RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Mary decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month. If Mary's savings by the end of the year from these monthly savings were TWO times the amount she spent per month, what should be the fraction of her salary that she spent each month?
A.6/7
B.1
C.2
D.3
Answer: A.6/7
Explanation: Saving = S, Expenditure = E, Income = I
At the end of 12months; 12S=2E=2(I-S)
=> 14S = 2I => Savings = 1/7 I
Hence Expenditure = 1-(1/7)I = 6/7 I
Answer (A)
Question: A certain high school has 500 students. Of these students, 50 are taking music, 20 are taking art, and 10 are taking both music and art. How many students are taking neither music nor art?
A.430
B.440
C.450
D.460
Answer: B.440
Explanation: We're given a series of facts to work with:
1) A certain high school has 500 students.
2) Of these students:
X are taking music,
Y are taking art, and
Z are taking BOTH music and art.
We're asked how many students are taking NEITHER music nor art?
Let's TEST
X = 50
Y = 20
Z = 10
So, we have 50 students taking music, 20 taking art and 10 taking BOTH music and art.
40 student taking JUST music
10 student taking JUST art
10 student taking BOTH music and art
Total = 60 students
We're asked for the total number of students who are taking NEITHER Course. That is 500 - 60 = 440.
B
Question: Mary decided to save a certain amount of her monthly salary each month and her salary was unchanged from month to month. If Mary's savings by the end of the year from these monthly savings were three times the amount she spent per month, what should be the fraction of her salary that she spent each month?
A.1/2
B.2/3
C.1/4
D.4/5
Answer: D.4/5
Explanation: Let Mary's monthly savings = S
Mary's monthly pay = P
Mary's monthly expenditure = P-S
Mary's savings by the end of the year from these monthly savings were three times the amount she spent per month
12S = 3*(P-S)
=>4S = P-S
=> P = 5S
Mary's monthly expenditure = P-S = 5S-S = 4S
fraction of her salary that Mary spent each month = 4S / 5S = 4/5
Answer D
Question: Evaluate : 986 x 237 - 986 x 37
A.197600
B.168000
C.278000
D.192700
Answer: D.192700
Explanation: 986 x 237 - 986 x 37 = 986 x (237 - 37) = 986 x 200 = 197200.
Answer is D.
Question: Using all the letters of the word "QUESTION", how many words can be formed, which begin with Q and end with N?
A.713
B.650
C.720
D.700
Answer: C.720
Explanation: There are five letters in the given word.
Consider 8 blanks ....
The first blank and last blank must be filled with Q and N all the remaining three blanks can be filled with the remaining 6 letters in 6! ways.
The number of words = 6! = 720.
Answer:C
Question: Current ages of Rahim and Thomas are in the ratio of 5 : 4 correspondingly. 0.6 decades hence, the ratio of their ages will become 11 : 9 correspondingly, What is Thomasâ€™s current age in years?
A.24 years
B.44 years
C.34 years
D.48 years
Answer: D.48 years
Explanation: If current ages of Rahim and Thomas be 5A years and 4A years correspondingly
Then, 5A + 6 = 11
4A + 6 = 9
9(5A + 6)=11(4A + 6)
A = 12
Thomasâ€™s current age = 4A
= 48 years.
D
Question: If the number is decreased by 5 and divided by 7 the result is 7. What would be the result if 34 is subtracted and divided by 10?
A.4
B.7
C.8
D.2
Answer: D.2
Explanation: Explanation:
Let the number be x. Then,
(x - 5)/7 = 7 => x - 5 = 49
x = 54
.: (x - 34)/10 = (54 - 34)/10 = 2
Answer: Option D
Question: If the sales tax be reduced from 4 (1/3) % to 2 (1/2) %, then what difference does it make to a person who purchases a bag with marked price of Rs. 8000?
