mathewhe/aqua_rat huggingface dataset:
Question: If the square root of p^2 is an integer greater than 1, which of the following must be true?
I. p^2 has an odd number of positive factors
II. p^2 can be expressed as the product of an even number of positive prime factors
III. p has an even number of positive factors
(A) I
(B) II
(C) III
(D) I and II
(E) II and III
Rationale: It is given that p2−−√p2>1 and is an integer..
Also p2−−√p2=p
so p^2 is a perfect square and p is an integer>1..
lets see three statements:-
I. p^2 has an odd number of positive factors-- TRUE
A perfect square has an Odd number of perfect square ..
WHY? Because all factors will have a different integer as a pair except p..
p*p=p^2.. so that will be just one factor
II. p^2 can be expressed as the product of an even number of positive prime factors
again TRUE
25 =5*5 ; 49= 7*7 ; 36 = 2*2*3*3
III. p has an even number of positive factors..
Since it uses 'HAS', if we find one which does not follow the statement is not true..
we already know that A perfect square has an Odd number of perfect square ..
so if p is a perfect square itself ans is No
ONLY I and II are true
ANSWER:D
Answer: (D) I and II
Question: Which of the below fractions has the highest value?
(A) A)23/77
(B) B)23/78
(C) C)23/84
(D) D)23/87
(E) E)23/40
Rationale: 23/40.
Now, all options have the same numerator 23. If numerator is same, the fraction with the highest value will be the one with the lowest denominator.
Answer (E).
Answer: (E) E)23/40
Question: A discount electronics store normally sells all merchandise at a discount of 10 percent to 30 percent off the suggested retail price. If, during a special sale, an additional 25 percent were to be deducted from the discount price, what would be the lowest possible price of an item costing $260 before any discount?
(A)  $136.50
(B)  $145.60
(C)  $163.80
(D)  $182.00
(E)  $210.00
Rationale: Since the question is essentially just about multiplication, you can do the various mathstepsin a variety of ways (depending on whichever method you find easiest).
We're told that the first discount is 10% to 30%, inclusive. We're told that the next discount is 25% off of the DISCOUNTED price....
We're told to MAXIMIZE the discount (thus, 30% off the original price and then 20% off of the discounted price). Thatmathcan be written in a number of different ways (fractions, decimals, etc.):
30% off = (1 - .3) = (1 - 30/100) = (.7) and the same can be done with the 20% additional discount...
The final price of an item that originally cost $260 would be.....
($260)(.7)(.75) =
($260)(.525)=136.5
Final Answer:
A
Answer: (A)  $136.50
Question: he ratio between the sale price and the cost price of an article is 4:7. What is the ratio between the profit and the cost price of that article?
(A) 2:6
(B) 3:7
(C) 3:8
(D) 2:1
(E) 8:3
Rationale: Let C.P. = Rs. 7x and S.P. = Rs. 4x.
Then, Gain = Rs. 3x
Required ratio = 3x : 7x = 3:7.
Answer:B
Answer: (B) 3:7
Question: In year Y imported machine tools accounted for 25 percent of total machine-tools sales in the United States, and Japanese imports accounted for 40 percent of the sales of imported machine tools. If the total sales of machine tools imported from Japan that year was x billion dollars, then the total sales of all machine tools in the United States was how many billion dollars?
(A) 9x/80
(B) 13x/20
(C) 80/9x
(D) 10x
(E) 80x/9
Rationale: Sales of imported tools = 25% of the total sales = 0.25*{total} = {total}/4;
Sales of Japanese tools = 40% of the sales of imported tools = 0.40*{total}/4 = 2/5*{total}/4 = 2*{total}/20.
Since the sales of of Japanese tools was x, then 2*{total}/20 = x --> {total} = 10x.
Answer: D.
Answer: (D) 10x
Question: The average of first ten prime numbers which are odd is?
(A) 15.7
(B) 15.0
(C) 15.2
(D) 15.8
(E) 15.1
Rationale: Sum of first 10 prime no. which are odd = 158
Average = 158/10 = 15.8
Answer: D
Answer: (D) 15.8
Question: If 1 kilometer is approximately 0.6 mile, which of the following best approximates the number of kilometers in 7 miles?
