mathewhe/aqua_rat huggingface dataset:
Question: For 6-digit integer 46x,y12, when x and y are drawn at random from {3,5,8}, what is the probability W that the integer drawn is divisible by 8?
* A solution will be posted in two days.
(A) 1/6
(B) 1/3
(C) 1/2
(D) 2/3
(E) 5/6
Rationale: In general, the remainder divided by integer n is the same as the remainder that up to tens of n is divided by 8.
Thus, in order for 46,x,y12 to be divided by 8, y12 should be divided by 8.
Amongst 3,5,8, 3 and 5 can be divided by 8.
Therefore,W= two out of three can be divided and the answer is D.
Answer: (D) 2/3
Question: 31 of the scientists that attended a certain workshop were Wolf Prize laureates, and 16 of these 31 were also Nobel Prize laureates. Of the scientists that attended that workshop and had not received the Wolf prize, the number of scientists that had received the Nobel Prize was 3 greater than the number of scientists that had not received the Nobel Prize. If 50 of the scientists attended that workshop, how many of them were Nobel Prize laureates?
(A) A)11
(B) B)18
(C) C)24
(D) D)27
(E) D)36
Rationale: lets solve by creating equation..
W = 31..
Total = 50..
Not W = 50 -31= 19..
Now let people who were neither be x, so out of 19 who won Nobel = x+3..
so x+x+3=19 or x=8..
so who won Nobel but not Wolf = x+3 = 11..
But people who won BOTH W and N = 13..
so total who won N = 11+16 = 27..
D
Answer: (D) D)27
Question: If y = 20! + 17, then y is divisible by which of the following?
I. 15
II. 17
III. 19
(A)  None
(B)  I only
(C)  II only
(D)  I and II
(E)  II and II
Rationale: Another crude way to answer this, if you did not know the properties above would be to consider that that 20! will have the number ending in 00 due to 10 and 20 being included.
So y!+17 = xxxx00 +17 = xxxx17 which is only possibly divisible by 17. Hence Option C is the answer.
Answer: (C)  II only
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 36 kmph and 72 kmph. In how much time will the trains cross each other?
(A) 40/6
(B) 40/3
(C) 40/9
(D) 40/2
(E) 40/1
Rationale: Relative speed = (36 + 72)* 5/18 = 30 mps.
The time required = d/s = (100 + 100 + 200)/30
= 400/30 = 40/3 sec.
Answer:B
Answer: (B) 40/3
Question: The sum of even numbers between 1 and 31 is
(A) 16
(B) 128
(C) 240
(D) 512
(E) None
Rationale: Solution
Required numbers are 2, 4, 6,..30.
This is an A.P containing 15 terms.
Required sum	= n/2(first term + last term)
‹=›15 / 2(2+30)
‹=› 240.
Answer C
Answer: (C) 240
Question: Every student at Warcy School is in at least one of three clubs: horseback riding, embroidery, and country dancing, which are the only clubs in existence at the school. The ratio of the number of students in exactly two clubs to the number of students in exactly one club is 4:3, while the ratio of the number of students in exactly two clubs to the number of students in at least two clubs is 5:7. Which of the following could be the total number of students at Warcy School?
(A) 63
(B) 69
(C) 74
(D) 82
(E) 86
Rationale: total number of students at Warcy School The answer is 86 or any multiple of 43.E
Answer: (E) 86
Question: Five machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 25 hours to fill a certain production order, how many fewer hours does it take all five machines, operating simultaneously, to fill the same production order?
(A)  3
(B)  5
(C)  6
(D)  16
(E)  24
Rationale: Total work = 4*25 machine hrs
Time taken = 4* 25 /5 => 20 hours...
Thus all five machines, operating simultaneously will take ( 25 - 20 ) 5 hours..
Answer will be (B) 5
Answer: (B)  5
Question: Teas worth Rs. 126 per kg and Rs. 135 per kg are mixed with a third variety in the ratio 1 : 1 : 2. If the mixture is worth Rs 157 per Kg , the price of the third variety per Kg will be?
(A) Rs. 147.50
(B) Rs. 785.50
(C) Rs. 179.50
(D) Rs. 258.50
(E) None of these
Rationale: Explanation :
Since first and second varieties are mixed in equal proportions.
So, their average price =Rs. (126+135)/2.
=>Rs. 130.50.
