mathewhe/aqua_rat huggingface dataset:
Question: The speed of a car increases by 2 kms after every one hour. If the distance travelling in the first one hour was 40 kms. what was the total distance traveled in 12 hours?
(A) 252 kms
(B) 152 kms
(C) 612 kms
(D) 752 kms
(E) 152 kms
Rationale: Explanation:
Total distance travelled in 12 hours =(40+42+44+.....upto 12 terms)
This is an A.P with first term, a=40, number of terms,
n= 12,d=2.
Required distance = 12/2[2 x 40+{12-1) x 2]
=6(102)
= 612 kms.
Answer: C
Answer: (C) 612 kms
Question: he average of 10 numbers is 23. If each number is increased by 4, what will the new average be?
(A) 26
(B) 27
(C) 88
(D) 99
(E) 12
Rationale: Sum of the 10 numbers = 230
If each number is increased by 4, the total increase =
4 * 10 = 40
The new sum = 230 + 40 = 270 The new average = 270/10 = 27.
Answer: B
Answer: (B) 27
Question: If x is a positive integer, and two sides of a certain triangle have lengths 5x+1 and x respectively, which of the following could be the length of the third side of the triangle?
I. x + 1
II. x + 0
III. 8x
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II and III
Rationale: Let the third side of triangle be AB
Triangle rule states that:
Difference of other 2 sides < any side < sum of other two sides
So 5x+1 - (x) < AB < 5x+1 + (x)
i.e. 4x + 1 < AB < 6x + 1
Let's take x = 1 :
So 5 < AB < 7
Check if the options lies between 5 and 7.
I: x+1 = 2 ; could be a possible value.
II: x+0 = 1 ; could be a possible value.
III: 8x = 8; could not be a possible value.
I and II could be a possible value.
Answer: C
Answer: (C) I and II only
Question: A certain list consists of 21 different numbers. If n is in the list and n is 7 times the average (arithmetic mean) of the other 20 numbers in the list, then n is what fraction of the sum of the 21 numbers in the list?
(A) 7/27
(B) 1/6
(C) 1/5
(D) 4/21
(E) 5/21
Rationale: series : a1, a2....a20,n
sum of a1+a2+...+a20 = 20*x (x = average)
so, n = 7*x
Hence, a1+a2+..+a20+n = 27x
So, the fraction asked = 7x/27x = 7/27
Answer A
Answer: (A) 7/27
Question: The smallest of three consecutive even integers is 40 less than three times the largest. What is the largest of these integers?
(A) 14
(B) 17
(C) 18
(D) 19
(E) 20
Rationale: let the three numbers be a,b and c..
now The smallest of three consecutive even integers is 40 less than three times the largest means 3c-40=a..
3c-a=40..
2c+c-a=40..
c-a=4, as a,b,and c are consecutive even integers..
2c+4=40..
2c=36 or c=18
ANSWER:C
Answer: (C) 18
Question: A car after travelling 100 km from point A meets with an accident and then proceeds at 3/4 of its original speed and arrives at the point B 90 minutes late. If the car meets the accident 60 km further on, it would have reached 15 minutes sooner. Find the original speed of the train?
(A) 60km/hr
(B) 80km/hr
(C) 100km/hr
(D) 120km/hr
(E) None of these
Rationale: Explanation :
let distance between A and B be D km and real speed of the car be S km/hr
First time car takes 90 minutes more and second time car takes 75 minutes more than scheduled time.
So, T1 – T2 = 15/60 = 100
15/60 = [100/s + (D -100)/(3s/4)] – [160/s + (D – 160)/(3s/4)] Solve this D will be cancelled and S comes out to be 80km/hr
Answer –B
Answer: (B) 80km/hr
Question: A 220 metres long train running at the speed of 120 kmph crosses another train running in opposite direction at the speed of 80 kmph in 9 seconds. What is the length of the other train?
