mathewhe/aqua_rat huggingface dataset:
Question: (x to power 1/3) - (x to power 1/9)=60
We have to find out the value of x ??
(A) 4^9
(B) 4^8
(C) 4^7
(D) 4^6
(E) 4^5
Rationale: let x^(1/9) =y
y^3-y =60
y(y^2-1) = 60
y=4
x^(1/9)= 4
x = 4^9
ANSWER:A
Answer: (A) 4^9
Question: A company recently conducted a survey and found that 20,000 of its customers live in rural areas. If the number of customers who live in urban areas is 100 percent greater than the number of customers who live in rural areas, how many customers live in urban areas?
(A) 40,000
(B) 45,000
(C) 50,000
(D) 55,000
(E) 60,000
Rationale: The number of customers in urban areas is 20,000+1*20,000=40,000.
The answer is A.
Answer: (A) 40,000
Question: The vertex of a rectangle are (1, 0), (5, 0), (1, 1) and (5, 1) respectively. If line L passes through the origin and divided the rectangle into two identical quadrilaterals, what is the slope of line L?
(A) 1/2
(B) 2
(C) 1/6
(D) 3
(E) 1/4
Rationale: If line L divides the rectangle into two identical quadrilaterals, then it must pass through the center (3, 0.5). The slope of a line passing through (0,0) and (3, 0.5) is 0.5/3 = 1/6.
The answer is C.
Answer: (C) 1/6
Question: If a and b are different values and a – b = 2(√a - √b), then in terms of b, a equals:
(A) √b
(B) b
(C) b - 4√b + 4
(D) b + 2√b + 1
(E) b^2 – 2b√b + b
Rationale: (√a)^2 - (√b)^2 = 2(√a - √b) -----> ( √a + √b) ( √a - √b) = 2(√a - √b ) -------> √a + √b = 2, so
√a = 2 - √b, square both sides and solve. Answer is C.
Answer: (C) b - 4√b + 4
Question: A computer manufacturer produces a certain electronic component at a cost of $80 per component. Shipping costs for delivering the components are $6 per unit. Further, the manufacturer has costs of $16,500 a month related to the electronic component regardless of how many it produces. If the manufacturer produces and sells 150 components a month, what is the lowest price it can sell them for such that the costs don't exceed the revenues?
(A) $28
(B) $82
(C) $110
(D) $138
(E) $196
Rationale: by the question, the equation would be 150 p - 86*150 - 16500 = 0
p being the price we want to find and equation resulting zero means revenue and costs are equal so we can get the minimum price of the component.
solving the equation, we get p = $ 196. Answer E for me.
Answer: (E) $196
Question: Out of the three numbers A, B and C, A exceeds B by 20 and C exceeds A by 55. If the sum of all the numbers is 230, What is the difference between the largest and the smallest number?
(A) 87
(B) 65
(C) 75
(D) 19
(E) 11
Rationale: Explanation:
We have , A = B + 20 & C = A + 55 = B + 75
Thus, (B + 20) + (B) + (B + 75) = 230
B = 45
Thus, A = 65 & C = 120. Hence, (C) – (B) = 120 – 45 = 75
Short-Cut Method : Since C is larger than A by 55 and A is larger than B by 20, we get, the Required difference = 55 + 20 = 75 (without calculating the actual values of A, B and C).
ANSWER:C
Answer: (C) 75
Question: In a board game, a stack of 44 cards, 6 of which have pictures of fruit, are shuffled and then placed face down. If the first 2 cards selected do not have pictures of fruit, what is the probability that the third card selected will have a picture of fruit?
(A) 3/22
(B) 1/11
(C) 1/9
(D) 1/7
(E) 1/5
Rationale: After 2 cards have been selected, there are 42 cards remaining.
P(third card has a picture of fruit) = 6/42 = 1/7
The answer is D.
Answer: (D) 1/7
Question: The speed of a car increases by 2kms after every one hour. If the distance travelled in the first one hour was 35kms, what was the total distance travelled in 12 hours?
(A) 456kms
(B) 482kms
(C) 552kms
(D) 556kms
(E) None of these
Rationale: Total distance travelled in 12 hours = (35+37+39+...upto 12 terms).
This is an A.P. with first term, a=35, number of terms, n=12, common difference d=2
Required distance = 12/2(2*35+(12-1)*2)=6(70+22)=552km.
Correct Option: C
Answer: (C) 552kms
Question: In an examination, 300 students appeared. Out of these students; 25 % got first division, 54 % got second division and the remaining just passed. Assuming that no student failed; find the number of students who just passed.