A.Rs. 156.66
B.Rs. 150.23
C.Rs. 146.66
D.Rs. 135.06
Answer: C.Rs. 146.66
Explanation: Explanation:
Required difference = (4 (1/3) of Rs. 8000) - (2 (1/2) of Rs. 8000)
= (13/3 – 5/2) % of Rs. 8000
= (11/6) x (1/100) x 8000
= Rs. 146.66
ANSWER C
Question: Of the 14,210 employees of the anvil factory, 2/7 are journeymen. If half of the journeymen were laid off, what percentage of the total remaining employees would be journeymen?
A.14.3%
B.16.67%
C.33%
D.28.6%
Answer: B.16.67%
Explanation: the number of employees is not reqd...
1/2 of 2/7 are shunted out so 1/7 left... there are another 5 equal parts(5/7)..
so total remaining parts=6, in which 1 part is journeyman....
therefore %=1/6*100=16.67%
ANSWER:B
Question: A and B can do a piece of work in 10 days. With the help of C they finish the work in 5 days. C alone can do that piece of work in?
A.15.5 days
B.19.5 days
C.10 days
D.16.5 days
Answer: C.10 days
Explanation: C = 1/5 – 1/10 = 5/50 => 10 days
ANSWER:C
Question: How many positive integers less than 5,000 are evenly divisible by neither 15 nor 23?
A.4,514
B.4,475
C.4,521
D.4,428
Answer: C.4,521
Explanation: integers less than 5000 divisible by 15 5000/15 =333.something , so 333
integers less than 5000 divisible by 23 5000/23 = 238.## , so 238
we have double counted some, so take LCM of 15 and 23 =105 and divide by 5000, we get 47. so all numbers divisible by 15 and 23 = 333 +238 -47 =524
now subtract that from 4999. 4999- 524 = 4521 answer C.
Question: At a local beach, the ratio of little dogs to average dogs to enormous dogs is 1:4:8. Late in the afternoon, the ratio of little dogs to average dogs doubles and the ratio of little dogs to enormous dogs increases. If the new percentage of little dogs and the new percentage of average dogs are both integers and there are fewer than 30 total dogs at the beach, which of the following represents a possible new percentage of enormous dogs?
A.20% or 70%
B.40%
C.50%
D.55%
Answer: A.20% or 70%
Explanation: Little Dogs(L), Average Dogs(A) and Enormous Dogs (E)
The initial ratio for L:A:E :: 1:4:8
Initial Total dogs = 13X ( x assumed; 1+4+8= 13), Since the total dogs are less than 30 therefore initial total value has to be 13
L = 1, A = 4 E = 8
L:A= 1:4
This ratio doubles
Hence New Dog count is
L= 2 , A = 4 E= X: Also 2+4+x<30
We need to Find X*100/(2+4+X)
Now it says that new percentage of little dogs and Average dogs is an integer
%L = 2*100/(6+x) %A = 4*100/(6+x); Only Value for X is 4 or 14; 6+x<30 and % integer
Therefore, Enormus Dogs % is = 4*100/(20) = 20% or 14*100/20 % =70%
20% or 70%
A
Question: What number should be added to or subtracted from each term of the ratio 17 : 24 so that it becomes equal to 1 : 2.
A.35
B.66
C.77
D.88
Answer: A.35
Explanation: Ans. 35
Question: Two hoses are pouring water into an empty pool. Hose 1 alone would fill up the pool in 6 hours. Hose 2 alone would fill up the pool in 7 hours. How long would it take for both hoses to fill up two-thirds of the pool?
A.5/12 hours
B.5/8 hours
C.28/13 hours
D.12/7 hours
Answer: C.28/13 hours
Explanation: Hose 1 would fill the pool alone in 6 hours
i.e. 1 Hour work of Hose 1 = 1/6
Hose 2 would fill the pool alone in 7 hours
i.e. 1 Hour work of Hose 2 = 1/7
i.e. 1 Hour work of Hose1 and Hose2 together = (1/6)+(1/7) = (13/42)
i.e. (13/42) work can be finished by Hose1 and Hose2 together in 1 hour
i.e. (2/3) work can be finished by Hose1 and Hose2 together in 1*(42/13)*(2/3) = 28/13 hour
Answer: Option C
Question: A man can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit his target?