(A) 230m
(B) 240m
(C) 250m
(D) 260m
(E) 280m
Rationale: speed = (120 + 80)km/h (because direction is opposite hence relative velocity is added)= 500/9 m/s
time= 9sec
let the lenght of second train is x
total distance covered= 220 + x
therefore, D= speed*time
thus 220 + x = 500/9 * 9
x= 500-220=280 m
ANSWER:E
Answer: (E) 280m
Question: A restaurant has 89 yellow dishes and 11 white dishes. If I go there with my wife, and we ordered one service each one, what is the probability that both dishes will be white?
(A)  1/100
(B)  2/100
(C)  1/90
(D)  2/90
(E)  1/89
Rationale: There are 11 white dishes in a group of 89 + 11 that is 100 dishes. Thus the probability of taking 2 white dishes is: (11/100)(10/99) = 1/90. The correct answer is C.
Answer: (C)  1/90
Question: The average of 9 numbers is 13.8. If the average of the first five numbers is 13.6 and that of the last five numbers is 13.4,then the middle number is?
(A) 11.8
(B) 10.8
(C) 9.8
(D) 8.8
(E) 8.6
Rationale: Middle number = 13.6*5 + 13.4*5- 13.8*9 = 68+67-124.2=10.8
Answer is B
Answer: (B) 10.8
Question: A bank offers 4.5% compound interest calculated on half-yearly basis. A customer deposits $ 1500 in 1st month. At the end of the year, the amount he would have gained by way of interest is?
(A) 100
(B) 90
(C) 60
(D) 77
(E) 85
Rationale: Amount = (1500)* (1 + (4.5/2*100))^2
Amount = 1500 * (1+0.0225)^2 = 1577 ------(for investment in 1st month)
Interest = 1577-1500 = 77.............. Ans -D
Answer: (D) 77
Question: According to a survey, at least 80% of people like apples, at least 75% like bananas and at least 80% like cherries. What is the minimum percentage of people who like all three?
(A) 15%
(B) 20%
(C) 25%
(D) 0%
(E) 35%
Rationale: It seems that something is wrong with your answer options.
1) minimum applesbananas:
[XXXXXXXXXXXXXX------] - apples
[-----XXXXXXXXXXXXXXX] - bananas
mimimum ab = 80 - (100-75) = 55%
2) minimum (applesbananas)cherries:
[XXXXXXXXX-----------] - applesbananas
[----XXXXXXXXXXXXXXXX] - cherries
mimimum ab = 55 - (100-80) =35%
E
Answer: (E) 35%
Question: What is the volume of an tetrahedron with edge length of 1?
(A) sqr(2)/12 = 0.11785113
(B) sqr(2)/14=0.13571785
(C) sqr(2)/12=0.15798562
(D) sqr(2)/13=0.21254478
(E) sqr(2)/12=0.12457896
Rationale: The following can be derived using the Pythagorean theorem:
The height of a face is 3.5/2.
The area of any face is 3.5/4.
The distance from any corner to the center of a joining face is 1/3.5.
The height of the tetrahedron is (2/3).5
The area is 1/3*base*height =
(1/3) * 3.5/4 * (2/3).5 = 21/2/12.
Answer: (A) sqr(2)/12 = 0.11785113
Question: Solve the given two equations and find the inequality of X and Y. (a) 225X^2-4 = 0 and (b) (225y)^(1/2) +2 = 0
(A) If x>y
(B) If x>=y
(C) If x<y
(D) If x<=y
(E) x=y or relationship cannot be established
Rationale: Solution:-
X= +2/15 and -2/15
Y= 4/225
Comparing we get X>Y and X<Y
Hence, no relationship can be established
E
Answer: (E) x=y or relationship cannot be established
Question: A sum of Rs. 1800 amounts to Rs. 9000 in 4 years at the rate of simple interest. What is the rate of interest?
(A) 50%
(B) 75%
(C) 100%
(D) 60%
(E) 25%
Rationale: S.I. = (9000 - 1800) = Rs. 7200\
Rate = (100 * 7200) / (1800* 4)
= 100%
Answer: C
Answer: (C) 100%
Question: Look at this series: 14, 7, (7/2), (7/4), ... What number should come next?
(A) 1/8
(B) 3/8
(C) 7/8
(D) 5/8
(E) 6/8
Rationale: Explanation:
28/2 = 14
14/2 = 7
7/2 = 7/2
(7/2)/2 = 7/4
(7/4)/2 = 7/8 and so on.
