mathewhe/aqua_rat huggingface dataset:
Question: sowdharya had 90 currency notes in all, some of which are of Rs 95 denomination and the remaining of Rs 45 denomination. The total amount of all these currency notes was Rs. 5000. How much amount (in Rs) did she have in the denomination of Rs 45?
(A) 75
(B) 72
(C) 71
(D) 76
(E) 73
Rationale: Let the number of 45-rupee notes = x
Then, the number of 95-rupee notes = (90 – x)
45x + 95(90 – x) = 5000 : x = 71
ANSWER:C
Answer: (C) 71
Question: Find the constant b so that the three points A(2 , 3), B(4 , 7) and C(8 , b) are collinear (i.e. on the same line).
(A) 5
(B) 10
(C) 15
(D) 20
(E) 25
Rationale: The slope of the line through A and B must be equal to the slope of the line through B and C.
(7 - 3)/(4- 2) = (b - 7)/(8 - 4)
solve the above for b to find b = 15.
correct answer C)15
Answer: (C) 15
Question: A bag contains 7 green and 8 white balls. If two balls are drawn simultaneously, the probability that both are of the same colour is?
(A) 7/19
(B) 7/12
(C) 7/97
(D) 7/29
(E) 7/15
Rationale: Drawing two balls of same color from seven green balls can be done in ⁷C₂ ways.
Similarly from eight white balls two can be drawn in ⁸C₂ ways.
P = ⁷C₂/¹⁵C₂ + ⁸C₂/¹⁵C₂
= 7/15
Answer: E
Answer: (E) 7/15
Question: The music class consists of 5 girls and 7 boys. How many ways can a group of 3 be formed if it has to include at least one boy?
(A) 155
(B) 158
(C) 161
(D) 165
(E) 210
Rationale: Reverse combinatorics approach is preferred method on this one
Note that at least 1 boy gives clue to using this method
All combinations - five girls = answer
All combinations is 12C3 = 220
All girls 5C3 = 10
So our answer is 220-10=210
Hence, answer is (E)
Answer: (E) 210
Question: If x^6 > x^9 > x^11, which of the following could be the value of x?
(A) -1/5
(B) 52
(C) 6
(D) 3
(E) -4.7
Rationale: x^6 > x^9 > x^11
1)Here we have an even power of a variable (x) that is greater than both a larger odd power of the variable x and a smaller odd power of the variable x.
This can be possible only if the base is negative; therefore, the variable, x, must be a negative number.
2) Now if the variable x is negative, the higher power results in a smaller number if x<-1, and a higher power results in a larger number if 0>x>-1.
With this information, we know that x is a negative number less than -1; therefore, E (-4.7) is the only option.
Answer: (E) -4.7
Question: A feed store sells two varieties of birdseed: Brand A, which is 60% millet and 40% sunflower, and Brand B, which is 65% millet and 35% safflower. If a customer purchases a mix of the two types of birdseed that is 50% millet, what percent of the mix is Brand A?
(A) 40%
(B) 60%
(C) 50 %
(D) 45 %
(E) 55 %
Rationale: Yes there is a simple method :
Consider the following method
Brand A : 60% millet and 40% sunflower
Brand B : 65% millet and 35% safflower
Mix : 50% millet
Here the weighted average is 50%,
Now Brand A has 60% millet, which is 10% more than the weighted average of mix = + 0.10 A --------------- I
Similarly, Brand B has 65 % millet, which is 15 % more than the weighted average of mix = + 0.15 B ------------ II
Now, both Brand A and Brand B are combined to give a 50% mix containing millet, so equate I and II
implies, 0.10 A = 0.15 B
Therefore A/B = 0.15/0.10 = 3/2
A : B : (A + B) = 3 : 2 : (3+2) = 3 : 2 : 5
We have to find, percent of the mix is Brand A i.e. A : (A + B) = 3 : 5 = (3 / 5) * 100 = 60 %
Here is a pictorial representation :
Brand A= 60%------------------------10% or 0.10 above average, A times-----------------Total above = + 0.10 A
----------------------------------------------------------------------------------------Average = 50% or 0.50
Brand B = 65 %--------------------------15% or 0.15 above average, B times-----------------Total above = + 0.15 B
Since the amount below the average has to equal the average above the average; therefore,
0.10 A = 0.15 B
A/B = 3/2
A:B: Total = 3:2:5
Therefore
A/Total = 3:5 = 60 %
Answer: B
Answer: (B) 60%
Question: In an institute, 60% of the students are boys and the rest are girls. Further 15% of the boys and 7.5% of the girls are getting a fee waiver. If the number of those getting a fee waiver is 90, find the total number of students getting 50% concessions if it is given that 50% of those not getting a fee waiver are eligible to get half fee concession?
(A) 360
(B) 280
(C) 320
(D) 330
(E) 350
Rationale: Solution: Let us assume there are 100 students in the institute.
Then, number of boys = 60
And, number of girls = 40
Further, 15% of boys get fee waiver = 9 boys
7.5 % of girls get fee waiver = 3 girls
Total = 12 students who gets fee waiver
But, here given 90 students are getting fee waiver. So we compare
12 = 90
So, 1 = 90/12 = 7.5
Now number of students who are not getting fee waiver = 51 boys and 37 girls.
50% concession = 25.5 boys and 18.5 girls (i.e. total 44).
Hence, required students = 44*7.5 = 330.