(A) 22/5
(B) 20/5
(C) 15/5
(D) 21/5
(E) 16/4
Rationale: 1 km is approxmately equal to 0.6 miles
So 7 km = 7*0.6 = 4.2 miles . Multiple & divide by 10
i.e 4.2*10/10 = 42/10 = 21/5
Answer : D
Answer: (D) 21/5
Question: A person’s age is 125% of what it was one decade ago, but 83(1/3)% of what it will be after one decade. What is his current age? [1 decade = 10 years]
(A) 50 years
(B) 60 years
(C) 30 years
(D) 70 years
(E) 80 years
Rationale: A
50 years
Let, current age is A years.
Then, 125% of (A – 10) = A
and, 83(1/3)% of (A + 10) = A
Therefore 125% of (A-10) = 83(1/3)% of (A+10)
or, (5/4) (A – 10) =(5/6)(A+10)
or, (5/4)A -(5/6)A = (50/6)+(50/4)
or, (5A/12)= (250/12) or,
A=50 years.
Answer: (A) 50 years
Question: A student took five papers in an examination, where the full marks were the same for each paper. His marks in these papers were in the proportion of 6 : 7 : 8 : 9 : 10. In all papers together, the candidate obtained 60% of the total marks. Then the number of papers in which he got more than 61% marks is
(A) 6
(B) 5
(C) 4
(D) 3
(E) 2
Rationale: Here we can assume that one subject is of 100 marks so total there are 5 subjects => 100*5 = 500.
Now according to the question he secured 60 % of those which is 60%of 500 = 300 marks in total.
The ratio between the marks is given as 6 : 7 : 8 : 9 : 10 , so now we can distribute 300 marks according to the ratio.
Total ratio = 40
For 6 : (300/40)*6 = 45
Similarly , we will get for others as 52.5 , 60 , 62.5 , 75.
Hence , there are 2 subject where he secured more that 50 %.
The answer is 2.
E
Answer: (E) 2
Question: If n = 14p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ?
(A)  Two
(B)  Three
(C)  Four
(D)  Six
(E)  Eight
Rationale: If n = 14p, where p is a prime number greater than 2, how many different positive even divisors does n have, including n ?
(A) Two
(B) Three
(C) Four
(D) Six
(E) Eight
Since we cannot have two correct answers just pick a prime greater than 2, and see how many different positiveevendivisors will 14p have.
p = 3 --> 14p = 42--> 42 has 4 even divisors: 2, 6, 14, 42 .
Answer: C.
Answer: (C)  Four
Question: In a stack of boards at a lumber yard, the 20th board counting from the top of the stack is immediately below the 17th board counting from the bottom of the stack. How many boards are in the stack?
(A) 38
(B) 36
(C) 35
(D) 34
(E) 32
Rationale: Counting from the top, after the 20th board, there are 15 boards left to count.
The answer is C.
Answer: (C) 35
Question: A man is standing on a railway bridge which is 240 m long. He finds that a train crosses the bridge in 20 seconds but himself in 8 seconds. Find the length of the train and its speed.
(A) 10 m/sec
(B) 15 m/sec
(C) 18 m/sec
(D) 20 m/sec
(E) 25 m/sec
Rationale: If length of train is l and speed of train is s, then
l/s = 8
(l+240)/s = 20
(l+240)/l = 20/8 =5/2
2l+480 =5*l
3*l= 480
l=160 mtrs
s= l/8 = 160/8 = 20 m/sec
ANSWER:D
Answer: (D) 20 m/sec
Question: For one toss of a certain coin, the probability that the outcome is heads is 0.3. If this coin is tossed 5 times, which of the following is the probability that the outcome will be heads at least 4 times?
(A) (0.3)^5
(B) 2(0.3)^4
(C) 3(0.3)^4
(D) 4(0.3)^4(0.7) + (0.3)^5
(E) 5(0.3)^4(0.7) + (0.3)^5
Rationale: P(5 heads) = (0.3)^5
There are 5 ways to get 4 heads: HHHHT, HHHTH, HHTHH, HTHHH, THHHH
P(4 heads) = 5*(0.3)^4(0.7)
The answer is E.
Answer: (E) 5(0.3)^4(0.7) + (0.3)^5
Question: A train traveled the first d miles of its journey it an average speed of 50 miles per hour, the next d miles of its journey at an average speed of y miles per hour, and the final d miles of its journey at an average speed of 160 miles per hour. If the train’s average speed over the total distance was 96 miles per hour, what is the value of y?
(A)  68
(B)  84
(C)  90
(D)  120
(E)  160
Rationale: Average speed=Total distance traveled /Total time taken
3d/d/50+d/y+d/160=96
Solving for d and y,
15y=11y+480
3y=480
y=160
Answer E
Answer: (E)  160
Question: If 75 percent of a girls answered the first question on a certain test correctly, 55 percent answered the second question on the test correctly, and 20 percent answered neither of the questions correctly, what percent answered both correctly?
