divelab/Sys2Bench huggingface dataset:
Question: X and Y invest Rs.12500 and Rs.17500 respectively in a business. At the end of the year, they make a profit of Rs.26400. What is the share of X in the profit?
Options:
A)Rs.14400
B)Rs.26400
C)Rs.11000
D)Rs.12500
E)Rs.13500
Rationale: Ratio of the investment=12000:17500=5:7
Share of X in the profit=(26400×5)/12=11000
ANSWER:C
Answer: C
Question: The sum of the first 50 positive even integers is 2550. What is the sum of the even integers from 302 to 400 inclusive?
Options:
A)11,550
B)14,550
C)17,550
D)20,550
E)23,550
Rationale: 2 + 4 + 6 + 8 +...+ 100 = 2550
302 + 304 + ... + 400 = 50(300) + (2+4+...+100) = 15,000 + 2550 = 17,550
The answer is C.
Answer: C
Question: If Janice was 24 years old z years ago and Lisa will be 22 years old in p years, what was the average (arithmetic mean) of their ages 6 years ago?
Options:
A)(z + p)/2
B)(z - p + 34)/4
C)(z - p + 24)/4
D)(z + p + 44)/2
E)(z - p + 34)/2
Rationale: Today, J = z+24 and L = 22-p
6 years ago, J = z+18 and L = 16-p
The average of their ages was (z-p+34) / 2
The answer is E.
Answer: E
Question: A train 225 m long passes a man, running at 10km/hr in the same direction in which the train is going, in10 seconds. The speed of the train is:
Options:
A)81
B)90
C)91
D)85
E)96
Rationale: Speed of the train relative to man =225/10 m/sec
=45/2m/sec.
=45/2x18/5km/hr
= 81 km/hr.
Let the speed of the train be x km/hr. Then, relative speed = (x - 5) km/hr.
x - 10 = 81 =91km/hr.
Answer:C
Answer: C
Question: A certain company assigns employees to offices in such a way that some of the offices can be empty and more than one employee can be assigned to an office. In how many ways can the company assign 3 employees to 4 different offices?
Options:
A)52
B)64
C)32
D)11
E)12
Rationale: Each of three employee can be assigned to either of offices, meaning that each has 2 choices --> 4*4*4=4^3=64.
Answer: B.
Answer: B
Question: If Janice was 22 years old z years ago and Lisa will be 20 years old in p years, what was the average (arithmetic mean) of their ages 7 years ago?
Options:
A)(z + p)/2
B)(z - p + 28)/4
C)(z - p + 18)/4
D)(z + p + 38)/2
E)(z - p + 28)/2
Rationale: Today, J = z+22 and L = 20-p
7 years ago, J = z+15 and L = 13-p
The average of their ages was (z-p+28) / 2
The answer is E.
Answer: E
Question: It takes John exactly 30 minutes to rake a lawn and it takes his son Todd exactly 60 minutes to rake the same lawn. If John and Todd decide to rake the lawn together, and both work at the same rate that they did previously, how many minutes will it take them to rake the lawn
Options:
A)16
B)45
C)36
D)20
E)90
Rationale: 1)POE- John takes 30 min so if he takes help of someone else, it has to be less than 30 min..
only A and B are left..
if both do the work in 30 mis each, the combined time will be 15 mins, so 16 is slightly less when the other person does in 60 mins..
ans 20 D
Answer: D
Question: The price of a certain product increased by the same percent from 1960 to 1970 as from 1970 to 1980. If its price of $2.00 in 1970 was 150 percent of its price in 1960, what was its price in 1980?
Options:
A)a) $ 1.80
B)b) $ 2.00
C)c) $ 2.40
D)d) $ 2.70
E)e) $ 3.00
Rationale: The price in 1970 was 150 percent of its price in 1960, means that the percent increase was 50% from 1960 to 1970 (and from 1970 to 1980).
Therefore the price in 1980 = $2.0*1.5 = $3.00.