A.175/256
B.256/175
C.451/784
D.451/864
Answer: A.175/256
Explanation: The man will hit the target if he hits it once or twice or thrice or all four times in the four shots that he takes.
So, the only possibility when the man will not hit the target is when he fails to hit the target in even one of the four shots that he takes.
The event of not hitting the target even once is the complement of the event of hitting the target at least once.
The probability that he will not hit the target in any given shot = 1 – 1/4 = ¾
Therefore, the probability that he will not hit the target in any of the four shots =3/4*3/4*3/4*3/4=81/256
The probability that he will hit the target at least in one of the four shots=1-81/256
=175/256
Ans: A
Question: The speed of a train is 90 kmph. What is the distance covered by it in 10 minutes?
A.15
B.66
C.77
D.88
Answer: A.15
Explanation: 90 * 10/60 = 15 kmph
Answer:A
Question: 34.	The side surface of a cylinder is rolled with a rectangular plate. If the perimeter of the circular base Is 9 feet, and the diagonal of the rectangular plate was 15 ft. What is height of the of the cylinder?
A.12
B.15
C.10
D.8
Answer: A.12
Explanation: Think of a Pringles can. If you took off the bottom and top and cut a slit down the length, it would flatten to a rectangle. The dimensions of the rectangle are the height of the can and the circumference of the circle. Since you know both, one side and thehypothenuse use pythagoreans theorem or properties of 3-4-5 triangles to solve for the other side, 12. Correct answer A
Question: The cost price of an article is 56% of the marked price. Calculate the gain percent after allowing a discount of 13%.
A.23.4%
B.44.5%
C.55.3%
D.57.4%
Answer: C.55.3%
Explanation: Sol.
Let marked price = Rs. 100. Then, C.P. = Rs. 56. S.P = Rs. 87.
âˆ´ Gain % = [31/56 * 100]% = 55.3%.
Answer C
Question: How many three letter combinations can be formed using the letters of the word STARE?
A.6
B.25
C.45
D.60
Answer: D.60
Explanation: The number of letters in the given word is five.
The number of three letter combinations that can be formed using these five letters is
= 5 * 4 * 3 = 60.
Answer: D
Question: A, B and C have Rs.400 between them, A and C together have Rs.300 and B and C Rs.150. How much does C have?
A.40
B.50
C.60
D.70
Answer: B.50
Explanation: A+B+C = 400
A+C = 300
B+C = 150
--------------
A+B+2C = 450
A+B+C = 400
----------------
C = 50
Answer : B
Question: Sahil purchased a machine at Rs 10000, then got it repaired at Rs 5000, then gave its transportation charges Rs 1000. Then he sold it with 50% of profit. At what price he actually sold it.
A.Rs. 22000
B.Rs. 24000
C.Rs. 26000
D.Rs. 28000
Answer: B.Rs. 24000
Explanation: Explanation:
Question seems a bit tricky, but it is very simple.
Just calculate all Cost price, then get 150% of CP.
C.P. = 10000 + 5000 + 1000 = 16000
150% of 16000 = 150/100 * 16000 = 24000
Option B
Question: If b does not equal zero, and ab = b/4, what is the value of a?
A.1/8
B.1/4
C.1/3
D.1/2
Answer: B.1/4
Explanation: Explanation:
To solve for a, divide both sides of the equation by b: ab = b/4
(ab)/b = (b/4)/b
a = (b/4)*1/b
a = 1/4
Answer: (B).
Question: The apartment on King-Williams street is an asset that its value is tramping about. From the year 1973 to 1983 it's value decreased by 16% and from 1983 to 1993 it's value increased by 16%. What is the value of the asset in 1993 if in 1973 it was worth $30,000?
