RikoteMaster/aqua-rat-mcqa huggingface dataset:
Question: Bradley owns b video game cartridges. If Bradley’s total is one-third the total owned by Andrew and five times the total owned by Charlie, how many video game cartridges do the three of them own altogether, in terms of b?
A.(16/3)b
B.(17/4)b
C.(13/4)b
D.(21/5)b
Answer: D.(21/5)b
Explanation: Step 1: Categorize the problem
This problem is testing basic algebra and equations, with an extra layer of complexity by having variables in the answer choices.
Step 2: Think like the test maker
What is the key detail or key details in the problem? The key detail to immediately recognize is that the problem gives you Andrew and Charlie’s totals in relation to Bradley’s total rather than giving you Bradley’s total in relation to the other two; and then the problem asks you to solve the problem in terms of b. This means that you have to relate Andrew and Charlie’s values in relation to Bradley’s total. The test maker is attempting to force you to structure the problem in the opposite way that most people are used to structuring information. By gaining this insight, it makes it easier to solve the problem.
Step 3: Solve the problem
b = Bradley’s total
3b = Andrew’s total
(1/5)b = Charlie’s total
Add each total
b + 3b+ (1/5)b = 4b + (1/5)b = (16/4)b + (1/5)b = (21/5)b
Therefore,choose D.
Question: If the volume of two cubes are in the ratio 27:1, the ratio of their edges is:
A.3:1
B.3:5
C.3:8
D.3:29
Answer: A.3:1
Explanation: Let the edges be a and b of two cubes, then
a3b3=271=>(ab)3=(31)3ab=31=>a:b=3:1
Answer: A
Question: The value of (34.31*0.473*1.567)/(0.0673*23.25*7.57) is close to
A.2
B.1.15
C.2.05
D.2.15
Answer: D.2.15
Explanation: (34.31*0.473*1.567)/(0.0673*23.25*7.57) = 25.4303/11.845
= 2.15
ANSWER:D
Question: Cricket match is conducted in US. The run rate of a cricket game was only 3.2 in first 10 over. What should be the run rate in the remaining 40 overs to reach the target of 252 runs?
A.6
B.6.25
C.7.25
D.5.5
Answer: D.5.5
Explanation: Required run rate = 252 - (3.2 x 10) =	220 = 5.5
40	40
D
Question: Raj is working on a set of Data Sufficiency problems for his December GMAT: a geometry problem, an algebra problem, and a data interpretation problem. He has determined that statement 1 of the geometry problem is insufficient on its own, that both statement 1 and 2 of the algebra problem are insufficient on their own, and that statement 2 of the data interpretation problem is insufficient on its own. If the probabilities are expressed as percents W, approximately how much greater is the probability that all three answers are “C” after Raj figures out that statement 1 of the data interpretation problem is also insufficient on its own?
A.W=2.3%
B.W=2.8%
C.W=3.3%
D.5.6%
Answer: B.W=2.8%
Explanation: Step 1: Figure out what we need to know.We have two probabilities that we need to figure out: the one before Raj figures out that statement 1 of the data interpretation problem is also insufficient, and the one after. The answer is the difference between them, in the form of a percent.
Step 2: The first probability.
If statement 1 of the geometry problem is insufficient, then the only valid answer choices are B, C, and E; the probability that it is C is 1/3.
If both statements of the algebra problem are insufficient on their own, then the only remaining valid answers are C and E; the probability that it is C is 1/2
If statement 2 of the data interpretation problem is insufficient, then the remaining answers are A, C, and E, and the probability that C is correct is 1/3.
The probability of all three occurring is the product of the probability fractions: (1/3)*(1/2)*(1/3) = 1/18.
Step 3: The second probability.
Only the third problem has changed; if Raj now knows that statement 1 is also insufficient, the valid answer choices are only C and E, leaving a 1/2 probability that the answer is C.
The probability of all three occurring is still the product of those fractions, but this time they are (1/3)*(1/2)*(1/2) = 1/12.
Step 4: The answer.Note that here, as will sometimes happen on the GMAT, values that you compute “along the way” appear as wrong answer choices. This problem calls for the difference between our two numbers,W (1/12)-(1/18) = 1/36, which is a 2.77777% chance, rounded to 2.8% —the correct answer is Choice B.
Question: At Company X, senior sales representatives visit the home office once every 15 days, and junior sales representatives visit the home office once every 10 days. The number of visits that a junior sales representative makes in a 2-year period is approximately what percent greater than the number of visits that a senior representative makes in the same period?