Answer: Option C
Answer: (C) 7/8
Question: A pharmacist has 4 quarts of a 15% solution of iodine. How much alcohol must be added to
reduce it to a 10% solution of iodine?
(A) 1 quart
(B) 2 quarts
(C) 3 quarts
(D) 4 quarts
(E) 5 quarts
Rationale: What’s being added? Hopefully, you said alcohol. Therefore our equation will look like this:
ALCOHOL + ALCOHOL = ALCOHOL
4 qts + x qts = (4 + x) qts
We start off with 4 quarts, add x quarts, then end up with (4 + x) quarts.
+ =
4 x (4 + x)
Notice that you started with 4 quarts and added x quarts on the left side of the equation and you
ended up with (4 + x) on the other side. The parentheses indicate that it’s one container, Neato!
Of the original 4 quarts, 15% is iodine. Since we are doing the problem in terms of what we are
adding – alcohol, we must change 15% iodine solution to an 85% solution of alcohol. Let’s write
the equation.
.85(4) + x = .90(4x)
Where’d the .90 come from? Well, since I wanted to end up with a 10% solution of iodine, that
meant it must be a 90% solution of alcohol.
Multiplying both sides of the equation by the common denominator – 100, we have
85(4) + 100x = 90(4 + x)
340 + 100x = 360 + 90x
10x = 20
x = 2
You would have to add 2 quarts of alcohol to reduce the mixture to 10% iodine.
correct answer B
Answer: (B) 2 quarts
Question: If x ¤ y = (x + y)^2 - (x - y)^2. Then √2 ¤ √2 =
(A) 0
(B) 8
(C) 10
(D) 15
(E) 20
Rationale: X = √2 and Y also =√2
Applying the function (√2+√2)^2 - (√2-√2)^2 = (2√2)^2 - 0 = 4 x 2 = 8.
Note: Alternative Approach is the entire function is represented as X^2 - Y^2 = (X+Y)(X-Y) which can be simplified as (x+y+x-y)(x+y-(x-y)) = (2x)(2y)=4xy. Substituting x=√2 and y = √2 you get the answer 8.
Answer B
Answer: (B) 8
Question: The first Republic Day of India was celebrated on 26th January, 1950. It was :
(A) Tuesday
(B) Wednesday
(C) Thursday
(D) Friday
(E) None of these
Rationale: 26th Jan., 1950 = (1949 years + Period from 1st Jan.,1950 to 26th Jan., 1950)
1600 years have 0 odd day. 300 years have 1 odd day.
49 years = (12 leap years + 37 ordinary years)
= [(12 × 2) + (37 × 1)] odd days = 61 odd days
= 5 odd days.
Number of days from 1st Jan. to 26th Jan. = 26
= 5 odd days
Total number of odd days = (0 + 1 + 5 + 5) = 11
= 4 odd days
∴ The required days was ‘Thursday’
Answer C
Answer: (C) Thursday
Question: The length of the bridge, which a train 130 metres long and travelling at 45 km/hr can cross in 30 seconds, is:
(A) 247 m
(B) 256 m
(C) 245 m
(D) 527 m
(E) 725 m
Rationale: Speed = [45 X 5/18] m/sec = [25/2] m/sec Time
= 30 sec Let the length of bridge be x metres. Then, (130 + x)/30
= 25/2 => 2(130 + x)
= 750 => x = 245 m.
Answer:C
Answer: (C) 245 m
Question: What is the reciprocal of (AB)/(A+B)^2?
(A) (AB)/(A^2+2AB+B^2)
(B) A/B+B/A+AB
(C) B/A+A/B+2
(D) (A+B)^2/AB
(E) A/B+2AB
Rationale: Answer:
Reciprocal = (A+B)^2/AB
= (A^2+B^2+2AB)/AB = B/A + A/B +2
ANSWER:C
Answer: (C) B/A+A/B+2
Question: 8 couples attend a dance show in a TV channel. A lucky draw in which 4 persons picked up for a prize is held, then the probability that there is at least 1 couple will be selected is :
(A) 1/41
(B) 11/23
(C) 15/39
(D) 15/18
(E) 21/31
Rationale: P( selecting atleast one couple) = 1 - P(selecting none of the couples for the prize)
= 15/39
C
Answer: (C) 15/39
Question: A courier charges for packages to a certain destination are 65 cents for the first 250 grams and 10 cents for each additional 100 grams or part thereof. What could be the weight in grams of a package for which the charge is $1.75?