So, the mixture is formed by mixing two varieties, one at Rs. 130.50 per kg and the other at say, Rs. x per kg in the ratio 2 : 2, i.e., 1 : 1.
We have to find x.
By the rule of alligation, we have:
Cost of 1 kg Cost of 1 kg
of 1st kind of 2nd kind
(Rs. 130.50) (Rs. x)
\ /
Mean Price
(Rs. 157)
/ \
xâˆ’157 22.50
=>xâˆ’(157/22.50)=1.
=>xâˆ’157=22.50.
=>x= 179.50 Rs.
Answer : C
Answer: (C) Rs. 179.50
Question: A shopkeeper has 280 kg of apples. He sells 35% of these at 20% profit and remaining 60% at 30% profit. Find his % profit on total.
(A) 24%
(B) 25%
(C) 26%
(D) 28%
(E) 35%
Rationale: If the total quantity was 100
Then 35X 20% + 60 X30%= 25
This profit will remain same for any total quantity unless the % of products remains the same. Hence 'B' is the answer
Answer: (B) 25%
Question: Company C produces toy trucks at a cost of $5.00 each for the first 100 trucks and $3.50 for each additional truck. If 500 toy trucks were produced by Company C and sold for $7.00 each, what was Company C’s gross profit?
(A)  $2,250
(B)  $2,500
(C)  $1,600
(D)  $1,250
(E)  $1,500
Rationale: Cost of 500 trucks: (100 * 5 ) + (400 * 3.5) = 500 + 1400 =$ 1900
Revenue : 500 * 7 = $3500
Profit: 3500 - 1900 = $ 1600
Option C is correct
Answer: (C)  $1,600
Question: The speed of the boat in still water in 12 kmph. It can travel downstream through 42 kms in 3 hrs. In what time would it cover the same distance upstream?
(A) 8 hours
(B) 6 hours
(C) 4.2 hours
(D) 5 hours
(E) 6 hours
Rationale: Still Water=12km/hr
Downstream=42/3=14km/hr
Upstream=>> still water=(u+v/2) =>> 12=u+14/2 = 10km/hr
So time taken in upstream = 42/10 =4.2hrs
ANSWER:C
Answer: (C) 4.2 hours
Question: The tax on a commodity is diminished by 20% and its consumption increased by 15%. The effect on revenue is?
(A) 9% decrease
(B) 8% decrease in revenue
(C) 6% decrease
(D) 1% decrease
(E) 2% decrease
Rationale: 100 * 100 = 10000
80 * 115 = 9200
-----------
10000-----------800
100-----------? => 8% decrease
Answer: B
Answer: (B) 8% decrease in revenue
Question: Because he’s taxed by his home planet, Mork pays a tax rate of 45% on his income, while Mindy pays a rate of only 25% on hers. If Mindy earned 4 times as much as Mork did, what was their combined tax rate?
(A) 29%
(B) 31%
(C) 33%
(D) 35%
(E) 37%
Rationale: Let x be Mork's income, then Mindy's income is 4x.
The total tax paid is 0.45x + 1.0x = 1.45x
1.45x / 5x = 0.29
The answer is A.
Answer: (A) 29%
Question: If y = x^2 + d x + 9 does not cut the x-axis, then which of the following could be a possible value of d?
I. 0
II. -3
III. 9
(A) III only
(B) II only
(C) I and II only
(D) II and III only
(E) I and III only
Rationale: Here C is the answer as A and B statements will provide the discriminant to be negative thereby making the x axis cutting impossible.
Hence only 1 and 2
thus C
Answer: (C) I and II only
Question: A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs.16.80 less, he would have gained 30%. Find the cost of the article.
(A) 30
(B) 40
(C) 50
(D) 60
(E) 80
Rationale: Let C.P=100
Gain=25%
S.P=125
Supposed C.P=80
Gain=30%
S.P=(130*80)/100=104
Diff=(125-104)=21
Diff 21 when C.P=100
then Diff 16.80 when C.P=(100*16.80)/21=50
ANSWER:E
Answer: (E) 80
Question: Square RSTU shown above is rotated in a plane about its center in a clockwise direction the minimum number of degrees necessary for S to be in the position where U is now shown. The number of degrees through which RSTU is rotated is
(A)  180 degree
(B)  160 degree
(C)  225 degree
(D)  270 degree
(E)  315 degree
Rationale: From the options, I am assuming the positioning of U and S relative to each other to be as shown. To replace U by S, focus on OS. Say, you rotate OS clockwise (and with it the entire square) and bring it in place of OU. How many degrees did you go? You covered 2 right angles i.e. 180 degrees.