A.10%
B.25%
C.33%
D.50%
Answer: D.50%
Explanation: Each 30-day period, senior representatives visit the home office 2 times while junior representatives visit 3 times, thus 50% more.
The answer is D.
Question: A survey of n people in the town of Eros found that 50% of them preferred Brand A. Another survey of 130 people in the town of Angie found that 60% preferred Brand A. In total, 55% of all the people surveyed together preferred Brand A. What is the total number of people surveyed?
A.50
B.100
C.150
D.260
Answer: D.260
Explanation: It is simply a weighted average question. Since the given average of 50% and 60% is 55% (right in the middle), it means the number of people surveyed in Eros (n) is same as the number of people surveyed in Angie.
So n = 130
Total = 130 + 130 = 260
Answer (D)
Question: A train starts full of passengers at the first station it drops 1/3 of the passengers and takes 280more at the second station it drops one half the new total and takes twelve more .on arriving at the third station it is found to have 248 passengers. Find the no of passengers in the beginning?
A.288
B.321
C.651
D.246
Answer: A.288
Explanation: Let no of passengers in the beginning be x
After first station no passengers=(x-x/3)+280=2x/3 +280
After second station no passengers =1/2(2x/3+280)+12
½(2x/3+280)+12=248
2x/3+280=2*236
2x/3=192
x=288
Option A is answer
Question: The ratio of the number of boys and girls in a college is 7:8. If the percentage increase in the number of boys and girls be 20% and 10% respectively. What will be the new ratio?
A.21:24
B.21:24
C.21:22
D.21:45
Answer: C.21:22
Explanation: Originally, let the number of boys and girls in the college be 7x and 8x respectively.
Their increased number is (120% of 7x) and (110% of 8x).
i.e., (120/100 * 7x) and (110/100 * 8x)
i.e., 42x/5 and 44x/5
Required ratio = 42x/5 : 44x/5 = 21:22
Answer: C
Question: A line has a slope of 3/4 and intersects the point W (-12, -39). At which point does this line intersect the x-axis?
A.(40,0)
B.(30,0)
C.(0,40)
D.(40,30)
Answer: A.(40,0)
Explanation: Assume that the equation of the line is y=mx+c, where m and c are the slope and y-intercept.
You are also given that the line crosses the point (-12,-39), this means that this point will also lie on the line above.
Thus you get -39=m*(-12)+c , with m=3/4 as the slope is given to be 3/4.
After substituting the above values, you get c = -30.
Thus the equation of the line is y=0.75*x-30 and the point where it will intersect the x-axis will be with y coordinate = 0.
Put y=0 in the above equation of the line and you will get, x=40.
Thus, the point W of intersection is (40,0).
A is the correct answer.
Question: 5 persons working eight hours daily can complete a wall in 10 days. When they have Worked for 4 days, 5 more persons are brought to work. The wall can now be completed in?
A.one more day
B.two more days
C.three more days
D.four more days
Answer: C.three more days
Explanation: Let D be the number of required days
Using the chain rule,
M1 x T1 = M2 x T2 + M3 x T3
5 x 8 x 10 = (4 x 5 x 8) + (10 x 8 x D)
D = 3.
Hence, the wall will be completed in 3 more days.
ANSWER:C
Question: At a certain committee meeting only associate professors and assistant professors are present. Each associate professor has brought 2 pencils and 1 chart to the meeting, while each assistant professor has brought 1 pencil and 2 charts. If a total of 11 pencils and 16 charts have been brought to the meeting, how many people are present?
A.6
B.7
C.8
D.9
Answer: D.9
Explanation: Say there are 'A' associate professors. So we have 2A pencils and A charts.
Say there are 'B' assistant professors. So we have B pencils and 2B charts.
Total pencils are 10 so 2A + B = 11
Total charts are 11 so A + 2B = 16
Add both: 3A + 3B = 27 so A + B = 9
Total number of people = 9
D
Question: A man can row with a speed of 20 kmph in still water. If the stream flows at 12 kmph, then the speed in downstream is?
A.27
B.23
C.20
D.32
Answer: D.32
Explanation: M = 20
S = 12
DS = 20 + 12 = 32
Answer: D
Question: The length of the bridge, which a train 160 meters long and travelling at 45 km/hr can cross in 30 seconds, is?