(A)  10%
(B) (8) 20%
(C)  30%
(D)  40%
(E)  50%
Rationale: {Total} = {First} + {Second} - {Both} + {Neither}
100% = 75% + 55% - {Both} + 20% --> {Both} = 50%.
Answer: E.
Answer: (E)  50%
Question: A certain quantity is measured on two different scales, the T-scale and the S-scale, that are related linearly. Measurements on the T-scale of 6 and 24 correspond to measurements on the S-scale of 30 and 60, respectively. What measurement on the T-scale corresponds to a measurement of 100 on the S-scale?
(A)  20
(B)  36
(C)  48
(D)  60
(E)  84
Rationale: First, we have to understand what linearly means. It's not a straight ratio (since 6:30 does NOT equal 24:60). We need to look at the increases in each measurement to see what the scalar actually is.
From 6 to 24 we have an increase of 18. From 30 to 60 we have an increase of 30. Therefore, the increase ratio is 18:30 or 3:5. In other words, for every 3 that T increases, S increases by 5.
We know that S is 100. To get from 60 to 100, we went up by 40, or 8 jumps of 5; therefore, T will go up by 8 jumps of 3.
24 + 8(3) = 24 + 24 = 48=C
Answer: (C)  48
Question: A, B and C can do a piece of work in 24, 30 and 40 days respectively. They start the work together but C leaves 4 days before the completion of the work. In how many days is the work done?
(A) 11 days
(B) 14 days
(C) 13 days
(D) 10 days
(E) 20 days
Rationale: x/24 + x/30 + x/40 = 1
x = 11 days
ANSWER A
Answer: (A) 11 days
Question: Set A {3,3,3,4,5,5,5} has a standard deviation of 1. What will the standard deviation be if every number in the set is multiplied by 8?
(A) A)1
(B) B)2
(C) C)4
(D) D)8
(E) E)16
Rationale: Points to remember -
1. If oneAdd/Subtractthe same amont from every term in a set, SD doesn't change.
2. If oneMultiply/Divideevery term by the same number in a set, SD changes by same number.
Hence the answer to the above question is D
Answer: (D) D)8
Question: Find the last 2 digits
65*29*37*63*71*87*62
(A) 70
(B) 30
(C) 10
(D) 90
(E) 80
Rationale: Similarly for this question,
Rof(201∗202∗203∗204∗246∗247∗248∗249)∗(201∗202∗203∗204∗246∗247∗248∗249)/100
=Rof(201∗101∗203∗204∗246∗247∗248∗249)∗(201∗202∗203∗204∗246∗247∗248∗249)/50
Note: I have left denominator as 50 since it will be easier in calculations.
=Rof[(1∗1∗3∗4∗(−4)∗(−3)∗(−2)∗(−1)]∗[(1∗2∗3∗4∗(−4)∗(−3)∗(−2)∗(−1)]/50
=Rof(12∗24∗24∗24)/50=Rof(6∗24∗24∗24)/25=Rof[6∗(−1)∗(−1)∗(−1)]/25=−6
Since remainder is coming negative, we add 25 to it.
Thus Remainder is 19. In decimal format, it is 19/25 or 0.76
Thus last two digits will be 0.76*100 = 76
[Note: Rather than calculating the decimal value first, it will be faster to combine the last two steps as follows: (19/25)*100 = 19*4 = 76. This is how I did it and it saved me valuable seconds!]
Answer should be (3).
ANSWER:C
Answer: (C) 10
Question: A thief is noticed by a policeman from a distance of 300 m. The thief starts running and the policeman chases him. The thief and the policeman run at the rate of 10 km and 11 km per hour respectively. What is the distance between them after 6 minutes?
(A) 150 m
(B) 200 m
(C) 170 m
(D) 100 m
(E) 250 m
Rationale: Relative speed of the thief and policeman = 11 - 10 = 1 km/hr.
Distance covered in 6 minutes = 1/60 * 6 = 1/10 km = 100 m.
Distance between the thief and policeman = 300 - 100 = 200 m
B
Answer: (B) 200 m
Question: The jogging track in a sports complex is 660 m in circumference. Deepak and his wife start from the same point and walk in opposite directions at 4.5 km/hr and 3.75 km/hr respectively. They will meet for the first time in?
(A) 5.29 min
(B) 5.28 min
(C) 5.08 min
(D) 4.8 min
(E) 5.988 min
Rationale: Clearly, the two will meet when they are 660 m apart.