Answer : A
Answer: (A)  180 degree
Question: A company has two types of machines, type R and type S. Operating at a constant rate, a machine of type R does a certain job in 18 hrs and a machine of type S does the same job in 9 hours. If the company used the same number of each type of machine to do the job in 2 hours, how many machines of type R were used?
(A) 3
(B) 4
(C) 6
(D) 9
(E) 12
Rationale: Rate of machine R =1/18
Rate of machine S =1/9
since same no of machines used for R and S to do the same work in 2 hrs
So collective rate needed to finish the work in 2 hrs= 1/2
Let the no of machine be x
So, x/18 +x/9 =1/2
3x/18=1/2
x=18/6=3
So no of machine R is 3
Answer A
Answer: (A) 3
Question: 361, 289, 225, 169, 121, ?
(A) 36
(B) 49
(C) 64
(D) 81
(E) 100
Rationale: Explanation :
The pattern is 19^2, 17^2, 15^2, 13^2, 11^2, ...
So next number is 9^2 = 81
Answer : Option C
Answer: (C) 64
Question: Shri Prakash walked 40 metres facing towards North. From there he walked 50 metres after turning to his left. After this he walked 40 metres after turning to his left. How far and in what direction is he now from his starting point?
(A) 40 m, North
(B) 50 m, West
(C) 10 m, East
(D) 10 m, West
(E) None of these
Rationale: 50 m , West
ANSWER:B
Answer: (B) 50 m, West
Question: James was hiking on a 10-mile loop trail at a rate of 2 miles per hour. Two hours into James’ hike, John started hiking from the same starting point on the loop trail at 4 miles per hour. What is the shortest time that John could hike on the trail in order to meet up with James?
(A) 0.5 hours
(B) 1 hour
(C) 2 hours
(D) 3 hours
(E) 4 hours
Rationale: we don't need to assume here the direction.we need to find which will take less time
so there are 2 cases
1)both moving in same direction...then time would be 2 hours
2)both moving in opposite direction then time would be 1 hour
as we need the shortest time it would be the second case
Answer:B
Answer: (B) 1 hour
Question: A reduction of 20% in the price of oil enables a house wife to obtain 4kgs more for Rs.684, what is the reduced price for kg?
(A) 72
(B) 27
(C) 34
(D) 28
(E) 20
Rationale: 684*(20/100) = 136 ---- 4
? ---- 1 => Rs.34
Answer:C
Answer: (C) 34
Question: Five persons enter the lift of a seven storey building at the ground floor. In how many ways can they get out of lift on any floor other than ground floor
(A) 720
(B) 1296
(C) 1540
(D) 7776
(E) 360
Rationale: Each person out of 5 has 6 floors (options) to get out of (since no one gets out on the ground floor), hence total ways is 6*6*6*6*6=6^5= 7776
Answer: D.
Answer: (D) 7776
Question: Let f(x,y) be defined as the remainder when (x–y)! is divided by x. If x=24, what is the maximum value of y for which f(x,y)=0?
(A) 12
(B) 15
(C) 18
(D) 20
(E) 21
Rationale: The question is finding y such that (24-y)! is a multiple of 24. That means we need to have 2^3*3 in (24-y)!
4! is the smallest factorial number with 2^3*3 as a factor.
24-y = 4
y = 20
The answer is D.
Answer: (D) 20
Question: The average age of a class of 39 students is 15 years. If the age of the teacher be included, then the average increases by3 months. Find the age of the teacher.
(A) 22
(B) 25
(C) 26
(D) 32
(E) 34
Rationale: Sol. Total age of 39 persons = (39 x 15) years
= 585 years.
Average age of 40 persons= 15 yrs 3 months
= 61/4 years.
Total age of 40 persons = (_(61/4 )x 40) years= 610 years.
:. Age of the teacher = (610 - 585) years=25 years.
ANSWER B
Answer: (B) 25
Question: In the fifth grade at Parkway elementary school there are 420 students. 312 students are boys and 250 students are playing soccer. 90% of the students that play soccer are boys. How many girl student are in Parkway that is not playing soccer?
(A) 69.
(B) 83.
(C) 81
(D) 91
(E) 108
Rationale: Total students = 420
Boys = 312, Girls = 108
Total playing soccer = 250
90%of 250 = 225 are boys who play soccer.