Answer: E.
Answer: E
Question: What will come in place of the x in the following Number series? 12, 38, 116, 350, x
Options:
A)1052
B)5464
C)3456
D)7554
E)3158
Rationale: 12
12 Ã— 3 + 2 = 38
38 Ã— 3 + 2 = 116
116 Ã— 3 + 2 = 350
350 Ã— 3 + 2 = 1052
A
Answer: A
Question: Machine A and machine G are each used to manufacture 660 sprockets. It takes machine A 10 hours longer to produce 660 sprockets than machine G. Machine G produces 10 percent more sprockets per hour than machine A. How many sprockets per hour does machine A produces?
Options:
A)6
B)6.6
C)60
D)100
E)110
Rationale: [Reveal]Spoiler:
TimeG: 660/x
TimeA: [660/x+10]
660/x = [660/x+10] *110/100
660/x =66*11/x+10
660x+10= 66*11*x
660x +6600 = 66*11*x
x= 100
plug in back to timeA
660/100+10 => 660/110 = 6
Answer: A
Question: 350 is increased by 50%. Find the final number.
Options:
A)725
B)625
C)225
D)525
E)425
Rationale: ExplanationFinal number = Initial number + 50%(original number) = 350 + 50%(350) = 350 + 175 = 525.Answer D
Answer: D
Question: If f(x) = 12 - x^2/2 and f(2k) = 5k, what is one possible value for k?
Options:
A)2
B)3
C)4
D)5
E)8
Rationale: First of all, see thisGMAT blog postand check the related lesson linked below for some background on function notation.
We can plug anything in for x and get a result. You can find f(1), for example, by plugging in 1 where x is, and you would get 12 - 1/2 = 11.5. Or we could find f(2), which would be 12 - 4/2 = 10.
So the notation f(2k) means that we are going to plug a 2k in for x everywhere in the formula for f(x). That would be:
f(2k) = 12 - (2k)^2/2 = 12 - 2k^2.
Remember that we have to square both the 2 and the k, to get 4k2. Now, this expression, the output, we will set equal to 2k.
12 - 2k^2 = 2k --> k = -3 or k =5.
All the answers are positive, so we choose k = 5.
Answer =D
Answer: D
Question: A card is drawn from a pack of 52 cards the probability of getting queen of club or aking of a heart?
Options:
A)8/58
B)9/25
C)1/26
D)6/25
E)8/45
Rationale: here n(s)=52
let E be the event of getting queen of the club or king of kings
n(E)=2
p(E)=n(E)/n(S)=2/52=1/26
Answer(C)
Answer: C
Question: A reduction of 40% in the price of oil enables a house wife to obtain 8 kgs more for Rs.2400, what is the reduced price for kg?
Options:
A)Rs.120
B)Rs.125
C)Rs.130
D)Rs.135
E)Rs.140
Rationale: Explanation:
2400*(40/100) = 960 ---- 8
? ---- 1 => Rs.120
Answer: A
Answer: A
Question: Eleven bags are bought for Rs.1000 and sold at 10 for Rs.1200. What is the gain or loss in percentage?
Options:
A)10%
B)22%
C)25%
D)20%
E)None of these
Rationale: Explanation:
As selling price is Rs.1200 for 10 bags, each bag is sold at Rs.120.
Hence, the profit is Rs.100 after selling 10 bags plus the selling price of 1 bag = 100 + 120 = Rs.220.
%profit = 220/1000 *100
= 22%
ANSWER B
Answer: B
Question: I. x + 2y + 3z = 2
II. x + y - z = 0
III. 2x + 2y - z = 1
What is the value of y in the system above?
Options:
A) -2
B) -1
C) 0
D) 1
E) 2
Rationale: 1. from the given system of equations i can make equation II. to be x + y = z
2. now put that in III. :
2x + 2y - (x + y) = 1
= 2x + 2y - x - y = 1
= x + y = 1
that gives usz = 1!