(A) 63
(B) 37
(C) 54
(D) 99
(E) 01
Rationale: The number of students with first division = 25 % of 300 = 25/100 × 300 = 8400/100 = 75
And, the number of students with second division = 54 % of 300
= 54/100 × 300
=16200/100
= 162
Therefore, the number of students who just passed = 300 – (75 + 162) = 63
Answer:A
Answer: (A) 63
Question: It is known that no more than 9 children will be attending a party. What is the smallest number of cookies that must be brought to the party so that each child receives the same number of cookies?
(A) 35
(B) 105
(C) 420
(D) 210
(E) 2520
Rationale: The question states that there are no more than 9 children in the party. Thus, the possibility is that there could be 1, 2, 3, 4, 5, 6, 7, 8 or 9 children.
If you assume answer as 35 and there are 3 children, you may not distribute be able to distribute cookies equally.
similarly if there were 105 cookies, and 2 children, cookies cannot be distributed equally.
or if there were 210 cookies, and 4 children, cookies cannot be distributed equally.
Thus, the question asks for a number of cookies which can be distributed to any number of children (from 1 to 9).
And therefore the smallest number of cookies would be lcm of (1, 2, 3, 4, 5, 6, 7,8,9), i.e., 2520.
Answer (E)
Answer: (E) 2520
Question: The arithmetic mean of the set S = {7, K, 6, 12, M, 7} is 8. If K and M are integers, and K ≠ M, what is the median of the numbers in the set?
(A) 6
(B) 6.5
(C) 7
(D) 7.5
(E) 8
Rationale: The sum of the numbers is 6*8 = 48
K+M = 48 - 12 - 7 - 7 - 6 = 16
Since K ≠ M, K and M do not equal 8.
Thus one of the two numbers is 7 or less and one is 9 or more.
Then middle two numbers in the set are 7 and 7.
The median is 7.
The answer is C.
Answer: (C) 7
Question: Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
(A) 1236
(B) 1346
(C) 1657
(D) 1874
(E) 1635
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Large number = 270+1365 = 1635
E
Answer: (E) 1635
Question: John has taken four (6) tests that have an average of 82. In order to bring his course grade up to a ‘B’, he will need to have a final average of 87. What will he need to average on his final two tests to achieve this grade?
(A) 87
(B) 90
(C) 92
(D) 94
(E) 102
Rationale: 87-82=5*6=30 points
2*87=174
174+30=204 points to be scored in the 2 tests.
Avg of 2 tests = 204/2=102
Answer: E
Traditional Method:
Total scored till now 82*6=492
Total score to avg 87 in 8 tests = 87*8=696
Total to be scored on 2 tests = 696-492=204
Avg on 2 tests = 204/2 = 102
Answer E
Answer: (E) 102
Question: A caterer ordered 125 ice-cream bars and 125 sundaes. If the total price was $250.00 and the price of each ice-cream bar was $0.60, what was the price of each sundae?
(A) $0.60
(B) $0.80
(C) $1.00
(D) $1.20
(E) $1.40
Rationale: Let price of a sundae = S
Price of ice cream bar = .6 $
125 * .6 + 125*S = 250
=> 125*S = 175
=> S = 1.4
Answer E
Answer: (E) $1.40
Question: Consider a set S given as {11,22,33,44,55,66,77,88,99} . If each element of the data set is multiplied by -4 then by what factors will the Mean,Variance and Standard Deviation respectively change ?
(A) -4,-4,-4
(B) -4,4,4
(C) 1,1,1
(D) -4,16,4
(E) 4,4,16
Rationale: Mean: If all values are multiplied by -4 then their sum will also be multiplied by -4 so Mean will also get -4
Variance:
Variance is equal to (Sum of (Square of (the difference between mean and individual values))/Total number of values
When we multiply all the values by -4 then the difference between the mean and the individual values also gets multiplied by -4 and the square of that difference becomes 16. So, the variance gets multiplied by a factor of 16
SD:
Standard Deviation is the square root of variance so sqrt(16)=4. So SD gets multiplied by a factor of 4.
So, answer will be D.
Answer: (D) -4,16,4
Question: If two-third of a bucket is filled in 90 seconds then the time taken to fill the bucket completely will be .