(A) 1280
(B) 1145
(C) 1040
(D) 950
(E) 260
Rationale: The charge is 65 cents for the first 250 grams.
This leaves a charge of $1.75 - $0.65 = $1.10
The charge for the next 1000 grams is $1.00 which leaves a charge of $0.10
The weight is somewhere between 1250 and 1350.
The answer is A.
Answer: (A) 1280
Question: 40 liters of a mixture is created by mixing Liquid P and Liquid Q in the ratio 5:3. How many liters of Liquid Q must be added to make the ratio 5:6?
(A) 5
(B) 8
(C) 10
(D) 12
(E) 15
Rationale: Let x be the amount of liquid Q to be added.
(3/8)*40 + x = (6/11)*(40+x)
1320 + 88x = 1920 + 48x
40x = 600
x = 15
The answer is E.
Answer: (E) 15
Question: In a store 6 different CDs are there. If John can buy 2 CDs, how many cases that he can buy are there?
(A) 12
(B) 15
(C) 18
(D) 21
(E) 24
Rationale: Let CDs are A, B, C, D, E, F
He may choose any pair as mentioned below
AB, AC, AD, AE, AF = 5 cases
BC, BD, BE, BF = 4 cases
CD, CE, CF = 3 cases
DE, DF = 2 cases
EF = 1 case
Total cases = 5+4+3+2+1 = 15
Answer: Option B
Answer: (B) 15
Question: What percent of a day is 15 hours?
(A) 37Ã—1/2%
(B) 16Ã—1/2%
(C) 18Ã—2/3%
(D) 22Ã—1/2%
(E) None
Rationale: Solution
Required percentage	= (15/24Ã—100)%
= (75 / 2)%.
= 37Ã—1/2%.
Answer A
Answer: (A) 37Ã—1/2%
Question: If P * Q implies (P2 + Q2), 8 * (3 * 2) = ?
(A) 239
(B) 278
(C) 233
(D) 2697
(E) 771
Rationale: Explanation:
We have, P * Q = (P2 + Q2) ......... Given
8 * (3 * 2) = ?
8 * 13 = (64 +169) = 233
ANSWER: C
Answer: (C) 233
Question: Anil and Suresh are working on a special assignment. Anil needs 6 hours to type 32 pages on a computer and Suresh needs 5 hours to type 40 pages. If both of them work together on two different computers, how much time is needed to type an assignment of 100 pages?
(A) 8 hours 30 mins
(B) 8 hours
(C) 9 hours
(D) 7 hours
(E) 6 hours
Rationale: Pages typed by Anil in 1 hour = 32/6 = 16/3
Pages typed by Suresh in 1 hour = 40/5 = 8
Pages typed by Anil and Suresh in 1 hour = 16/3 + 8 = 40/3
Time taken to type 100 pages when Anil and Suresh work together = 100 × 3 /40 = 75/10
= 7 1/2 hours = 7 hour 30 minutes
Answer is A.
Answer: (A) 8 hours 30 mins
Question: Country X taxes each of its citizens an amount equal to 10 percent of the first $40,000 of income, plus 20 percent of all income in excess of $40,000. If a citizen of Country X is taxed a total of $8,000, what is her income?
(A) $40,000
(B) $56,000
(C) $60,000
(D) $66,667
(E) $80,000
Rationale: Equation is correct, so math must be a problem.
0.10*40,000+0.2*(x-40,000)=8,000 --> 4,000+0.2x-8,000=8,000 --> 0.2x=12,000 --> x=60,000.
Answer: C.
Answer: (C) $60,000
Question: The total weight of eight nougat nuggets is 3 oz. What is the average (arithmetic mean) weight of one such nougat nugget?