3. put z = 1 in I. and solve:
x + 2y + 3 = 2; calculate minus 3
= x + 2y = -1; calculate minus x
=2y = -1 - x;
4. now put 2y = -1 - x in III. and solve:
2x + (-1 - x) - 1 = 1
= x - 2 = 1; calculate plus 2
that gives usx = 3
5. now solve for y with x = 3 and z = 1:
x + y = 1
= 3 + y = 1; calculate minus 3
that gives y = -2, and hence answer (A) -2
Answer: A
Question: Steve gets on the elevator at the 11th floor of a building and rides up at a rate of 47 floors per minute. At the same time Joyce gets on an elevator on the 51st floor of the same building and rides down at a rate of 53 floors per minute. If they continue traveling at these rates, at which floor will their paths cross?
Options:
A)19
B)28
C)30
D)33
E)44
Rationale: Steve gets on the elevator at the 11th floor of a building and rides up at a rate of 47 floors per minute. At the same time Joyce gets on an elevator on the 51st floor of the same building and rides down at a rate of 53 floors per minute. If they continue traveling at these rates, at which floor will their paths cross?
40 floors/100 floors per minute=2/5 minutes
11+57/3=33
51-63/3=33
Answer : D
Answer: D
Question: A tap can fill the tank in 15 minutes and another can empty it in 8 minutes. If the tank is already half full and both the taps are opened together, the tank will be:
Options:
A)filled in 12 min
B)emptied in 12 min
C)filled in 8 min
D)will be empty in 8 min
E)emptied in 10 min
Rationale: work done by both taps= 1/15+(-1/8)= -7/120 so tank will be emptied becoz of minus sign.
so time taken= 120/7
given the tank is already half filled
so another half will be emptied in 120/7*1/2
nearly 8 minutes
ANSWER:D
Answer: D
Question: For my anniversary, I decided to surprise my wife. Since she is a voracious reader, I decided to collect a lot of books for her. On the first day of the month, I bought one book, on the second, I bought two and on the third, I bought three. This process went on till the anniversary and on the day, I had 231 books with me to gift her.
Can you calculate, on which day is our anniversary?
Options:
A)31
B)28
C)23
D)21
E)25
Rationale: D
21rd day
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 + 21 = 231
Thus our anniversary falls on the 21rd day of the month.
You can apply other formulas to shorten the process but that is the simplest way to do it.
Answer: D
Question: After M students took a test, the average score was 56%. If the test has 50 questions, what is the least number of questions that the next student has to get right to bring the average score up to 60%?
Options:
A)M + 30
B)0.56M + 30
C)M + 28
D)2M + 28
E)2M + 30
Rationale: The total number of correct answers for M students is (0.56)*50*M=28*M
For an average of 75%: (total correct answers) / (M+1) = 0.6*50=30
Let x be the number of correct answers for the next student.
(x + 28M) / M+1 = 30
x + 28M= 30M+30
x = 2M + 30
The answer is E.
Answer: E
Question: A company has two models of computers, model X and model Y. Operating at a constant rate, a model X computer can complete a certain task in 72 minutes and a model Y computer can complete the same task in 36 minutes. If the company used the same number of each model of computer to complete the task in 1 minute, how many model X computers were used?
Options:
A)22
B)23
C)24
D)25
E)26
Rationale: Let's say 1 work is processing 72 gb of data.
Model X : 1 gb per min
Model Y : 2 gb per min
Working together, 1 X and 1 Y = 3 gb per min
So, 24 times as many computers would work at 72 gb per min.
So no. of X =24
Answer is C
Answer: C
Question: Laura has a deck of standard playing cards with 13 of the 52 cards designated as a "heart." If Laura shuffles the deck thoroughly and then deals 10 cards off the top of the deck, what is the probability that the 10th card dealt is a heart?
Options:
A)1/4
B)1/5
C)5/26
D)12/42
E)13/42
Rationale: Desired outcomes= 13
Total outcomes= 52
Probability of getting any card as the heart card= 13/52= 1/4
And the same probability will be for 10th card as well.