(A) 90 seconds
(B) 70 seconds
(C) 135 seconds
(D) 100 seconds
(E) 120 seconds
Rationale: 2/3 filled in 90 seconds
1/3 filled in 45 seconds
then 2/3+1/3=90 + 45 seconds = 135 seconds
ANSWER: C
Answer: (C) 135 seconds
Question: Stalin and Heather are 20 miles apart and walk towards each other along the same route. Stalin walks at constant rate that is 1 mile per hour faster than heather's constant rate of 5 miles/hour. If Heather starts her journey 20 minutes after Stalin, how far from the original destination has Heather walked when the two meet?
(A) 4 miles
(B) 6 miles
(C) 9 miles
(D) 10 miles
(E) 12 mile
Rationale: Original distance between S and H = 20 miles.
Speed of S = 5+1 = 6 mph, Speed of H = 5 mph.
Time traveled by H = t hours ---> time traveled by S = t+20/60 = t+2/6 hours.
Now, the total distances traveled by S and H = 20 miles ---> 6*(t+2/6)+5*t=20 ---> t= 8/11 hours. Thus H has traveled for 8/11 hours giving you a total distance for H = 5*8/11 ~ 4 miles.
A is thus the correct answer.
P.S.: based on the wording of the question, you should calculatehow far from theoriginal destination has Heather walkedwhen the two meet. 'Original destination' for H does not make any sense. Original destination for H was situated at a distance of 20 miles.
Answer: (A) 4 miles
Question: A person travels equal distances with speeds of 3 km/hr, 4 km/hr and 5 km/hr and takes a total time of 47 minutes. The total distance is?
(A) 6 km
(B) 3 km
(C) 9 km
(D) 5 km
(E) 1 km
Rationale: Let the total distance be 3x km.
Then, x/3 + x/4 + x/5 = 47/60
47x/60 = 47/60 => x = 1.
Total distance = 3 * 1 = 3 km.
Answer: B
Answer: (B) 3 km
Question: A can do a particular work in 6 days . B can do the same work in 8 days. A and B signed to do it for Rs. 3200. They completed the work in 3 days with the help of C. How much is to be paid to C?
(A) 200
(B) 230
(C) 300
(D) 350
(E) 400
Rationale: Amount of work A can do in 1 day = 1/6
Amount of work B can do in 1 day = 1/8
Amount of work A + B can do in 1 day = 1/6 + 1/8 = 7/24
Amount of work A + B + C can do = 1/3
Amount of work C can do in 1 day = 1/3 - 7/24 = 1/24
work A can do in 1 day: work B can do in 1 day: work C can do in 1 day
= 1/6 : 1/8 : 1/24 = 4 : 3 : 1
Amount to be paid to C = 3200 × (1/8) = 400
E)
Answer: (E) 400
Question: A trader marked the price of a car 20% above the cost price and allowed the purchaser 5% discount on the marked price there by gained Rs.8400. Find the cost price of the car?
(A) 16 m
(B) 77 m
(C) 44 m
(D) 28 m
(E) 11 m
Rationale: n:
Speed Ratio = 1:7/6 = 6:7
Time Ratio = 7:6
1 -------- 7
4 --------- ? è 28 m
Answer:D
Answer: (D) 28 m
Question: A man goes from A to B at a speed of 60 kmph and comes back to A at a speed of 40 kmph. Find his average speed for the entire journey?
(A) 49 kmph
(B) 58 kmph
(C) 44 kmph
(D) 47 kmph
(E) 48 kmph
Rationale: Distance from A and B be 'd'
Average Speed = total distance/total time
Average Speed = (2d)/[(d/60) + (d/40]
= (2d)/[5d/120) => 48 kmph.
Answer:E
Answer: (E) 48 kmph
Question: Find the simple interest on Rs. 72,000 at 16 2/3% per year for 9 months.
(A) 7500
(B) 6500
(C) 9000
(D) 9500
(E) None of them
Rationale: P = Rs.72000,R = 50/3% p.a and T = 9/12 years = 3/4years.
Simple Interest = (P*R*T)/100 = Rs.(72,000*(50/3)*(3/4)*(1/100))= Rs.9000
Answer is C.
Answer: (C) 9000
Question: Tim went to a shop and bought things worth Rs. 25, out of which 30 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items?
(A) 17.13
(B) 18
(C) 19.7
(D) 21.3
(E) 21.5
Rationale: Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 30 Paise is given as tax
=> Total tax incurred = 30 Paise = Rs.30/100
Let the cost of the tax free items = x
Given that tax rate = 6%
∴ (25−30/100−x)6/100 = 30/100
⇒ 6(25 −0.3 −x) = 30
⇒ (25 − 0.3 − x) = 5
⇒ x = 25 − 0.3 − 5 = 19.7
C)
Answer: (C) 19.7
Question: The width of a rectangular hall is ½ of its length. If the area of the hall is 578 sq.m, what is the difference between its length and breadth?