(A) 0.18 oz.
(B) 0.375 oz.
(C) 1.8 oz.
(D) 5 oz.
(E) 18 oz
Rationale: Average = Total/Number of items
= 3/8 = 0.375.
Hence, B
Answer: (B) 0.375 oz.
Question: Last year a certain bond price with a face value of 5000 yielded 6% of its face value in interest. If that interest was approx 6.5 of the bond's selling price approx what was the bond's selling price?
(A) 4615
(B) 5325
(C) 5351
(D) 6000
(E) 6154
Rationale: Interest = 0.06*5000 = 0.065*selling price --> selling price = 0.06*5000/0.065 --> selling price = ~4,615
Answer: A.
Answer: (A) 4615
Question: On a map, 1 inch represents 28 miles. How many Z inches would be necessary to represent a distance of 383.6 miles?
(A) 5.2
(B) 7.4
(C) 13.7
(D) 21.2
(E) 28.7
Rationale: Z inches necessary to represent a distance of 383.6 miles = 383.6/28
= 13.7
Answer C
Answer: (C) 13.7
Question: Three friends A, B and C decided to share a lot of apples. Each of them had half of the total plus half an apple in order. After each of them took their share thrice, no apples were left.How many apples were there?
(A) 500
(B) 510
(C) 511
(D) 501
(E) 504
Rationale: Whenever the rate of reduction is 'half of the total and half of it', the answer is always (2^n)-1, where 'n' is the number of times the process is repeated. Here, the process is repeated 9 times. So answer is (2^9)-1=511.
ANSWER:C
Answer: (C) 511
Question: 4 years ago, Paula was 4 times as old as Karl. In 12 years, Paula will be twice as old as Karl. What is the sum of their ages now?
(A) 36
(B) 40
(C) 44
(D) 48
(E) 52
Rationale: P-4 = 4(K-4) and so P = 4K-12
P+12 = 2(K+12)
(4K-12)+12 = 2K+24
K = 12
P = 36
P+K = 48
The answer is D.
Answer: (D) 48
Question: Find the average of the series : 220, 180, 328, 147 and 160?
(A) 230
(B) 200
(C) 250
(D) 201
(E) 207
Rationale: Average = (220 + 180 + 328 + 147 + 160)/5
= 1035/5
= 207
Answer: E
Answer: (E) 207
Question: If 20% of a number = 1000, then 120% of that number will be?
(A) 20
(B) 120
(C) 360
(D) 6000
(E) 820
Rationale: Let the number x. Then,
20% of x = 1000
x = (1000 * 100)/20 = 5000
120% of x = (120/100 * 5000) = 6000.
ANSWER:D
Answer: (D) 6000
Question: In a LAB experiment, a 100 ml compound of element X and element Y needs to be increased to 300 ml by adding some quantity of element X, and some quantity of element Y. If the original compound contains 40% of element X, how much (in ml) of element Y must be added so that element X will be exactly one third of the resulting mixture ?
(A) 40 ml
(B) 100/3 ml
(C) 140 ml
(D) 20/3 ml
(E) 10 ml
Rationale: There are 0.4*100=40 ml of element X in the initial solution.
We need X to be 1/3rd of 300 ml in the resulting solution, so 100 ml. Thus out of 200 ml of solution added, 60 must be X (in order it to become 100 ml) ans the remaining 140 must be Y.
Answer: C
Answer: (C) 140 ml
Question: What is the probability that the position in which the consonants appear remain unchanged when the letters of the word "Math" are re-arranged?
(A) 1/4
(B) 1/6
(C) 1/3
(D) 1/24
(E) 1/12
Rationale: Explanatory Answer
Step 1: Compute denominator
In any probability question, the denominator represents the total number of outcomes for an event. The numerator represents the number of favorable outcomes.
The total number of ways in which the word MATH can be re-arranged = 4! = 4*3*2*1 = 24 ways.
Step 2: Compute numerator and the probability
If the positions in which the consonants appear do not change, the first, third and the fourth positions are reserved for consonants and the vowel A remains at the second position.