A is the answer
Answer: A
Question: Find the area of the sector whose are is making an angle of 90° at the center of a circle of radius 3.2 Cm.
Options:
A)56.72 Sq.Cm
B)56.22 Sq.Cm
C)56.82 Sq.Cm
D)56.42 Sq.Cm
E)56.32 Sq.Cm
Rationale: Area of the sector = 90/360 × πr(power)2
= 90/360 × 22/7 × 3.2 × 3.2
= (11 × 10.24)/2 = 112.64/2 = 56.32 Sq.Cm
Answer is E.
Answer: E
Question: If P = Q-R, -1 < R < 0 and Q=0, which of the following is correct?
Options:
A)P < -1.
B)0 < P <2
C)P > 0
D)0 < P <4
E)P < -20
Rationale: Q is 0 & R is -ve
For min. value max. numerator and minimize denominator
take Q=0 & R=-0.9
P=0-(-0.9)
P > 0
Ans C
Answer: C
Question: Approximately what percentage of the world’s forested area is represented by Finland given that Finland has 53.42 million hectares of forested land of the world’s 8.076 billion hectares of forested land.
Options:
A)0.0066%
B)0.066%
C)0.66PERCENT
D)6.6%
E)66%
Rationale: Approximation is a strategy that helps us arrive at less than an exact number and the inclusion in this problem of the word “approximately” is an obvious clue. First, 8.076 billion is 8,076 million. Next, 8,076 million rounds to 8,000 million and 53.42 million rounds to 53 million. Dividing 53 million by 8,000 million we arrive at 0.0066 (53M/8,000M). We convert this decimal figure to a percentage by multiplying by 100 (or moving the decimal point two places to the right) and adding a percent sign in order to obtain our answer of 0.66%. Note that the shortcut method involves comparing 53 million to 1% of 8,000 million or 80 million. Since 53 million is approximately two-thirds of 80 million then the answer is some two-thirds of 1% or 0.66%.
Answer: C.
Answer: C
Question: Kim can walk 4 kilometers in one hour. How long does it take Kim to walk 18 kilometers?
Options:
A)7 hours and 30 minutes.
B)8 hours and 30 minutes.
C)9 hours and 30 minutes.
D)3 hours and 30 minutes.
E)4 hrs and 30 min
Rationale: The time it takes Kim to walk 18 kilometers is equal to
18 / 4 = 4.5 hours = 4 hours + 0.5 * 60 minutes
= 4 hours and 30 minutes.
correct answer E
Answer: E
Question: If y = 2 + 2K and y≠0y≠0, then 2/y + 1/y + 1/y + 1/y = ?
Options:
A)1/(8+8k)
B)5/2(1+k)
C)1/(8+k)
D)4/(8+k)
E)4/(1+k)
Rationale: 2/Y + 1/Y + 1/Y + 1/Y
= 5/Y
= 5/(2 + 2K)
= 5/2(1 + K)
ANSWER:B
Answer: B
Question: Two trains are running at 40 km/hr and 20 km/hr respectively in the same direction. Fast train completely passes a man sitting in the slower train in 5 sec. What is the length of the fast train?
Options:
A)27 7/9
B)27 7/6
C)27 7/2
D)27 7/9
E)27 7/1
Rationale: Relative speed = (40 - 20) = 20 km/hr.
= 20 * 5/ 18 = 50/9 m/sec.
Length of faster train = 50/9 * 5 = 250/9 = 27 7/9 m.
Answer:D
Answer: D
Question: P, Q, R enter into a partnership. P initially invests 25 lakh and adds another 10 lakh after one year. Q initially invests 35 lakh and withdraws 10 lakh after 2 years. R's investment is Rs 30 lakh. In what ratio should the profit be divided at the end of 3 years?