(A) 8m
(B) 10m
(C) 12m
(D) 15m
(E) 17m
Rationale: Let the length of the hall be x m
Breadth of the hall = 1x/2 m
Area of the hall = Length * Breadth
578 = x * 1x/2
x² = 1156
x =34
Difference between the length and breadth of the hall = x - 1x/2 = x/2
=34/2 = 17m
ANSWER:E
Answer: (E) 17m
Question: Country C imposes a two-tiered tax on imported cars: the first tier imposes a tax of 12% of the car's price up to a certain price level. If the car's price is higher than the first tier's level, the tax on the portion of the price that exceeds this value is 8%. If Ron imported a $14,000 imported car and ended up paying $1640 in taxes, what is the first tier's price level?
(A) $1600
(B) $6000
(C) $6050
(D) $7050
(E) $13000
Rationale: Let T be the tier price, P be total price = 14000
Per the given conditions:
0.12T + 0.08(P-T) = 1640 ----> T= 13000. E is the correct answer.
Answer: (E) $13000
Question: A squirrel can climb 5 metres of a pole in one minute but slips 2 metres in the next minute. How much time will the squirrel take to climb 26 metres?
(A) 14 minutes
(B) 12 minutes
(C) 15 minutes
(D) 18 minutes
(E) None of these
Rationale: Explanation:
As the squirrel climbs 5 m in one minute and slips 2 metres in the next minute, it climbs 3 metres in 2 minute
To climb 26 metres, the time required is:
The squirrel will climb (26 – 5) = 21 metres = 7 * 3 metres in 7 * 2 = 14 minutes
Also, the last 5 metres it climbs in another 1 minute
Hence, total time required = 14 + 1 = 15 minutes
ANSWER C
Answer: (C) 15 minutes
Question: A certain league has two divisions. The respective divisions had 11 and 13 teams qualify for the playoffs. Each division held its own double-elimination tournament -- where a team is eliminated from the tournament upon losing two games -- in order to determine its champion. The four division champions then played in a single-elimination tournament -- where a team is eliminated upon losing one game -- in order to determine the overall league champion. Assuming that there were no ties and no forfeits, what is the maximum number of games that could have been played in order to determine the overall league champion?
(A)  41
(B)  42
(C)  45
(D)  47
(E)  49
Rationale: Overall, there can be 47 minuses. Tus, it is D.
Answer: (D)  47
Question: On a wedding catering service, An experienced chef can prepare a service for a wedding in 10 hours while an novice chef would finish the preparations in 18 hours.
If the catering service employs the same number of novice and experienced chefs, then how many chefs would it take to prepare a wedding service in 1 hour and 36 minutes?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 8
Rationale: Experienced chefs work = 1 wedding/10 hours
Novice chefs work = 1 wedding/18 hours
Since we don't know the number of experienced or novice chefs but know that there is an equal number each, let the number of chefs for each group equalx
1hr and 36mins = 8/5 an hour
x/10 + x/18 = 1 wedding / (8/5)
x/10 + x/18 = 5/8
x=4
So there are 4 novice chefs and 4 experienced chefs. In total there are 8. The answer is E.
Answer: (E) 8
Question: A rectangular swimming pool is 20 feet by 22 feet. A deck that has uniform width surrounds the pool. The total area of the pool and deck is 728 square feet. What is the width of the deck?
(A) 2
(B) 4
(C) 3
(D) 5
(E) 6
Rationale: Let the width =W
Total Area of the pool and deck= (2W+20)(2W+22)
We can Test the answer choices along with unit digit method
A) 2 feet ...........24*26 has unit digit 8..........Eliminate
B) 2.5 feet.........25*33 has unit digit 5..........Eliminate
C) 3 feet............26*28 has unit digit 4...........Hold
D) 4 feet............28*30 has unit digit 0...........Eliminate
E) 5 feet............30*32 has unit digit 0...........Eliminate
Answer: C w=3
Answer: (C) 3
Question: The value of a machine depreciates at 21% per annum. If its present value is $1,50,000, at what price should it be sold after two years such that a profit of $24,000 is made?
(A) $257615
(B) $437615
(C) $127615
(D) $117615
(E) $157615
Rationale: The value of the machine after two years = 0.79 * 0.79 * 1,50,000 = $96,000
SP such that a profit of $24,000 is made = 93,615 + 24,000 = $1,17,615
D
Answer: (D) $117615
Question: Find the principle on a certain sum of money at 5% per annum for 2 2/5 years if the amount being Rs.1568?