A.$38,796.
B.$40,000.
C.$38,976.
D.$29,232.
Answer: D.$29,232.
Explanation: 30,000 *1.16*.84=29,232
Answer D
Question: Ron walks to a viewpoint and returns to the starting point by his car and thus takes a total time of 6 hours 45 minutes. He would have gained 2 hours by driving both ways. How long Y would it have taken for him to walk both ways.
A.8 h 45 min
B.7 h 45 min
C.6 h 45 min
D.5 h 30 min
Answer: A.8 h 45 min
Explanation: 1.Walking to to a viewpoint+Driving back=6 hours 45 minutes
2.Driving to a viewpoint+Driving back=6 hours 45 minutes - 2 hours=4 hours 45 minutes, thereforeone way driving=4 hours 45 minutes/2 =2 hours 22.5 minutes.
3. From 1.one way driving=6 hours 45 minutes-2 hours 22.5 minutes=4 hours 22.5 minutes.
4.Walking to to a viewpoint+Walking back Y=4 hours 22.5 minutes+4 hours 22.5 minutes=8 hours 45 minutes.
Answer: A.
Question: There are 35 students in a hostel. If the no. of students increases by 2, the expenses of the mess increase by Rs.42/day while the average expenditure per head diminishes by Rs1. Find the original expenditure of the mess?
A.s. 234.50
B.s. 239.50
C.s. 242.50
D.s. 248.50
Answer: A.s. 234.50
Explanation: Suppose the average join the mess , total expenditure = 35x + 42
Now, the average expenditure = (35x + 42)/ (35 + 2) = x – 1
or, 35x + 42 = 37x – 37
or, x = 39.50
Thus the original expenditure of the mess = 35 x 39.5 =1382.50
Therefore x-1 = 38.5
hence 42 x 38.5 = 1617
1617-1382.50 = Rs. 234.50
A
Question: An optometrist charges $150 per pair for soft contact lenses and $85 per pair for hard contact lenses. Last week she sold 5 more pairs of soft lenses than hard lenses. If her total sales for pairs of contact lenses last week were $1,220, what was the total number of pairs of contact lenses that she sold?
A. 9
B. 13
C. 15
D. 17
Answer: A. 9
Explanation: (x+5)*150 +x*85=1220
=>x=2
total lens=2+(2+5)= 9
Answer A
Question: The average age of three boys is 18 years and their ages are in the proportion 3 : 3 : 6. The age of the youngest boy is:
A.21 years
B.18 years
C.15.5 years
D.13.5 years
Answer: D.13.5 years
Explanation: Total age of 3 boys = (18 Ã— 3) years = 54 years. Ratio of their ages = 3 : 3 : 6.
Age of the youngest = (54 Ã— 3â„12) years = 13.5 years.
Answer D
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively and they cross each other in 20 seconds. The ratio of their speeds is?
A.3/7
B.3/2
C.3/5
D.3/1
Answer: A.3/7
Explanation: Let the speeds of the two trains be x m/sec and y m/sec respectively. Then, length of the first train = 27 x meters, and length of the second train = 17 y meters. (27 x + 17 y) / (x + y) = 20
==> 27 x + 17 y = 20 x + 20 y ==> 7 x = 3 y ==> x/y
= 3/7.
Answer: A
Question: At what price must an article costing Rs.47.50 be marked in order that after deducting 10% from the list price. It may be sold at a profit of 25% on the cost price?
A.60.5
B.65.9
C.67.5
D.62.5
Answer: B.65.9
Explanation: CP = 47.50
SP = 47.50*(125/100) = 59.375
MP*(90/100) = 59.375
MP = 65.9
Answer:B
Question: Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many straight lines can be formed by joining them ?
