28 is the least number which can be subtracted from 13600 such that the remainder
is divisible by 87
Answer is C
Answer: C
Question: You collect baseball cards. Suppose you start out with 16. Since you're nice, you give John 4 baseball cards. How many baseball cards do you have at the end?
Options:
A)11
B)12
C)13
D)14
E)15
Rationale: Solution
Start with 16 baseball cards.
John takes 4 baseball cards from you: 16 - 4 = 12 baseball cards.
So you have 12 at the end.
Correct answer : B
Answer: B
Question: If Rs.7500 are borrowed at C.I at the rate of 4% per annum, then after 2 years the amount to be paid is?
Options:
A)3377
B)2688
C)2688
D)8112
E)1268
Rationale: A = 7500(26/25)2 = 8112
Answer: D
Answer: D
Question: If x and y are integers and 3^(x-4) = 3^(y-2), what is y in terms of x?
Options:
A)x - 6
B)x - 5
C)x - 2
D)x + 2
E)x + 6
Rationale: Answer: A
3^(x-4) = 3^(y-2)
Since the base is the same, I isolated the equations and solved for y.
x-4 = y-2
y=x-2
Ans : C
Answer: C
Question: A train 250 m long passed a pole in 25 sec. How long will it take to pass a platform 650 m long?
Options:
A)78
B)43
C)51
D)66
E)90
Rationale: Speed = 250/25 = 10 m/sec.
Required time = (250 + 650)/10 = 90 sec.
Answer: E
Answer: E
Question: From a group of 5men and 4 women, 3 persons are to be selected to form a committee so that at least 2 men are there are on the committee. In how many ways can it be done?
Options:
A)20
B)50
C)65
D)86
E)96
Rationale: We have (2men and 1 woman) or (3men only)
Therefore, Required number of ways= (5C2*4C1) + (5C3)
= (5*4)/(2*1) * 4 + 5C2
= 10*4 + 10
= 40 +10
=50
ANSWER:B
Answer: B
Question: A man walking at a rate of 10km/hr crosses a bridge in 24 minutes. The length of the bridge is?
Options:
A)1521
B)1492
C)1667
D)4000
E)1112
Rationale: Speed = 10*5/18 = 50/18 m/sec
Distance covered in 24 minutes = 50/18 * 24 *60 = 4000 m
Answer is D
Answer: D
Question: 40 is subtracted from 60% of a number, the result is 50. Find the number?
Options:
A)150
B)887
C)769
D)266
E)291
Rationale: (60/100) * X – 40 = 50
6X = 900
X = 150
Answer: A
Answer: A
Question: If Sharon's weekly salary increased by 16 percent, she would earn $406 per week. If instead, her weekly salary were to increase by 20 percent, how much would she earn per week?
Options:
A) $420
B) $382
C) $385
D) $392
E) $399
Rationale: (406/116)120 =420
In this case long division does not take much time.
(406/116)=3.5
35*12=420(350+70)
Answer A
Answer: A
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)12
B)20
C)24
D)26
E)29
Rationale: 1/x + 1/(x + 10) = 1/12
x = 20
B
Answer: B
Question: A bike covers a certain distance at the speed of 56km/h in 5 hrs. If the bike was to cover the same distance in approximately 7 hrs, at what approximate speed should the bike travel?
Options:
A)39 km/h
B)35 km/h
C)55 km/h
D)40 km/h
E)50 km/h
Rationale: Ans.(D)
Sol. Total distance = 56 × 5 = 280 km
Now speed = 280/7 = 40 km/h
Answer: D
Question: A hall is 15 m long and 12 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:
Options:
A)3348
B)3898
C)1200
D)2881
E)7881
Rationale: Answer: C) 1200
Answer: C
Question: Lagaan is levied on the 60 percent of the cultivated land. The revenue department collected total Rs. 3,94,000 through the lagaan from the village of Mutter. Mutter, a very rich farmer , paid only Rs.480 as lagaan. The percentage of total land of Mutter over the total taxable land of the village is:
Options:
A)0.20833
B)0.14544
C)0.25632
D)0.35466
E)0.20304
Rationale: Total land of Sukhiya = \inline \frac{480x}{0.6} = 800x
\therefore Cultivated land of village = 394000x
\therefore Required percentage = \inline \frac{800x}{394000}\times 100 = 0.20304
E
Answer: E
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)8428
B)8199
C)8400
D)8419
E)8412
Rationale: Ratio of their shares = 22500 : 35000 = 9:14
Deepak's share = 13800 * 14/23
= Rs. 8400.
Answer:C
Answer: C
Question: A cube of side one meter length is cut into small cubes of side 10 cm each. How many such small cubes can be obtained?
Options:
A)1278
B)1728
C)1000
D)8732
E)2881
Rationale: Along one edge, the number of small cubes that can be cut
= 100/10 = 10
Along each edge 10 cubes can be cut. (Along length, breadth and height). Total number of small cubes that can be cut
= 10 * 10 * 10
= 1000
Answer:C
Answer: C
Question: A rectangular lawn of dimensions 80 m * 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m?
Options:
A)2987
B)2768
C)2775
D)3900
E)2675
Rationale: Area = (l + b – d) d
(80 + 60 – 10)10 => 1300 m2
1300 * 3 = Rs.3900
Answer:D
Answer: D
Question: Find the value of x from the below equation: x^2−7x+10=0
Options:
A)1
B)2
C)3
D)4
E)5
Rationale: Here we need to find out a and b such that a + b = -7 and ab = +10
a = -5 and b = -2 satisfies the above condition.
Hence
x^2−7x+10=(x−5)(x−2)
x2−7x+10=(x−5)(x−2)
x^2−7x+10
=0
⇒(x−5)(x−2)
=0
x2−7x+10=0⇒(x−5)(x−2)=0
Step 3: Equate each factor to 0 and solve the equations
(x−5)(x−2)
=0
⇒(x−5)
=0or (x−2)=0
⇒x= 5 or 2
B
Answer: B