(A) 1000
(B) 2777
(C) 2889
(D) 1400
(E) 2771
Rationale: 1568 = P [1 + (5*12/5)/100]
P= 1400.Answer:D
Answer: (D) 1400
Question: For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum y of all the even integers between 99 and 301?
(A) 10,100
(B) 20,200
(C) 22,650
(D) 40,200
(E) 45,150
Rationale: I would solve it in a different way.
First of all, total number of even integers between 99 and 301 are, (301-99)/2 = 202/2=101
Average = (301+99)/2 = 400/2 = 200
Sum y= Average*total count = 200*101 = 20,200
Answer is B
Answer: (B) 20,200
Question: John went to the Hospital at the speed of 60 km per hour while returning for his home he covered the half of the distance at the speed of 10 per hour, but suddenly he realized that he was getting late so he increased the speed and reached the home by covering rest 1/2 of the distance at the speed of 30km per hour. The average speed of the John in the whole length of journey is?
(A) 20 km/hr
(B) 22 km/hr
(C) 24 km/hr
(D) 26 km/hr
(E) 30 km/hr
Rationale: Let distance between his home and hospital =
d
d km
Total distance travelled
=
d
+
d
=
2
d
=d+d=2d km
Total time taken
=
d
60
+
(
d
2
)
10
+
(
d
2
)
30
=d60+(d2)10+(d2)30
=
d
60
+
d
20
+
d
60
=
5
d
60
=
d
12
=d60+d20+d60=5d60=d12 hr
Average speed in the whole journey
=
2
d
(
d
12
)
=
2
d
×
12
d
=
24
=2d(d12)=2d×12d=24 km/hr
C
Answer: (C) 24 km/hr
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?
(A) 22887
(B) 2778
(C) 2797
(D) 8112
(E) 1712
Rationale: Explanation:
A = 7500(26/25)2 = 8112
Answer:D
Answer: (D) 8112
Question: Martha has the unique talent of being able to guess other people’s height and weight. For every four people that Martha meets, she consistently guesses the people’s correct height three times, and for every six people that she meets, she consistently guesses the people’s correct weight four times. If Martha meets three people and her success rate remains constant, what is the probability that Martha correctly guesses a person’s weight and height at least once?
(A) 8/27
(B) 7/8
(C) 49/81
(D) 98/125
(E) 125/144
Rationale: Probability that she guesses the height correctly P(h)=3/4
Probability that she guesses the weight correctlyP(w)=4/6
Probability that she guesses both weight and height correctly(P(h)*P(w))=3/4 * 4/6= 12/24
Now the Q asks about the probability of this happening atleast once.
We calculate it by finding the probability of not being able to guess in any of the three occasions.
Probability of not being able to guess any no. of times =1-12/24=12/24=1/2
For all three occasions P(A)=1/2 * 1/2 * 1/2=1/8
Probability of the event happening atleast once=1- P(A)=1-1/8=7/8
Ans should be B
Answer: (B) 7/8
Question: Express a speed of 46 kmph in meters per second?
(A) 10.78 mps
(B) 12.78 mps
(C) 97.78 mps
(D) 17.78 mps
(E) 18.78 mps
Rationale: 46 * 5/18
= 12.78 mps
Answer: B
Answer: (B) 12.78 mps
Question: From a pack of 52 cards, 1 card is drawn at random. Find the probability of a face card drawn.
(A) 4/13
(B) 1/52
(C) 1/4
(D) 1/3
(E) None of these
Rationale: Explanation:
Total number of cases = 52
Total face cards = 16 [favourable cases]
So probability = 16/52 = 4/13
Option A
Answer: (A) 4/13
Question: David bought a 1-year, $5,000 certificate of deposit that paid interest at an annual rate of 10 percent compounded semiannually. What was the total amount of interest paid on this certificate at maturity?
(A) $310
(B) $425
(C) $450
(D) $300
(E) $312.50
Rationale: 10 percent compounded semiannually --> 5% in 6 moths.
For the first 6 moths interest was 5% of $5,000, so $250;
For the next 6 moths interest was 5% of $5,250, so $262.50
Total interest for 1 year was $250+$262.50=$312.50
Answer : E
Answer: (E) $312.50
Question: If f(f(n)) + f(n) = 2n+3, f(0) = 1 then f(2014) = ?