Options:
A)19:18:19
B)18:19:19
C)19:17:18
D)19:19:18
E)17:18:19
Rationale: P : Q : R
=(25×1+35×2):(35×2+25×1) :(30×3)
=95:95:90=19:19:18
Answer is D.
Answer: D
Question: The sale price of a trolley bag including the sale tax is Rs. 1232. The rate of sale tax is 10% . If the shopkeeper has made a profit of 12%, the cost price of the trolley bag is:
Options:
A)Rs 1000
B)Rs 1515
C)Rs 1525
D)Rs 1250
E)None of these
Rationale: Explanation :
110% of S.P. = 1232
S.P. = Rs.(1232 x 100/110) = Rs.1120.
C.P. = Rs (100/112 x 1120) = Rs 1000
Answer : A
Answer: A
Question: Vishal and Raghu jointly started a business. Vishal invested three times as Raghu did and invested his money for double time as compared to Raghu. Raghu earned Rs. 4000. If the gain is proportional to the money invested and the time for which the money is invested then the total gain was ?
Options:
A)28,000
B)28,129
C)28,109
D)28,009
E)28,011
Rationale: Investments ratio is = 3:1
Time period ratio is = 2:1
As they are proportional to gain
------
Gain ratio of Vishal and raghu = 6:1
But given Raghu got Rs. 4000,
=? 1 ----- 4000
7 ----- ?
=> Rs.28,000
The total gain = Rs.28,000
Answer: A
Answer: A
Question: Suppose we have six marbles: 3 blue marbles, 2 red marbles, and one green marble. Suppose we are going to put them into three cups: a grey cup, a white cup, and a purple cup. We could put all six in any cup and leave two cups empty; or we could put marbles in two cups and leave one cup empty; or we could put some marbles in each of the three cups. How many combinations are possible?
Options:
A)150
B)160
C)200
D)180
E)240
Rationale: # ways to distribute Blue marbels(3) is :
1 in each cup= 1
2 in one cup and 1 in other=6
all 3 in one cup = 3
total 1+6+3=10 possibilities
# ways to distribute Red marbels(2) is :
1 in each cup = 3 ways
all in one cup = 3ways
total 6ways.
# ways to distribute Green marbels(1) is :
3 ways
total number of ways = 10*6 *3 = 180
D
Answer: D
Question: The diameter of two circles are 18 cm and 8 cm. The distance between their centres is 13 cm. What is the number of common tangents?
Options:
A)3
B)2
C)1
D)5
E)7
Rationale: A
3
Here, r1 = 9 cm and r 2 = 4 cm
r 1 + r 2 = 9 + 4 = 13 cm
and r 1 – r 2 = 9 – 4 = 5cm
Also, d = 13 cm
Here, d = r 1 + r 2
= 13 cm
Hence, two circles touch each other externally, so three total no of common tangents are three.
Answer: A
Question: It was Sunday on Jan 1, 2006. What was the day of the week Jan 1, 2010?
Options:
A)Sunday
B)Sarurday
C)Friday
D)Wednesday
E)Monday
Rationale: Explanation:
On 31st December, 2005 it was Saturday. Number of odd days from the year 2006 to the year 2009 = (1 + 1 + 2 + 1) = 5 days. On 31st December 2009, it was Thursday. Thus, on 1st Jan, 2010 it is Friday.
Answer: C
Answer: C
Question: The length of a train and that of a platform are equal. If with a speed of 90 k/hr, the train crosses the platform in one minute, then the length of the train (in meters) is?
Options:
A)752
B)799
C)719
D)750
E)712
Rationale: Speed = [90 * 5/18] m/sec = 25 m/sec; Time = 1 min. = 60 sec.
Let the length of the train and that of the platform be x meters.
Then, 2x/60 = 25 è x = 25 * 60 / 2 = 750
Answer: D
Answer: D
Question: A train running at the speed of 60 km/hr crosses a pole in 6 seconds. What is the length of the train?