The consonants M, T and H can be re-arranged in the first, third and fourth positions in 3! = 6 ways so that the positions in which the positions in which the consonants appear remain unchanged.
Therefore, the required probability 6/24=/14
Choice A
Answer: (A) 1/4
Question: Of the 3,600 employees of Company X, 1/3 are clerical. If the clerical staff were to be reduced by 1/4, what percent of the total number of the remaining employees would then be clerical?
(A)  25%
(B)  28.1%
(C)  20%
(D)  12.5%
(E)  11.1%
Rationale: Welcome, just post the question and the choices
Let's see, the way I did it was
1/3 are clerical out of 3600 so 1200 are clerical
1200 reduced by 1/4 is 1200*1/4
so it reduced 300 people , so there is 900 clerical people left
but since 300 people left, it also reduced from the total of 3600 so there are 3300 people total
since 900 clerical left / 3200 people total
Answer : B
Answer: (B)  28.1%
Question: You have a bag of 9 letters: 3 Xs, 3 Ys and 3 Zs. You are given a box divided into 3 rows and 3 columns for a total of 9 areas. How many different W ways can you place one letter into each area such that there are no rows or columns with 2 or more of the same letter?
(A) 5
(B) 6
(C) 9
(D) 12
(E) 18
Rationale: Consider one particular arrangement of the first row: XYZ, then we can construct only two boxes with so that no rows or columns have 2 or more of the same letter:
XYZ
YZX
ZXY
And:
XYZ
ZXY
YZX
Now, the first row itself can be arranged in 3!=6 ways (since there are three distinct letter), hence the total number of boxes possible W is 2*6=12.
Answer: D.
Answer: (D) 12
Question: {-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10}
A number is to be selected at random from the set above. What is the probability that the number selected will be a solution of the equation (x-5)(x+10)(2x-5) = 0?
(A) 1/12
(B) 1/6
(C) 1/4
(D) 1/3
(E) 1/2
Rationale: Roots of the equation (x-5)(x+10)(2x-5)=0 are x=5, x=-10 and x=5/2=2.5. So, two solutions present in our set of 12 distinct numbers, therefore P=2/12=1/6.
Answer: B.
Answer: (B) 1/6
Question: At a certain high school, the senior class is twice the size of the junior class. If 7/8 of the seniors and 1/2 of the juniors study Japanese, what fraction of the students in both classes study Japanese?
(A) 3/4
(B) 1/2
(C) 1/4
(D) 3/8
(E) 5/16
Rationale: Start by deciding on a number of students to represent the number of students in the senior class. For this example I will choose 200 students. That would make the number of students in the junior class 100. Then we can find out how many students are taking Japanese in each grade and add them together. (7/8)*200=175 and (1/2)*100=50. 175+50=225. There are a total of 300 students in the junior class and senior class combined (100+200=300), and there are 225 total students in Japanese, so 225 students in Japanese / 300 total students equals 3/4 of the students in both classes that study Japanese.
Answer: A
Answer: (A) 3/4
Question: A bat is bought for Rs.400 and sold at a gain of 20% find its selling price?
(A) Rs.430/-
(B) Rs.440/-
(C) Rs.480/-
(D) Rs.490/-
(E) Rs.500/-
Rationale: 100 % ------> 400 (100 * 4 = 400)
120 % ------> 480 (120 * 4 = 480)
Selling price = Rs.480/-
C
Answer: (C) Rs.480/-
Question: The ratio of two quantities is 5 : 8. If each of the quantities is increased by 10, what is the ratio of the new quantities?
(A) 5:8
(B) 50:78
(C) 2:3
(D) It cannot be determined from the information given.
(E) 6:7
Rationale: Since the ratio is 5:8 we can put the quantities as 5K and 8K.
Moreover increasing quantities implies that the quantities become 5K+10 and 8K+10. So the ratio is (5K+10):(8K+10). The ratio value depend on the value of K. So It cannot be determined from the information given.
The answer is D
Answer: (D) It cannot be determined from the information given.
Question: $364 is divided among A, B, and C so that A receives half as much as B, and B receives half as much as C. How much money is C's share?