To be (4.5 + 3.75) = 8.25 km apart, they take 1 hour.
To be 660 m apart, they take (100/825 * 660/1000) hrs = (660/8250 * 60) min = 4.8 min.
Answer: D
Answer: (D) 4.8 min
Question: If 30% of a number is 12.6, find the number?
(A) 42
(B) 40
(C) 26
(D) 36
(E) 66
Rationale: A
40
Answer: (A) 42
Question: During a trip, Francine traveled x percent of the total distance at an average speed of 100 miles per hour and the rest of the distance at an average speed of 90 miles per hour. In terms of x, what was Francineâ€™s average speed for the entire trip?
(A) (180-x)/2
(B) (x+60)/4
(C) (300-x)/5
(D) 600/(115-x)
(E) 9,000/(100+8x)
Rationale: E....
X% traveeled at 10 mph
100-X% traveeled at 90 mph
total timt taken = x/10 +(100-x)/90 = (100+8x)/90
Total distance = x+(100-x) = 100
Av speed = Tot Dis/Time Taken which is E
Answer: (E) 9,000/(100+8x)
Question: If the wheel is 14 cm then the number of revolutions to cover a distance of 1056 cm is?
(A) 18
(B) 26
(C) 14
(D) 12
(E) 91
Rationale: 2 * 22/7 * 14 * x = 1056 => x
= 12
Answer: D
Answer: (D) 12
Question: Find the simple interest for Rs. 2000 at 8% p/a for 2years.
(A) Rs.300
(B) 3Rs.20
(C) Rs.420
(D) Rs.520
(E) Rs.460
Rationale: S.I= (2000*8*2)/100
P = 320
Answer: B
Answer: (B) 3Rs.20
Question: Which of the following is larger than 3/5?
(A) 1/2
(B) 39/50
(C) 7/25
(D) 3/10
(E) 59/100
Rationale: if we want to compare two fraction number
a/b =c/d
then a*d (answer to a/b)
c*b (ans to c/d) (apply this conditions to all the options)
Therefore (3*5=15) (39*5=195)
39/5 is greater than 3/5..
ANSWER:B
Answer: (B) 39/50
Question: A father was as old as his son's present at the time of your birth. If the father's age is 34 years now, the son's age 5years back was?
(A) 10 years
(B) 12 years
(C) 14 years
(D) 16 years
(E) 20 years
Rationale: Let the son's present age be x years. Then, (34 - x) = x
2x = 34.
x = 17.
Son's age 5 years back (17 - 5) = 12 years.
B
Answer: (B) 12 years
Question: At a contest with 3,500 participants, 1/2 of the people are aged 18 to 22. Next year, the number of people aged 18 to 22 will increase by 1/7. After this change, what percentage of the total 3,500 people will the 18- to 22-year-olds represent?
(A) 33%
(B) 40%
(C) 55%
(D) 57.14%
(E) 66.14%
Rationale: I just wanted to mention a couple of things here:
* this is a pure ratio question; the number 3,500 is completely irrelevant, and you can ignore it if you like. When we increase something by 1/7, we are multiplying it by 1 + 1/7 = 8/7, so the answer here must be (1/2)*(8/7) = 4/7 = 57.14 %.
Answer : D
Answer: (D) 57.14%
Question: Bradley owns 3b video game cartridges. If Bradleyâ€™s total is one-fourth the total owned by Andrew and triple 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) 16b
(E) 7/12)b
Rationale: 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 Charlieâ€™s totals in relation to Bradleyâ€™s total rather than giving you Bradleyâ€™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 Charlieâ€™s values in relation to Bradleyâ€™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
3b = Bradleyâ€™s total
4*3b = Andrewâ€™s total
(1/3)*3b = Charlieâ€™s total
Add each total
3b + 4*3b+ (1/3)3b = 3b + 12b + b = 16b
Therefore,choose D.
Answer: (D) 16b
Question: An auto assembly plant performs six functions with each frame that arrives: add axles, add wheels to the axles, install the windshield to the frame, install the instrument panel, install the steering wheel, and install the interior seating. Once those six tasks are performed, each car goes to a separate building for finishing touches. If these tasks can be arranged along a linear assembly line in any order, except that the axles must be installed before the wheels can be added, how many Y ways can the assembly line be arranged?