Options:
A)100
B)130
C)150
D)170
E)160
Rationale: Speed=(60x5/18)m/sec = (50/3) m/sec.
Length of the train = (Speed x Time).
Length of the train = (50/3 x 6)m = 100 m.
Answer is A.
Answer: A
Question: Jackie has two solutions that are 2 percent sulfuric acid and 12 percent sulfuric acid by volume, respectively. If these solutions are mixed in appropriate quantities to produce 60 liters of a solution that is 10 percent sulfuric acid, approximately how many liters of the 12 percent solution will be required?
Options:
A)18
B)20
C)48
D)36
E)42
Rationale: let a=amount of 2% acid and b= amount of 12% acid.
Now, The equation translates to,
0.02a + .12b = .1(a+b)
but a+b= 60
therefore .02a + .12b = .1(60)
=> 2a + 12b = 600
but b=60-a
therefore
2a+ 12(60-a) = 600
=> 10a = 120
hence a = 12. b = 60 -12 = 48.
Answer : C
Answer: C
Question: If after successive discounts of 20% and 25/4% on the marked price of an article, a trader gets 20% profit on the cost price,then by what percent is the marked price above the cost price?
Options:
A)50%
B)60%
C)70%
D)80%
E)90%
Rationale: Let the market price be RS 100. Then after first discount S.P becomes 80 and after another discount it becomes Rs. 75.
so S.P = 75. now with this S.P he has made a profit of 20% and hence the
C.P = (75/120)*100 = 62.5
so percentage change with respect to market price is = (37.5/62.5)*100
giving 60%
ANSWER:B
Answer: B
Question: 4/9 × 6/3 + 11/27 – 18/81 = ?
Options:
A)27(5/24)
B)13 (2/7)
C)24 (5/27)
D)17 (3/21)
E)None of these
Rationale: Explanation:
= 4/9 × 6/3 + 11/27 – 18/81
=4/9 × 6/3 + 11/27 – 6/27
= 12*54+11-6/27 = 653/27 = 24 (5/27)
Answer: Option C
Answer: C
Question: When 30 is divided by the positive integer k, the remainder is 6, for how many different values of k is this true?
Options:
A)2
B)3
C)5
D)7
E)8
Rationale: When 30 is divided by k, remainder is 6 i.e. there are 6 balls leftover after grouping. so k must be greater than 6.
It also means that 30 is completely divisible by k.
Factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24
Out of these, k can be 4, 6, 8, 12, 24.
Answer (C)
Answer: C
Question: A letter lock consists of three rings each marked with eight different letters. The number of distinct unsuccessful attempts to open the lock is at the most?
Options:
A)176
B)511
C)518
D)519
E)172
Rationale: Since each ring consists of eight different letters, the total number of attempts possible with the three rings is
= 8 * 8 * 8 = 512. Of these attempts, one of them is a successful attempt.
Maximum number of unsuccessful attempts
= 512 - 1 = 511.
Answer: B
Answer: B
Question: What least value should be replaced by * in 223*431 so the number become divisible by 9
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: Explanation:
Trick: Number is divisible by 9, if sum of all digits is divisible by 9, so (2+2+3+*+4+3+1) = 15+* should be divisible by 9,
15+3 will be divisible by 9,
so that least number is 3.
Answer: Option A
Answer: A
Question: In a group of 5 boys and 5 girls, four children are to be selected. In how many different ways can they be selected such that at least one girl is included?
Options:
A)175
B)190
C)205
D)220
E)235
Rationale: The total number of ways to choose 4 children is 10C4 = 210
The number of ways to choose only boys is 5C4 = 5
The number of groups which include at least one girl is 205.
The answer is C.
Answer: C
Question: What is the sum of the integers from -194 to 195 inclusive?
Options:
A)0
B)5
C)195
D)875
E)965
Rationale: sum/n= average.
sum=(average)(n)
average=a+b/2=194+195/2=0.5
number of items(n)=B-A+1=195-(-194)+1=195+195=390.
sum=average*n=0.5*390=195.
answer is C
Answer: C
Question: If a man buys 10 lollipops for $80 and sold them for $2 dollars determine his loss.