A.124
B.144
C.134
D.142
Answer: B.144
Explanation: The number of straight lines formed joining the 18 points, taking 2 at a time = 18C2=153. Number of straight lines formed by joining the 5 points, taking 2 at a time =5C2=10. But 5 collinear point, when joined pairwise give only one line. Required number of straight lines =153-10+1 =144. Answer :B
Question: If Rs. 782 be divided into three parts, proportional to 1/2:1/3:3/4, then the second part is?
A.A)426
B.B)526
C.C)207
D.D)165
Answer: D.D)165
Explanation: Given ratio
= 1/2:2/3:3/4 = 6:4:9
1st part = 782 * 4/19
= Rs. 165
Answer:D
Question: Two interconnected, circular gears travel at the same circumferential rate. If Gear A has a diameter of 60 centimeters and Gear B has a diameter of 50 centimeters, what is the ratio of the number of revolutions that Gear A makes per minute to the number of revolutions that Gear B makes per minute?
A.6:5
B.9:25
C.5:6
D.25:9
Answer: C.5:6
Explanation: Same circumferential rate means that a point on both the gears would take same time to come back to the same position again.
Hence in other words, time taken by the point to cover the circumference of gear A = time take by point to cover the circumference of gear B
Time A = 2*pi*25/Speed A
Time B = 2*pi*30/Speed B
Since the times are same,
50pi/Speed A = 60pi/Speed B
SpeedA/Speed B = 50pi/60pi = 5/6
Correct Option: C
Question: An even and an odd integer are multiplied together. Which of the following could not be the square of their product?
A.36
B.100
C.144
D.225
Answer: D.225
Explanation: 2*3=6 and 6^2=36
5*2=10 and 10^2=100
3*4=12 and 12^2=144
5*4=20 and 20^2=400
Answer D
Question: A and B together have $ 1210. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have?
A.$400
B.$489
C.$484
D.$365
Answer: C.$484
Explanation: 4/15A = 2/5B -> A= (2/5 * 15/4) B -> A = 3/2B -> A/B = 3/2
A: B = 3:2
B'S SHARE = RS (1210 * 2/5) = $484
ANSWER C $464
Question: An error 2% in excess is made while measuring the side of a square. The percentage of error in the calculated area of the square is?
A.4.04%
B.5%
C.7%
D.9%
Answer: A.4.04%
Explanation: 100 cm is read as 102 cm.
A1 = (100 x 100) cm2 and A2 (102 x 102) cm2.
(A2 - A1) = [(102)2 - (100)2]
= (102 + 100) x (102 - 100)
= 404 cm2.
Percentage error = 404	x 100	%	= 4.04%
100 x 100
A)
Question: The average salary of a person for the months of January, February, March and April is Rs.8000 and that for the months February, March, April and May is Rs.8500. If his salary for the month of May is Rs.6500, find his salary for the month of January?
A.277
B.2667
C.4500
D.2688
Answer: C.4500
Explanation: Sum of the salaries of the person for the months of January, February, March and April = 4 * 8000 = 32000 ----(1)
Sum of the salaries of the person for the months of February, March, April and May = 4 * 8500 = 34000 ----(2)
(2)-(1) i.e. May - Jan = 2000
Salary of May is Rs.6500
Salary of January = Rs.4500
Answer: C
Question: A’s speed is 32/27 times that of B. If A and B run a race, what part of the length of the race should A give B as a head start, so that the race ends in a dead heat?
A.5/32
B.5/27
C.1/27
D.1/32
Answer: A.5/32
Explanation: We have the ratio of A’s speed and B’s speed. This means, we know how much distance A covers compared with B in the same time.
This is what the beginning of the race will look like:
(Start) A_________B______________________________
If A covers 32 meters, B covers 27 meters in that time. So if the race is 32 meters long, when A reaches the finish line, B would be 5 meters behind him. If we want the race to end in a dead heat, we want B to be at the finish line too at the same time. This means B should get a head start of 5 meters so that he doesn’t need to cover that. In that case, the time required by A (to cover 32 meters) would be the same as the time required by B (to cover 27 meters) to reach the finish line.