A.328
B.279
C.215
D.288
Answer: C.215
Explanation: Speed = (45 * 5/18) m/sec = (25/2) m/sec. Time = 30 sec. Let the length of bridge be x meters. Then, (160 + X)/30 = 25/2 ==> 2(160 + X) = 750 ==> X = 215 m.Answer: C
Question: Two dice are thrown together .What is the probability that the sum of the number on the two faces is divided by 4 or 6
A.7/18
B.2/7
C.7/9
D.4/7
Answer: A.7/18
Explanation: Clearly n(S)=6*6=36
Let E be the event that the sum of the numbers on the two faces is divided by 4 or 6.Then
E={(1,3),(1,5),(2,2),(2,4),(2,6),(3,1),(3,3),(3,5),(4,2),(4,4),(5,1),(5,3),(6,2),
(6,6)}
n(E)=14.
Hence p(e)=n(e)/n(s)=14/36=7/18
Option A
Question: There are two numbers. If 30% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?
A.A)3/7
B.B)5/8
C.C)5/6
D.D)6/7
Answer: C.C)5/6
Explanation: Let the two numbers be x and y.
30/100 * x + y = 5/4y
=> 3/10 x = 1/4 y => x/y = 5/6
C)
Question: 10% people of a village in Sri Lanka died by bombardment, 20% of the remainder left the village on account of fear. If now the population is reduced to 4554, how much was it in the beginning?
A.7349
B.6300
C.6325
D.6939
Answer: C.6325
Explanation: X * (90/100) * (80/100) = 4554
X = 6325
Answer: C
Question: An Olympic diver received the following scores: 4, 3, 7, 6, and 5. The standard deviation of her scores is in which of the following ranges?
A.2.4 to 2.8
B.1.4 to 1.8
C.3.4 to 3.8
D.4.4 to 4.8
Answer: B.1.4 to 1.8
Explanation: 4+3+7+6+5/5 = 5
|4-5| = 1 1^2 = 0
|3-5| = 2 2^2 = 4
|7-5| = 2 2^2 = 4
|6-5| = 1 1^2 = 1
|5-5| = 0 0^2 = 0
SD = sqrt 10/5 =1.41
Answer : B
Question: In a division, a student took 63 as divisor instead of 36. his answer was 24 . The correct answer is-
A.42
B.32
C.48
D.28
Answer: A.42
Explanation: X/63 = 24.
X = 24 *63.
So correct answer would be,
(24 *63) /36 = 42.
ANSWER : A
Question: A shopkeeper purchased 150 identical pieces of calculators at the rate of 250 each. He spent an amount of 2500 on transport and packing. He fixed the labelled price of each calculator at 320. However, he decided to give a discount of 5% on the labelled price. What is the percentage profit earned by him ?
A.14 %
B.15 %
C.16 %
D.20 %
Answer: A.14 %
Explanation: C.P. of 150 calculators
= 150 × 250 + 2500 = 37500 + 2500 = 40000
Labelled price of 150 calculators
= 150 × 320 = 48000
Discount allowed = 5%
∴ S.P. of 150 calculators
= 48000 – 5% = 45600
∴ Profit % = 5600⁄40000 × 100 = 14
Answer A
Question: The largest six digit number which is a perfect cube, is:
A.970299
B.907289
C.992289
D.900279
Answer: A.970299
Explanation: Explanation:
99*99*99 = 970299
Answer: A
Question: if x = 4 + 4 - 4 + 4 - ......¥ find the value of x
A.1
B.2
C.3
D.4
Answer: D.4
Explanation: x=4+4-x.
2x=8.
x=4
ANSWER:D
Question: A women walking at 5 Kmph reaches her office 8 minutes late. If she walks at 6 Kmph, she reaches there 8 minutes earlier. How far is the office from her house?
A.2 1/5 Km
B.3 1/5 Km
C.4 1/3 Km
D.8 Km
Answer: D.8 Km
Explanation: Formula = S1*S2/S2-S1 * T1+T2/60
= 5*6/1 * 16/60
= 30/1 * 16/60
= 30 * 4/15
= 8 Km
D
Question: In a company 10% of male staff are same in number as 1/4th of the female staff. What is the ratio of
male staff to female staff
A.3 : 2
B.5 : 2
C.2 : 1
D.4 : 3
Answer: B.5 : 2
Explanation: Expl : 10% of MS = 1/4th of FS -> 10MS/100 = 1/4FS -> MS = 5/2 FS
:. MS/FS = 5/2 = MS : FS = 5 : 2
Answer: B
Question: What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58?