Options:
A)50
B)60
C)70
D)80
E)90
Rationale: Cost of 10 lollipops = $80
Sold each lollipop for $2
So, he sold 10 lollipops for $(10 × 2) = $20
Loss = $(80 – 20) = $60
answer :B
Therefore, loss = $ 60.
Answer: B
Question: What is the tens' digit R of the sum of the first 40 terms of 1, 11, 111, 1111, 11111, 111111, ...?
Options:
A)R=2
B)R=3
C)R=4
D)8
E)9
Rationale: All of the first 40 terms have 1 at the units place.
Except the first term, the tens digit of all the remaining 39 terms is 1.
So now if you do the addition
1 1
1 1
. . .
. . .
. . .
1 1
0 1
3 0
Answer is B
Answer: B
Question: On flipping 3 coins together what is the outcomes for at least two tails?
Options:
A){HHH, HHT, HTH, THH}
B){HHT, HHT, HTH, THH}
C){TTH, HHT, HTH, THH}
D){TTH,THT, HTT,TTT}
E)None
Rationale: Sample space, S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT}
Favorable outcomes for at least two tails
= favorable outcomes for exactly two heads and favorable outcomes for more than two heads
= {TTH, THT, HTT, TTT}
D
Answer: D
Question: A person can swim in still water at 4 km/h. If the speed of water 2 km/h, how many hours will the man take to swim back against the current for 6km?
Options:
A)3
B)4
C)2
D)5
E)7
Rationale: M = 4
S = 2
US = 4 - 2 = 2
D = 6
T = 6/2 = 3
Answer: A
Answer: A
Question: If the operation ∆ is defined by a ∆ b = (b - a)^2/a^2 for all numbers a and b, and a ≠ 0, then what is the result when we evaluate this expression: (-6) ∆ (6 ∆ −6) ?
Options:
A)36/25
B)81/4
C)25/4
D)49/9
E)25/9
Rationale: (-6) ∆ (6 ∆ −6) =
(-6) ∆ (12^2/6^2) =
(-6) ∆ (4) =
(-10^2) / (-6)^2 = 100/36 = 25/9
The answer is E.
Answer: E
Question: The average of five results is 46 and that of the first four is 35. The fifth result is?
Options:
A)50
B)90
C)77
D)66
E)51
Rationale: 5 * 46 â€“ 4 * 35
= 90
Answer: B
Answer: B
Question: Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:
Options:
A)1by7
B)1/8
C)1/9
D)7/8
E)1/5
Rationale: Original share of 1 person = 1/8
New share of 1 person = 1/7
Increase =(1/7-1/8) = 1/56
Required fraction = (1/56)/(1/8)
= (1/56)*8
= 1/7
ANSWER:A
Answer: A
Question: A solid yellow stripe is to be painted in the middle of a certain highway. If 1 gallon of paint covers an area of r square feet of highway, how many gallons of paint will be needed to paint a stripe of t inches wide on a stretch of highway m miles long? (1 mile = 5,280 feet and 1 foot = 12 inches)
Options:
A)(5,280 mt) / 12 r
B)(5,280 pt) / 12m
C)(5,280 pmt) /12
D)(5,280)(12m) / pt
E)(5,280)(12p) / mt
Rationale: Given that: 1 gallon of paint covers an area ofrsquare feet. Question:how many gallonsof paint will be needed ...
In any case you will have:(total area in square feet)/(gallons per feet)=(total area in square feet)/r, so r must be in the denominator: eliminate all but A and D.
Now, lets see where should be t: (area in square feet)=(width in feet)*(length in feet) --> width=tinchesas1 feet=12 inchesthent inches=t/12 feet, so (area in square feet)=(t/12) * (length in feet), so t must be in the nominator: only A is left.
Answer: A.
Answer: A