(A) 2015
(B) 2088
(C) 270
(D) 1881
(E) 1781
Rationale: f (f(0)) + f(0) = 2(0) + 3 ⇒⇒ f(1) = 3-1 = 2, f(1) = 2
f(f(1)) + f(1) = 2(1) + 3 ⇒⇒ f(2) = 5-2 = 3, f(2) = 3
f(f(2)) + f(2) = 2(2) + 3 ⇒⇒ f(3) = 7-3 = 4, f(3) = 4
..............
f(2014) = 2015
Ans: A
Answer: (A) 2015
Question: With # andeach representing different digits in the problem below, the difference between #and ## is 712. What is the value of?
#
-##
____
712
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: 100x
-(10x +x)
-----------
89 x= 712
x = 8
B
Answer: (B) 8
Question: A man walking at a rate of 10km/hr crosses a bridge in 15 minutes. The length of the bridge is?
(A) 1521
(B) 1492
(C) 1667
(D) 2500
(E) 1112
Rationale: Speed = 10*5/18 = 50/18 m/sec
Distance covered in 15 minutes = 50/18 *15 *60 = 2500 m
Answer is D
Answer: (D) 2500
Question: A 300 meter long train crosses a platform in 48 seconds while it crosses a signal pole in 18 seconds. What is the length of the platform?
(A) 500
(B) 289
(C) 350
(D) 882
(E) 281
Rationale: Speed = [300 / 18] m/sec = 50/3 m/sec.
Let the length of the platform be x meters.
Then, x + 300 / 48 = 50/3
3(x + 300) = 2400 è x = 500m.
Answer: A
Answer: (A) 500
Question: A doctor prescribed 18 cubic centimeters of a certain drug to a patient whose body weight was 135 pounds. If the typical dosage is 2 cubic centimeters per 15 pounds of the body weight, by what percent was the prescribed dosage greater than the typical dosage?
(A) 8%
(B) 9%
(C) 11%
(D) 12.5%
(E) 14.8%
Rationale: Typical dosage is Dose : weight :: 2: 15.
Now if weight is 135 (Multiplying factor is 9: (135/15)) then typical dosage would be 2 *9 = 18cc.
Dosage = 18 cc. Dosage is greater by 2 cc.
% dosage is greater: (2 / 18)*100 = 11.11 %
C is the answer.
Answer: (C) 11%
Question: If x is an integer such that 3 < x < 10, 5 < x < 18, 9 > x > –2, 8 > x > 0, and x + 1 < 9, then x is
(A) 3
(B) 5
(C) 7
(D) 9
(E) 11
Rationale: 3 < x < 10,
6 < x < 18,
-2 < x <9
0 < x < 8
x<8
From above: 6< x < 8 --> x = 7.
Answer: C.
Answer: (C) 7
Question: In an election between two candidates, the winner has a margin of 20% of the votes polled. If 1000 people change their mind and vote for the loser, the loser would have won by a margin of 20% of the votes polled. Find the total number of votes polled in the election?
(A) 10000
(B) 5000
(C) 15000
(D) 20000
(E) 6000
Rationale: Winner - Looser
60% - 40%
If 1000 people change their mind and vote for the loser:
Winner - Looser
40% - 60%
Thus 1,000 people compose 20% of all voters, which means that the total number of votes is 5,000.
Answer: B
Answer: (B) 5000
Question: Find the area of trapezium whose parallel sides are 20 cm and 18 cm long, and the distance between them is 15 cm.
(A) 287 cm2
(B) 785 cm2
(C) 285 cm2
(D) 785 cm2
(E) 295 cm2
Rationale: Explanation:
Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them) = 1/2 (20 + 18) * (15) = 285 cm2
Answer: Option C
Answer: (C) 285 cm2
Question: A summer camp has 150 children coming for the summer. Out of them, 60% have applied for the water sports programme and 80% have applied for rock climbing. How many campers have applied for both?
(A) 50
(B) 60
(C) 70
(D) 80
(E) 90
Rationale: The total number of campers coming for the summer is n = 150.
The number of campers who have applied for the water sports activities is 60% of it, thus
n (A)=60/100×150=6×15=90
The number of campers who have applied for rock climbing is 80%, thus
n (B)=80/100×150=8×15=120.
In order to calculate the number of campers who have applied for both programs we can use the following equation:
n (AnB)=n (A)+n (B) -n =90+120-150=50=60.
So, 60 campers have applied for both water sports and rock climbing.
ANSWER: B
Answer: (B) 60