(A) 120
(B) 240
(C) 360
(D) 480
(E) 720
Rationale: C) 360
short way: there are 6C! ways to do the six tasks. Half will have wheels before axles and half will have axles before wheels. So we want Y=6C!/2 -> 720/2 = 360
Answer: (C) 360
Question: Of the 80 people in a room, 1/4 are women. If 3/4 of the people are married, what is the maximum number of women in the room who could be unmarried?
(A) 20
(B) 24
(C) 26
(D) 28
(E) 30
Rationale: women = 1/4 * 80 = 20
married = 3/4 * 80 = 60
unmarried = 20
max(un-married women) = 20
Answer A
Answer: (A) 20
Question: The sum of the ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
(A) 4
(B) 5
(C) 6
(D) 7
(E) 9
Rationale: Let the ages of the children be x, (x + 3), (x + 6), (x + 9) and (x +12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
5x = 20 => x = 4.
Age of youngest child = x = 4 years.Answer: A
Answer: (A) 4
Question: A shopkeeper buys two articles for Rs.1000 each and then sells them, making 20% profit on the first article and 20% loss on second article. Find the net profit or loss percent?
(A) 200
(B) 99
(C) 88
(D) 77
(E) 112
Rationale: Profit on first article = 20% of 1000 = 200.
This is equal to the loss he makes on the second article. That, is he makes neither profit nor loss.
Answer:A
Answer: (A) 200
Question: David mixed 20 kg of butter at Rs. 200 per kg with 30 kg butter at the rate of Rs. 100 per kg. At what price per kg should he sell the mixture to make a profit of 40% in the transaction?
(A) Rs. 96
(B) Rs. 196
(C) Rs. 296
(D) Rs. 190
(E) Rs. 195
Rationale: Cost of Butter = 20*200+ 30*100 /50 =7000/50 = 140
40% of 140 = 56
S.P. should be = 140+56 = Rs. 196/ kg
Answer : B
Answer: (B) Rs. 196
Question: A pump can fill a tank with water in 2 hours. Because of a leak, it took 2 2/3 hours to fill the tank. The leak can drain all the water of the tank in
(A) 6 hours
(B) 8 hours
(C) 9 hours
(D) 10 hours
(E) 12 hours
Rationale: Explanation:
Solution 1
The pump can fill the tank in 2 hour. But, because of the leak, it took 2 2/3 hours to fill the tank.
i.e., the additional water filled by the pump in 2/3 hour is emptied by the leak in 2 2/3 = 8/3 hours.
Therefore, the water filled by pump in 2 bour can be emptied by the leak in 8/3 X 3 = 8 hours.
i.e., The leak can drain all the water of the tank in 8 hours.
ANSWER IS B
Answer: (B) 8 hours
Question: When Ravi was 8 years old, his father was 31 years old,. Now his father is twice Ravi's age. How old is Ravi now?
(A) 45 yrs
(B) 46 yrs
(C) 47 yrs
(D) 48 yrs
(E) 49 yrs
Rationale: When Ravi was 8 years old, his father was 31 years old,.
Means father's age is 23 years more than Ravi.
Now his father is twice Ravi's age.
It means difference between their ages is equal to present age of Ravi.
So Ravi's present age = 23 years. and father's age = 2*23 = 46 yrs
ANSWER:B
Answer: (B) 46 yrs
Question: A no.when divided by 223 gives a remainder 43, what remainder will beobtained by dividingthe same no.17?
(A) 2
(B) 7
(C) 9
(D) 11
(E) 15
Rationale: 223 + 43 = 266/17 = 11 (Remainder)
D
Answer: (D) 11
Question: Dhoni spends $250 buying his favorite dolls. If he buys only small Barbie dolls, which are $5 cheaper than the large Barbie dolls, he could buy 25 more dolls than if he were to buy only large Barbie dolls. How much does a large Barbie doll cost?
(A) $10.5
(B) $10
(C) $11
(D) $12
(E) $13
Rationale: A is not an integer. So we start with B.
If large doll costs $10, then he can buy 250/10 = 25 large dolls and 250/5 =50 small dolls.
Difference is 25, which is we wanted.
Answer B.
Answer: (B) $10
Question: A certain car's price decreased by 2.5% (from the original price) each year from 1996 to 2002, during that time the owner of the car invested in a new carburetor and a new audio system for the car, which increased car's price by $2,500. If the price of the car in 1996 was $22,000, what is the car's price in 2002?