A.3944
B.2877
C.267
D.2787
Answer: A.3944
Explanation: Let the side of the square plot be a ft.
a2 = 289 => a = 17
Length of the fence = Perimeter of the plot = 4a = 68 ft.
Cost of building the fence = 68 * 58 = Rs. 3944.
Answer:A
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.1
B.1/256
C.81/256
D.175/256
Answer: D.175/256
Explanation: "A man can hit a target once in 4 shots" means that the probability of hitting the target is 1/4, thus the probability of missing the target is 1-1/4=3/4.
The probability that he will hit a target while shooting 4 times is basically the probability that he will hit at least once, so 1-(the probability that he will miss all 4 times): P=1−(34)^4=175/256.
Answer: D.
Question: Of the 200 candidates who were interviewed for a position at a call center, 100 had a two-wheeler, 70 had a credit card and 140 had a mobile phone. 40 of them had both, a two-wheeler and a credit card, 30 had both, a credit card and a mobile phone and 60 had both, a two wheeler and mobile phone and 10 had all three. How many candidates had none of the three?
A.0
B.20
C.10
D.8
Answer: C.10
Explanation: Solution:
Number of candidates who had none of the three = Total number of candidates - number of candidates who had at least one of three devices.
Total number of candidates = 200.
Number of candidates who had at least one of the three = A U B U C, where A is the set of those who have a two wheeler, B the set of those who have a credit card and C the set of those who have a mobile phone.
We know that AUBUC = A + B + C - {A n B + B n C + C n A} + A n B n C
Therefore, AUBUC = 100 + 70 + 140 - {40 + 30 + 60} + 10
Or AUBUC = 190.
As 190 candidates who attended the interview had at least one of the three gadgets, 200 - 190 = 10 candidates had none of three.
Answer C
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 46 years. What will be the age of the B ten years hence?
A.22
B.92
C.26
D.96
Answer: B.92
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 = 46 => b + c = 92 --- (2)
From (1) and (2), we cannot find b.
Answer: B
Question: By selling 22 pencils for a rupee a man loses 40%. How many for a rupee should he sell in order to gain 40%?
A.8.56
B.9.35
C.9.43
D.6.56
Answer: C.9.43
Explanation: 60% --- 22
140% --- ?
60/140 * 22 = 9.43
Answer: C
Question: In a bag there are coins of 50 paisa, 25 paisa and one rupee in the proportion 5:6:2. If there are in all Rs.42, the number of 25 paisa coins is?
A.31
B.42
C.102
D.52
Answer: B.42
Explanation: Answer: Option B
5x 6x 2x
50 25 100
250x + 150x + 200x = 4200
600x = 4200
x = 7 => 6x = 42
Question: A car covers a distance of 624 km in 6 ½ hours. Find its speed?
A.104 kmph
B.187 kmph
C.164 kmph
D.175 kmph
Answer: A.104 kmph
Explanation: 624/6
= 104 kmph
Answer: A
Question: Lexy walks 5 miles from point A to point Q in one hour, then bicycles back to point A along the same route at 15 miles per hour. Ben makes the same round trip, but does so at half of Lexy’s average speed. How many minutes does Ben spend on his round trip?
A.40
B.80
C.120
D.160
Answer: D.160
Explanation: Lexy walks 5 miles from point A to point Q in one hour, then bicycles back to point A along the same route at 15 miles per hour. Ben makes the same round trip, but does so at half of Lexy’s average speed. How many minutes does Ben spend on his round trip?
Average speed = total distance/total time
We know the total distance is 5+5 (going from A to Q then from Q to A)
Time = distance/speed
Time = 5/15
Time = 1/3 hour
Average speed = (10)/(1hr + 1/3hr)
Average speed (lexi) = 10 / 1.33
Therefore, if Ben's average speed is 1/2 of lexi's then his speed = 10/2.66.
This means it took him 2.66 hours to cover the same 10 miles Lexi did. 2.66 hours = roughly 160 minutes.
Answer: D). 160
Question: If a - b = 3 and a^2 + b^2 = 33, find the value of ab.
A.12
B.15
C.10
D.18
Answer: A.12
Explanation: 2ab = (a^2 + b^2) - (a - b)^2
= 33 - 9 = 24
ab = 12.
Answer is A.
Question: A car travels from A to B at an average speed of 50 km/hour. At what average speed would it have to travel from B to A to average 60 km/hour for the whole trip?