Girls who play soccer = 25.
Total girls who do not play soccer = 108 - 25 = 83.
Correct option: B
Answer: (B) 83.
Question: An analysis of the monthly incentives received by 5 salesmen : The mean and median of the incentives is $7000. The only mode among the observations is $12,000. Incentives paid to each salesman were in full thousands. What is the difference between W the highest and the lowest incentive received by the 5 salesmen in the month?
(A) $4000
(B) $5000
(C) $9000
(D) $11,000
(E) $13,000
Rationale: Break down the question in to steps:
Step #1: incentives received by 5 salesmen -->abcde
Step #2: mean and median of the incentives is $7000: via number properties --> total incentives = 7,000 * 5 = 35, 000ab7,000de
Step #3: only mode among the observations is $12,000: mode is the value that appears most often in a set of data. Therefore 12,000 must occur more then once and since 12,000 is larger than the mean (7,000) the most it can occur is twice in our list. If we place the numbers in ascending order we haveab7,00012,00012,000
Step #4: What is the difference between the highest and the lowest incentive:
- The total paid has to equal mean * # of numbers = 7,000 * 5 = 35 000.
- The three values we have so far (12,000 12,000 and 7, 000) equal 31,000.
- Therefore the first two numbers( ab) must equal 4, 000
- There is only one mode which is 12,000, therefore 4,000 must be equal to a set of two numbers that are not the and a < b
if a = 1,000 b = 3,000 --> difference W between the highest and the lowest incentive = 12,000 - 1,000 =11, 000
no other options for a or b to fit the criteria
Final List:1,0003,0007,00012,00012,000
Answer D
Answer: (D) $11,000
Question: The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 7 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
(A) 23 years
(B) 24 years
(C) 25 years
(D) 26 years
(E) 27 years
Rationale: EXPLANATION
Let the average age of the whole team by x years.
11x â€“ (26 + 33) = 9(x -1)
11x â€“ 9x = 50 2x =50
x = 25.
So, average age of the team is 25 years.
Answer C
Answer: (C) 25 years
Question: A man rows his boat 95 km downstream and 45 km upstream, taking 2 1/2 hours each time. Find the speed of the stream?
(A) 10 kmph
(B) 6 kmph
(C) 5 kmph
(D) 8 kmph
(E) 7 kmph
Rationale: Speed downstream = d/t = 95/(2 1/2) = 38 kmph
Speed upstream = d/t = 45/(2 1/2) = 18 kmph
The speed of the stream = (38 - 18)/2 = 10 kmph
Answer:A
Answer: (A) 10 kmph
Question: Apple,INC recently conducted a survey and found that 50,000 of its customers live in rural areas. if the number of it customers who live in urban areas is 200 percents grater than the numbers of customers who live in rural areas, how many of Apple,INC customers live in urban areas ?
(A) 150,000
(B) 216,000
(C) 360,000
(D) 480,000
(E) 540.0
Rationale: Let's say that we have a starting value of X...
100% of X = X
100% MORE than X = X + X = 2X
200% MORE than X = X + 2X = 3X
300% MORE than X = X + 3X = 4X
Etc.
Here, we're told that 50,000 customers live in rural areas and the number who live in urban areas is 200% GREATER than the number who live in rural areas. That means that the number who are in urban areas is 3 times the number in rural areas...
3(50,000) = 150,000
Final Answer:A
Answer: (A) 150,000
Question: The present age of the father is 4years more than 4 times the age of his son. 4 years hence, father's age will be 20 years more than twice the age of the son. Find the present age of the father?
(A) 25
(B) 56
(C) 45
(D) 36
(E) 44
Rationale: Let the son's present age be x years
father's present age = (4x+4)
4x+4+4 = 2(x+4)+10
4x+8 = 2x+18
x = 5
father's present age = 4x+4 = 4*10+4 = 44 years
Answer is E
Answer: (E) 44
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.8700. If his salary for the month of May is Rs.6500, find his salary for the month of January?
(A) s.3700
(B) s.4570
(C) s.4500
(D) s.4550
(E) s.2500
Rationale: 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 * 8700
= 34800 ----(2)
(2)-(1) i.e. May - Jan = 2800
Salary of May is Rs.6500
Salary of January = Rs.3700
Answer:A
Answer: (A) s.3700
Question: Divide 110 into two parts so that one will be 150 percent of the other. What are the 2 numbers?