(A) $200
(B) $204
(C) $208
(D) $212
(E) $216
Rationale: Let the shares for A, B, and C be x, 2x, and 4x respectively.
7x = 364
x = 52
4x = 208
The answer is C.
Answer: (C) $208
Question: If the tens digit of positive integers q, y are 6, how many values of the tens digit of 2(q+y) can be there?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: If the tens digit of positive integers q, y are 6, how many values of the tens digit of 2(q+y) can be there?
A. 2
B. 3
C. 4
D. 5
E. 6
-> If q=y=60, 2(q+y)=240 is derived. If q=y=69, 2(q+y)=276 is derived, which makes 4,5,6,7 possible for the tens digit. Therefore, the answer is C.
Answer: (C) 4
Question: The difference between a number and its three-fifth is 50. What is the number ?
(A) 75
(B) 100
(C) 125
(D) none of these
(E) 95
Rationale: Let the number be x. Then, x-(3/5)x=50
=>(2/5)*x=50
=>x=(50*5)/2=125
Answer :C
Answer: (C) 125
Question: In the equation 2x â€“ cy = 18, c is a constant. If the value of y is 2 when x is 6, what is the value of x when y is 2 ?
(A) âˆ’9/2
(B) -4
(C) -3
(D) 6
(E) 9/2
Rationale: 2x - cy = 18
x=6, y=2;
12-2c=18
c=-3
2x-cy=18
when y=3, c=-3, x=
x=6
ANSWER:D
Answer: (D) 6
Question: A man can row a distance of 5 km in 60 min with the help of the tide. The direction of the tide reverses with the same speed. Now he travels a further 25 km in 10 hours. How much time he would have saved if the direction of tide has not changed?
(A) 2
(B) 5
(C) 1
(D) 6
(E) 7
Rationale: Explanation:
He covered 5 km in 1 hour , so he might cover 25 km in 5 hours.
But he took 10 hours.
He would have saved 10 â€“ 5 = 5 hours.
Answer: B
Answer: (B) 5
Question: Five machines at a certain factory operate at the same constant rate. If four of these machines, operating simultaneously, take 35 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)  7
(D)  16
(E)  24
Rationale: Total work = 4*35 machine hrs
Time taken = 4* 35 /5 => 28 hours...
Thus all five machines, operating simultaneously will take ( 35 - 28 ) 7 hours..
Answer will be (C) 7
Answer: (C)  7
Question: What least number must be added to 9879, so that the sum is completely divisible by 10 ?
(A) 3
(B) 4
(C) 1
(D) 2
(E) 6
Rationale: If we divide 9879 by 10 remainder is 9
10-9 =1
Answer : C
Answer: (C) 1
Question: IN Common Wealth Games an athlete runs 200 meters in 24 seconds. Hisspeed is ?
(A) 25 km/hr
(B) 27 km/hr
(C) 30 km/hr
(D) 32 km/hr
(E) None of these
Rationale: Explanation :
(200/1000)/(24/3600)=30 km/hr
Answer : C
Answer: (C) 30 km/hr
Question: There are two examinations rooms A and B. If 10 students are sent from A to B, then the number of students in each room is the same. If 20 candidates are sent from B to A, then the number of students in A is double the number of students in B. The number of students in room A is:
(A) 20
(B) 30
(C) 40
(D) 50
(E) 10
Rationale: A
20
Let the number of students in rooms A and B be x and y respectively.
Then, x - 10 = y + 10 x - y = 20 .... (i)
and x + 20 = 2(y - 20) x - 2y = -60 .... (ii)
Solving (i) and (ii) we get: x = 100 , y = 80.
The required answer A = 100.
Answer: (A) 20
Question: Anand and Deepak started a business investing Rs. 6,000 and Rs. 7,000 respectively. Out of a total profit of Rs. 1,300. Deepak's share is?
(A) s. 650
(B) s. 780
(C) s. 800
(D) s. 760
(E) s. 700
Rationale: Ratio of their shares = 6000 : 7000 = 7 : 13
Deepak's share = Rs. (1300 * 7/13) = Rs. 700 ANSWER "E
Answer: (E) s. 700