A.55 km/h
B.65 km/h
C.85 km/h
D.75 km/h
Answer: D.75 km/h
Explanation: Let d be the distance bewteen A and B
T1 = d / 50 : travel time from A to B
Let S be the speed from B to A
T2 = d/S : travel time from B to A
60 = 2d/(T1 + T2) : average speed for the whole trip
60 = 2d/(d/50 + d/S) : substitute T1 and T2
S = 75 km/hour : solve the above equation for S.
correct answer is D)75 km/h
Question: In what time will a train 100 m long cross an electric pole, it its speed be 144 km/hr?
A.2.5 sec
B.1.9 sec
C.8.9 sec
D.6.9 sec
Answer: A.2.5 sec
Explanation: Speed = 144 * 5/18
= 40 m/sec
Time taken = 100/40
= 2.5 sec.
Answer: A
Question: The current birth rate per thousand is 32, where as corresponding death rate is 11 per thousand. The net growth rate in terms of population increase in percent is given by?
A.2.1%
B.3.2%
C.3.9%
D.4%
Answer: A.2.1%
Explanation: Net growth on 1000 = 32-11 = 21
Net growth on 100 = 21*100/1000 = 2.1%
Answer is A
Question: An amount of Rs.80,000 is to be distributed amongst P, Q, R and S such that “P” gets twice as that of “Q” and “S” gets four times as that of “R”. If “Q” and “R” are to receive equal amount, what is the difference between the amounts received by S and P?
A.2378
B.20000
C.2697
D.5000
Answer: B.20000
Explanation: Explanation:
We have, P = 2Q & S = 4R
Further Q = R & P + Q + R + S = 80,000
Thus we get, 2Q + Q + Q + 4Q = 80,000
8Q = 80,000 or Q = Rs. 10000
Thus, R = Rs. 10000, P = 20000 & S = Rs. 40000
Hence, the required difference = (S – P) = (40000 – 20000) = Rs. 20000
ANSWER:B
Question: A man bought a horse and a carriage for 3000. He sold the horse at a gain of 20% and the carriage at a loss 10%, there by gaining 2% on the whole. Find the cost of the horse.
A.1000
B.1200
C.1500
D.1700
Answer: B.1200
Explanation: Let the C.P. of horse = x
Then the C.P. of carriage = (3000 – x)
20% of x – 10% of (3000 – x) = 2% of 3000
⇒ x⁄5 - (3000−x)/10=60
⇒ 2x - 3000 + x = 600
⇒ 3x = 3600 ⇒ x = 1200
Answer B
Question: Noelle walks from point A to point B at an average speed of 3 kilometers per hour. At what speed, in kilometers per hour, must Noelle walk from point B to point A so that her average speed for the entire trip is 5 kilometers per hour?
A.15
B.12.5
C.10
D.8
Answer: A.15
Explanation: Let's suppose that speed while returning was xkm/h
Since the distance is same, we can apply the formula of avg speed
Avg speed= 2S1S2/S1+S2
5= 2*3*x/3+x
x= 15
A is the answer
Question: A 6% stock yields 8%. The market value of the stock is:
A.48
B.75
C.55
D.46
Answer: B.75
Explanation: For an income of Rs. 8, investment = Rs. 100.
For an income of Rs. 6, investment = Rs.100
---- x 6	= Rs. 75.
8
Market value of Rs. 100 stock = Rs. 75.
Answer: Option B
Question: The price of 3 chudi and 6 tops is Rs. 1500. With the same money one can buy 1 chudi and 12 tops. If one wants to buy 5 tops, how much shall she have to pay ?
A.500
B.1000
C.1200
D.1300
Answer: A.500
Explanation: Let the price of a chudi and a top be Rs. x and Rs. y respectively.
Then, 3x + 6y = 1500 .... (i)
and x + 12y = 1500 .... (ii)
Divide equation (i) by 3, we get the below equation.
= x + 2y = 500. --- (iii)
Now subtract (iii) from (ii)
x + 12y = 1500 (-)
x + 2y = 500
----------------
10y = 1000
----------------
cost of 5 tops = 5*100 = 500
Answer : A
Question: 20 people with two sisters among them want to sit around a round table such that the two sisters are exactly separated by one person sitting in between them. Find the probability.