So B should get a head start of 5/32 th of the race.
Answer (A)
Question: There are 4 numbers W, X, Y, and Z. If W:X = 4/5, X:Y = 5/6, Y:Z = 6/7, then W:Z will be?
A.4 : 5
B.2 : 3
C.4 : 7
D.1 : 2
Answer: C.4 : 7
Explanation: Solution
W : X = 4 : 5, X : Y = 5 : 6, Y : Z = 6 : 7
âˆ´Wâˆ¶Xâˆ¶Yâˆ¶Z= 4 : 5 : 6 : 7.
Thus, W : Z = 4 : 7
Correct Option C
Question: The difference between compound and simple interest on a particular sum of money for 3 years at 6 and 2/3% p.a is Rs.184. What is the sum?
A.13000
B.13500
C.14000
D.14500
Answer: B.13500
Explanation: P = (184*10^6) / (6 2/3 * 6 2/3*(300*6 2/3))
==> 13500
ANSWER B
Question: Four dice are thrown simultaneously. Find the probability that all of them show the same face.
A.1/45
B.1/35
C.1/216
D.4/216
Answer: C.1/216
Explanation: The total number - four dice simultaneously is:
=6×6×6×6=64=6×6×6×6=64
n(S)=64n(S)=64
Let X be the event that all dice
X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}X={(1,1,1,1,),(2,2,2,2),(3,3,3,3),(4,4,4,4),(5,5,5,5),(6,6,6,6)}
n(X)=6n(X)=6
Hence required probability, = 6/6^4
==>1/216
ANSWER C
Question: A shopkeeper buys mangoes at the rate of 4 a rupee and sells them at 2 a rupee. Find his net profit or loss percent?
A.100 %
B.200 %
C.250%
D.300%
Answer: A.100 %
Explanation: The total number of mangoes bought by the shopkeeper be 12.
If he buys 4 a rupee, his CP = 3
He selling at 2 a rupee, his SP = 4
Profit = SP - CP = 4 - 2 = 2
Profit Percent = 2/2 * 100 = 100 %
Answer:A
Question: A carpenter makes 2 bunk beds every day. A military school needs to organize a place to sleep for 143 soldiers. If there are 5 carpenters working on the job, how many whole days in advance should they receive the order and start working in order to finish the right number of beds assuming that each bunk- bed is used by two soldiers?
A.3.
B.4.
C.5.
D.6.
Answer: B.4.
Explanation: I believe it is C because if 1C makes 3 beds in 1 day then:
1C's rate = 3/1
So 5c's = 3/1 * 5 = 15/1 = 15 beds in a day.
Since we have 173 soldiers who need beds and bunk beds come in pairs, 72 is the least amount of beds needed.
Time = Amount / Rate
Time = 72 / (15/1) = 72/15, simplifying we get 72/15 = 24/5 = 3.8
So, in order for the carpenters to be able to finish they need 4 whole days. At first I made the mistake of thinking how many whole days it took them to finish (as in ignore the partial day) but the prompt clarifiesdays in advance, meaning how many days would they need to finish so even if they finish early, theyusedthat day.
B
Question: If (n + 2)! = 2550 (n!); find ’n’
A.38
B.35
C.49
D.43
Answer: C.49
Explanation: (n + 2)! = 2550(n!)
(n + 2)(n + 1)(n!) = 2550(n!)
(n + 2)(n + 1) = 2550
2n + 3n + 2 - 2550 = 0
2n + 3n - 2548 = 0
2n + 52n - 49n - 2548 = 0
n(n - 49)(n + 52) = 0
n = 49 or n = - 52
ANSWER:C
Question: What is the place value of 5 in the numeral 4529
A.200
B.300
C.500
D.600
Answer: C.500
Explanation: 5*100 = 500
ANSWER C
Question: In a certain country, 60 percent of the population likes basketball, and 34 percent of the population likes both basketball and golf. What percentage of the people who like basketball also like golf?