(A) 42 and 68
(B) 43 and 77
(C) 47 and 66
(D) 44 and 56
(E) 44 and 66
Rationale: E
44 and 66
Answer: (E) 44 and 66
Question: Difference between two numbers is 5, six times of the smaller lacks by 6 from the four times of the greater. Find the numbers?
(A) 12, 9
(B) 12,7
(C) 7, 14
(D) 13,12
(E) 12,8
Rationale: x â€“ y = 5
4x â€“ 6y = 6
x = 12 y = 7
Answer B
Answer: (B) 12,7
Question: From a container having pure milk, 20% is replaced by water and the process is repeated thrice. At the end of the third operation, the milk is
(A) 40% pure
(B) 50% pure
(C) 51.2% pure
(D) 58.8% pure
(E) None
Rationale: Solution
Let total quantity of original milk = 100 gm.
Milk after first operation = 80% of 1000
‹=› 800gm.
Milk after second operation = 80% of 800
‹=› 640gm.
Milk after third operation = 80% of 640
‹=› 512gm.
Strength of final mixtures = 51.2%.
Answer C
Answer: (C) 51.2% pure
Question: If Y is the smallest positive integer that is not prime and not a factor of 50!, what is the sum of the factors of Y?
(A) 162
(B) 54
(C) 72
(D) 51
(E) 50!+2
Rationale: In fact 51=3*17 IS a factor of 50!.
The smallest positive integer that is NOT prime and NOT a factor of 50! is 106=2*53. The sum of the factors of 106 is 162.
Answer: A.
Answer: (A) 162
Question: Ramesh purchased a refrigerator for Rs. 12500 after getting a discount of 20% on the labelled price. He spent Rs. 125 on transport and Rs. 250 on installation. At what price should it be sold so that the profit earned would be 10% if no discount was offered?
(A) 34778
(B) 26888
(C) 2899
(D) 17600
(E) 12778
Rationale: Price at which the TV set is bought = Rs. 12,500
Discount offered = 20%
Marked Price = 12500 * 100/80 = Rs. 15625
The total amount spent on transport and installation = 125 + 250 = Rs. 375\Total price of TV set = 15625 + 375 = Rs. 16000
The price at which the TV should be sold to get a profit of 10% if no discount was offered = 16000 * 110/100
= Rs. 17600
Answer: D
Answer: (D) 17600
Question: How long does a train 110 m long traveling at 60 kmph takes to cross a bridge of 170 m in length?
(A) 12.8 sec
(B) 12.9 sec
(C) 13.9 sec
(D) 16.8 sec
(E) 12.3 sec
Rationale: D = 110 + 170 = 280 m
S = 60 * 5/18 = 50/3
T = 280 * 3/50 = 16.8 sec
Answer:D
Answer: (D) 16.8 sec
Question: What is the least number which when divided by 7, 9, 12 and 18 leaves remainder 4 in each care?
(A) 230
(B) 240
(C) 236
(D) 256
(E) 266
Rationale: Explanation:
LCM of 7, 9, 12 and 18 is 252
Required number = 252 + 4 = 256
Answer: Option D
Answer: (D) 256
Question: How many multiples of 10 are there between 10 and 290 ?
(A) 8
(B) 18
(C) 27
(D) 51
(E) 60
Rationale: It should be mentioned whether 10 and 290 are inclusive.
If 10 and 290 are inclusive, then the answer is (290-10)/10+1=29.
If 10 and 290 are NOT inclusive, then the answer is (280-20)/10+1=27.
Since OA is C, then we have NOT inclusive case.
Answer: (C) 27
Question: Solve This
5 + 4 + 1 = 145
8 + 2 + 3 = 328
9 + 6 + 5 = 569
4 + 0 + 2 = 204
Then, 7 + 7 + 4 = ???
(A) 407
(B) 417
(C) 477
(D) 427
(E) 584
Rationale: 477
ANSWER:C
Answer: (C) 477
Question: The length E of a rectangle is decreased by 15% and its width is increased by 40%. Does the area of the rectangle decrease or increase and by what percent?
(A) Decreases by 19%
(B) Decreases by 25%
(C) Increases by 6%
(D) Increases by 19%
(E) Increases by 25%
Rationale: Let the length E of the rectangle be 100x, and width be 100y. Area = 100x * 100y = 10000xy
Now after the change Length = 85x, and width = 140 y. Area = 11900xy
% Change = (11900xy - 10000xy)/(10000xy) = 19 % Increase. Hence D.