A.1/19
B.2/29
C.3/29
D.4/29
Answer: B.2/29
Explanation: 20 people in which 2 sisters are there and the condition is that 2 sisters should be seperated by 1 person
(s1 p s2) be 1 set
then 20-3 persons => 17 persons + 1 set= 18
18 can be arranged in 17! ways bcz it is circular permutuation
the 2 sis can be arranged in 2! ways
and the p place can be filled in 18 ways
and the total permutations are 19!
probability is = (2!*18*17!)/(19!)
= 2/19
ANSWER:B
Question: A train , having a length of 110 meter is running at a speed of 60 kmph. In what time, it will pass a man who is running at 6 kmph in the direction opposite to that of the train
A.10 sec
B.8 sec
C.6 sec
D.4 sec
Answer: C.6 sec
Explanation: Explanation:
Distance = 110 m
Relative speed = 60+6 = 66 kmph (Since both the train and the man are in moving in opposite direction)
= 66×10/36 mps = 110/6 mps
Time = distance/speed = 110/(110/6) = 6 s
Answer: Option C
Question: Henry solved a certain number of algebra problems in an hour, his older brother Frank solved
four times as many. Together they solved 80. How many were solved by each?
A.H-12 F-49
B.H-30 F-83
C.H-20 F-90
D.H-16 F-64
Answer: D.H-16 F-64
Explanation: I am looking for the number of problems solved by Henry (H) and Frank (F).
Who solved the least number of problems? Hopefully, you said Henry.
So let H = x
Frank solved four times as many, therefore
F = 4x
Read the problem again to find a relationship. Together they solved 80. That means that
H + F = 80 Substituting
x + 4x = 80 Solving for x
5x = 80
x = 16
Therefore Henry solved 16 and Frank solved 4 times 16 of 64 problems.
correct answer D
Question: A warehouse is labeling computer inventory with 4-digit codes. Each code is to consist of four digits between the numbers 0 and 9. The manager is debating whether to allow any 4-digit codes to have leading zero's before a non-zero number is used. If not allowed, then numbers like "0025" cannot be used.
The manager wants to measure the magnitude of the number of 4-digit code possibilities that are lost if he disallows the use of leading zero's. How many such codes would be lost?
A.981
B.1000
C.1011
D.1101
Answer: B.1000
Explanation: The number of codes possible if leading zero is allowed = 10*10*10*10=10^4
The number of codes possible if leading zero is NOT allowed = 9*10*10*10=9*10^3
The difference = 10^4 - 9*10^3 = 10^3(10-9) = 10^3.=1000
Answer: B.
Question: Jonathan’s grandparents lend $30,000 to Jonathan at a simple annual interest rate of 10%. He pays them back 5 years later. How much do they receive?
A.30,000∗0.1^5
B.30,000∗0.5
C.30,000∗1.5
D.30,000∗1.1^5
Answer: C.30,000∗1.5
Explanation: if you are like me and have used S.I = P x R x T formula in school, while the question is asking for Amount in 5 years. so (c) 30,000∗ 1.5
Ans : C
Question: The sum e of prime numbers that are greater than 60 but less than 70 is
A. 67
B. 128
C. 191
D. 197
Answer: B. 128
Explanation: A prime number is a number that has only two factors: 1 and itself. Therefore, a prime number is divisible by two numbers only.
Let's list the numbers from 61 to 69.
61, 62, 63, 64, 65, 66, 67, 68, 69
Immediately we can eliminate the EVEN NUMBERS because they are divisible by 2 and thus are not prime.
We are now left with: 61, 63, 65, 67, 69
We can next eliminate 65 because 65 is a multiple of 5.
We are now left with 61, 63, 67, 69.
To eliminate any remaining values, we would look at those that are multiples of 3. If you don’t know an easy way to do this, just start with a number that is an obvious multiple of 3, such as 60, and then keep adding 3.
We see that 60, 63, 66, 69 are all multiples of 3 and therefore are not prime.
Thus, we can eliminate 63 and 69 from the list because they are not prime.
Finally, we are left with 61 and 67, and we must determine whether they are divisible by 7. They are not, and therefore they must be both prime. Thus, the sum e of 61 and 67 is 128.
Answer B.
Question: If a = 1 and b = -2, then (2a^2 + b)(w + y) + (a + b)(w - y) =
A.0
B.2x
C.y - w
D.x - y
Answer: C.y - w
Explanation: Putting A=1 and B = -2 => 2A^2-B=0 ; so the first part of the term is zero
with second term => (1-2) *(w+y)=y-w => Smash C