A.20%
B.33%
C.40%
D.57%
Answer: D.57%
Explanation: Correct Answer: (D).
Since this is a percent problem without concrete numbers, we can assign our own. If we assume that there are 100 people in the country, then 60 people like basketball, and 34 people like basketball and golf. We’re looking for people who like both divided by people who like basketball, so 34/60 = 57%, or choice D.
Question: An auction house charges a commission of 16% on the first $50,000 of the sale price of an item, plus 10% on the amount of of the sale price in excess of $50,000. What was the price of a painting for which the house charged a total commission of $24,000?
A.$115,000
B.$160,000
C.$210,000
D.$240,000
Answer: C.$210,000
Explanation: Say the price of the house was $x, then 0.16*50,000+0.1*(x-50,000)=24,000 --> x=$210,000 (16% of $50,000 plus 10% of the amount in excess of $50,000, which is x-50,000, should equal to total commission of $24,000).
Answer: C.
Question: The true discount on a bill due 9 months hence at 16% per annum is Rs. 240. The amount of the bill is
A.2200
B.2240
C.1600
D.1354
Answer: B.2240
Explanation: Explanation:
Let P.W. be Rs.x.
Then, S.I. on Rs. x at 16% for 9 months = Rs. 240.
x Ã— 16 Ã— (9/12) Ã— (1/100) = 240 or x = 2000.
P.W. = Rs. 2000.
Sum due = P.W. + T.D. = Rs.(2000
240) = Rs. 2240.
Answer: B
Question: Five years ago the average of the ages of A and B was 40 years and now the average of the ages of B and C is 48 years. What will be the age of the B ten years hence?
A.39
B.23
C.28
D.96
Answer: D.96
Explanation: Let the present ages of A, B and C be a, b and c respectively.
Given, [(a - 5) + (b - 5)] / 2 = 40 => a + b = 90 --- (1)
(b + c)/2 = 48 => b + c = 96 --- (2)
Answer: D
Question: If 3y + x > 2 and x + 2y <= 3 , What can be said about the value of y?
A.y = 1
B.y >1
C.y > -2
D.y > -1
Answer: D.y > -1
Explanation: Explanation :
3y + x > 2 -----(1)
x + 2y < = 3
=> x + 2y + y < = 3 + y
=> x + 3y < = 3 + y -----(2)
From (1)&(2)
2 < 3y + x < 3 + y
=> 2 < 3 + y
=> -1 < y
=> y > -1
Hence (D) is the correct answer.
Answer : D
Question: If the sum of 7 consecutive negative integers is -70, what is the value of the 2nd number in the sequence?
A.8
B.-9
C.-8
D.9
Answer: C.-8
Explanation: if sum is -70, the average = median = -70/7 = -10 = which is the middle in the sequence.
7/2 = 3.5. When rounded up = 4. So -10 is the 4th in the sequence.
4th - 2nd = 2 numbers away.
-10 + 2= -8
Answer: C
Question: Roberto has three children: two girls and a boy. All were born on the same date in different years. The sum of the ages of the two girls today is smaller than the age of the boy today, but a year from now the sum of the ages of the girls will equal the age of the boy. Seven years from today, the difference between the age of the boy and the combined ages of the girls will be
A.1
B.2
C.-3
D.–6
Answer: D.–6
Explanation: Approach I (Plugin's)
Girl I ............... Girl II ................ Boy
1 ....................... 1 ........................ 3 (Assume the current ages)
1 + 1 < 3 .......... (Satisfies the given condition)
1 Year later there ages are
2 ....................... 2 ......................... 4
2 + 2 = 4 ............ (Satisfies the given condition)
After 7 years there ages are
8 ....................... 8 ............................ 10
Difference = 10 - (8+8) = 10 - 16 = -6
Answer = D