Answer: (D) Increases by 19%
Question: P can do a work in 24 days. Q can do the same work in 9 days and R can do the same in 12 days. Q and R start the work and leave after 3 days. P finishes the remaining work in --- days.
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Rationale: Explanation :
Work done by P in 1 day = 1/24
Work done by Q in 1 day = 1/9
Work done by R in 1 day = 1/12
Work done by Q and R in 1 day = 1/9 + 1/12 = 7/36
Work done by Q and R in 3 days = 3×7/36 = 7/12
Remaining work = 1 – 7/12 = 5/12
Number of days in which P can finish the remaining work = (5/12) / (1/24) = 10
Answer : Option D
Answer: (D) 10
Question: Eight friends met for lunch at an expensive restaurant, and everyone decided to contribute equally to the total bill of $480. If one of the friends had a coupon for 25% off the total bill, and if each friend still contributed equally after the coupon was applied to the bill, how much did each friend pay?
(A) $90
(B) $70
(C) $45
(D) $37
(E) $35
Rationale: 480 * 0,25 = 120
480 - 120 = 360
360 / 8 = 45
Answer C
Answer: (C) $45
Question: Four person are chosen at random from a group of 3 men, 2 women and 4 children. The chance that exactly 2 of them are children, is
(A) 1/9
(B) 1/5
(C) 1/12
(D) 10/21
(E) 4/6
Rationale: n(S)=9C4=126
n(E)=4C2x5C2=60
P(E)=10/21
ANSWER D 10/21
Answer: (D) 10/21
Question: Find the mean proportional between 64 & 81?
(A) A)59
(B) B)61
(C) C)63
(D) D)72
(E) E)67
Rationale: Formula = √a×b
A = 64 and B = 81
√64×81 = 8 × 9 = 72
D
Answer: (D) D)72
Question: The product of the prime integers between 43 and 50, inclusive, is:
(A) 50! – 40!
(B) 99,029
(C) 2,303
(D) 2,021
(E) 2,000
Rationale: Prime integers with in the range specified is 43,47
Product results as = 43X47 = 2021
ANSWER:E
Answer: (E) 2,000
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 2?
(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 B
Answer: (B) B)2
Question: In the xy-plane, the points (c, d), (c, -d), and (-c, -d) are three vertices of a certain square. If c < 0 and d > 0, which of the following points N is in the same quadrant as the fourth vertex of the square?
(A) (-5, -3)
(B) (-5, 3)
(C) (5, -3)
(D) (3, -5)
(E) (3, 5)
Rationale: The question:In the xy-plane, the points N=(c, d), (c, -d), and (-c, -d) are three vertices of a certain square.If c < 0 and d > 0,which of the following points is in the same quadrant as the fourth vertex of the square?
I marked the tricky part in red. It seems c is anegativenumber and d is a positive number. This means
Vertex #1 = (c, d) is in QII (that is, negative x and positive y)
Vertex #2 = (c, -d) is in QIII (that is, both xy negative)
Vertex #3 = (-c, -d) is in QIV (that is y is negative, but x is positive)
That means the last vertex should be in the first quadrant --- the only first quadrant point is (5, 3), answer =E.
Answer: (E) (3, 5)
Question: 0.05 x 0.0173 is equal to:
(A) 8.65 x 10(power -4)
(B) 6.84 x 10(power -4)
(C) 4.68 x 10(power -4)
(D) 5.48 x 10(power -4)
(E) None of them
Rationale: 5 x 173 = 865. Sum of decimal places = 6.
So, 0.05 x 0.0173 = 0.000865 = 8.65 x 10(power -4)
Answer is A.
Answer: (A) 8.65 x 10(power -4)
Question: A loan of Rs.700 is made at 9.5% simple interest for 4 months. How much interest is owed when the loan is due?
(A) 22.167
(B) 23.167
(C) 24.167
(D) 25.167
(E) 26.167
Rationale: si=p*r*t/100
=700*9.5*4/100*12
=22.167
ANSWER:A
Answer: (A) 22.167
Question: If a number is 30% more than the another, how much % is the smaller number less than the first ?
(A) 23%
(B) 25%
(C) 16(1/3)%
(D) 17%
(E) none of these
Rationale: Take a number 100,
Then the other number is 130
% the smaller number is less than the first = [(30/(130)) x 100]% = 23%.
ANSWER:A
Answer: (A) 23%