(A) $18,400
(B) $19,500
(C) $20,200
(D) $20,400
(E) $21,200
Rationale: Price in 96 = 22000
Price decrease each year = 2.5/100*22000 = 550
Price in 97 = 22000 - 550
Price in 98 = 22000 - 2*550
Price in 99 = 22000 - 3*550
Price in 00 = 22000 - 4*550
Price in 01 = 22000 - 5*550
Price in 02 = 22000 - 6*550 = 18700
Investment in the car = 2500
Net price of the car in 02 = 18700 + 2500 = $21200
Correct Option: E
Answer: (E) $21,200
Question: If 2 men or 3 women can reap a field in 5 days how long will 5 men and 6 women take to reap it?
(A) 2/24
(B) 6/18
(C) 2/22
(D) 5/12
(E) 9/10
Rationale: Explanation:
2 men reap 2/5 field in 1 day
1 man reap 1/(2 x 5)
3 women reap 1/43 field in 1 day
1 woman reap 1/(5 x 3)
5 men and 6 women reap (5/(2 x 5)+ 6/(3 x 5)) =9/10 in 1 day
5 men and 6 women will reap the field in 9/10 days
Answer: Option E
Answer: (E) 9/10
Question: Calculate the ratio between x and y if 25% of x equal to 40% of y?
(A) 5 : 8
(B) 5 : 9
(C) 5 : 7
(D) 5 : 6
(E) 5 : 4
Rationale: Explanation:
25 x = 40 y
x: y = 25 : 40 = 5 : 8
Answer:A
Answer: (A) 5 : 8
Question: Ayesha's father was 40 years of age when she was born while her mother was 32 years old when her brother six years younger to her was born. What is the difference between the ages of her parents?
(A) 6
(B) 14
(C) 5
(D) 1
(E) 2
Rationale: Mother's age when Ayesha's brother was born = 32 years.
Father's age when Ayesha's brother was born = (40 + 6) years = 46 years.
Required difference = (46 - 32) years = 14 years.
Answer:B
Answer: (B) 14
Question: 150 125 60 120 95 60 70 ? ?
(A) 25 15
(B) 25 85
(C) 35 25
(D) 60 60
(E) 20 75
Rationale: 150-25=125
again 60
125-25=120
120-25=95
again 60
95-25=70
70-25=55
again 60
then answer is 60 ,60
ANSWER:D
Answer: (D) 60 60
Question: Sales price is $91, gross profit is 160% of cost, what is the value of gross profit?
(A) 32
(B) 33
(C) 39
(D) 40
(E) 56
Rationale: Cost + Profit = Sales
Cost + (160/100)Cost = 91
Cost = 35
Profit = 91 - 35 = 56
Answer (E)
Answer: (E) 56
Question: There are 9 baskets with pebbles in it.Every basket have pebbles weighing 1gm except one which has pebbles weighing 2gm.There is a weighing machine. Use the weighing machine only once and find which basket have pebbles that weigh 2gm?
(A) 9th
(B) 8th
(C) 6th
(D) 4th
(E) 5th
Rationale: Take 1 pebble form 1st basket, 2 from 2nd, 3 from 3rd,...9 from the 9th basket and weigh them. If all the baskets contained 1gm pebbles the weight would have been 45 [ 1+2+3+..9 = 45]
Since 1 of the basket contains 2 gm pebbles the weight will be more than 45.
Subtract 45 from the weight to get the basket number.
ie
if the weight is 49
49 - 45 = 4
4th basket
ANSWER:D
Answer: (D) 4th
Question: The five sides of a pentagon have lengths of 2, 3, 4, 5 and 6 inches. one pentagons are considered different only when the positions of the side lengths are different relative to each others. What is the total number of different possible pentagons that could be drawn using these five side lengths ?
(A)  5
(B)  12
(C)  24
(D)  32
(E)  120
Rationale: CONCEPT: The number of ways to arrange n elements around a circular Manner is (n-1)!.
But the number of ways to arrange n elements in circular manner where the arrangement can be flipped around (e.g. Necklace, Garland, Bracelet) = (n-1)!/2.
The pentagon in the problem above can be flipped over (Clockwise Arrangement of Sides = Counter-clockwise arrangement), the number of distinct ways to arrange the 5 sides = (5-1)!/2 = 5.
Answer: option A
Answer: (A)  5
Question: Positive integer y is 50 percent of 50 percent of positive integer x, and y percent of x equals 4. What is the value of x?
(A) 40
(B) 100
(C) 200
(D) 400
(E) 600
Rationale: y = 0.5*0.5*x = x/4
y%*x = 4
(y/100)*x = 4
(x/400)*x = 4
x^2 = 4*400
x = 40
The answer is A.
Answer: (A) 40