Answer: Option D
Answer: (D) 330
Question: The parameter of a square is double the perimeter of a rectangle. The area of the rectangle is 480 sq cm. Find the area of the square.
(A) 200
(B) 345
(C) 255
(D) Cannot be determined
(E) 342
Rationale: Let the side of the square be a cm. Let the length and the breadth of the rectangle be l cm and b cm respectively.
4a = 2(l + b)
2a = l + b
l . b = 480
We cannot find ( l + b) only with the help of l . b. Therefore a cannot be found .
Area of the square cannot be found.
Answer: Option D
Answer: (D) Cannot be determined
Question: Find the value of 72519 x 9999 = m?
(A) 673223454
(B) 695546788
(C) 634899013
(D) 725117481
(E) 734576909
Rationale: 72519 x 9999 = 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
D
Answer: (D) 725117481
Question: Find the area of trapezium whose parallel sides are 30 cm and 12 cm long, and the distance between them is 16 cm?
(A) 288 cm2
(B) 277 cm2
(C) 285 cm2
(D) 336 cm2
(E) 340 cm2
Rationale: Area of a trapezium = 1/2 (sum of parallel sides) * (perpendicular distance between them)
= 1/2 (30 + 12) * (16)
= 336 cm2
Answer: D
Answer: (D) 336 cm2
Question: A sum of money invested for a certain number of years at 8% p.a. simple interest grows to Rs.180. The same sum of money invested for the same number of years at 4% p.a. simple interest grows to Rs.120 only. For how many years was the sum invested?
(A) 25
(B) 37
(C) 36
(D) 29
(E) 21
Rationale: Explanation:
From the information provided we know that,
Principal + 8% p.a. interest on principal for n years = 180 …….. (1)
Principal + 4% p.a. interest on principal for n years = 120 ……… (2)
Subtracting equation (2) from equation (1), we get
4% p.a. interest on principal for n years = Rs.60.
Now, we can substitute this value in equation (2),
i.e Principal + 60 = 120
= Principal = Rs.60.
We know that SI = , where p is the principal, n the number of years and r the rate percent of interest.
In equation (2), p = Rs.60, r = 4% p.a. and the simple interest = Rs.60.
Therefore, 60 =(60*n*4)/100
=> n = 100/4 = 25 years.
Answer: A) 25years
Answer: (A) 25
Question: The first term of an arithmetic progression is 3 and the 10 th term is 21. Find 15 th and 22 nd terms.
(A) 21,35
(B) 31,45
(C) 30,46
(D) 29,40
(E) 39,40
Rationale: Exp. a = 3, T 10 = a +9d =21, 3 +9d = 21, d =18/9 = 2
T 15 = a + 14d =3 +14*2 = 31, T22 = a + 21d = 3+ 21*2 = 45
ANSWER:B
Answer: (B) 31,45
Question: Look at this series: 1.25, 7.5, ____, 270, 1620, ... What number should fill the blank?
(A) 50
(B) 65
(C) 45
(D) 55
(E) 40
Rationale: This is a simple multiplication series. Each number is 6 times greater than the previous number.
Answer: C
Answer: (C) 45
Question: Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together?
(A) 4
(B) 10
(C) 15
(D) 16
(E) 17
Rationale: L.C.M of 2,4,6,8,10,12 is 120. i.e after each 2 min they will toll together.So in 30 min they will toll 15 times.As they have initially tolled once,The answer will be 15+1=16.
ANSWER:D
Answer: (D) 16
Question: If the sales tax reduced from 3 1/2 % to 3 1/3%, then what difference does it make to a person who purchases an article with market price of Rs. 9000 ?
(A) 11
(B) 13
(C) 15
(D) 18
(E) 10
Rationale: Required difference = [3 ½ % of Rs.9000] – [3 1/3 % of Rs.9000]
= [(7/20-(10/3)]% of Rs.9000 =1/6 % of Rs.9000
= Rs. [(1/6)8(1/100)*9000] = Rs. 15.
Answer is C.
Answer: (C) 15
Question: Solve this logic number sequence puzzle by the correct digit
8080 = 6
1357 = 0
2022 = 1
1999 = 3
6666 = ?
(A) four (4)
(B) 2
(C) 5
(D) 7
(E) 8
Rationale: A
4
No Of circles in the number.
Answer: (A) four (4)
Question: A fish can go upstream at 35 kmph and downstream at 55 kmph, and then find the speed of the fish in still water?
(A) 45
(B) 55
(C) 35
(D) 65
(E) 70
Rationale: US = 35
DS = 55
M = (35 + 55)/2
= 45
Answer:A
Answer: (A) 45
Question: The average age of a committee of 10 members is 30 years. A member aged 60 years retired and his place was taken by another member aged 40 years . The average age of
present committee is;
(A) 39 years
(B) 28 years
(C) 36 years
(D) 35 years
(E) 37 years
Rationale: Total age of the committee = 30*10 = 300,
Total age when a member is retired
and a new one was joined = 300-60 +40, =280
Average age of present committee = 280/10 = 28.
ANSWER:B
Answer: (B) 28 years
Question: The function f is defined for all the positive integers s by the following rule: f(s) is the number of positive integers each of which is less than s and has no positive factor in common with s other than 1 . if p is a prime number then f(p)?
(A) p-1
(B) p-2
(C) (p+1)/2
(D) (p-1)/2
(E) 2
Rationale: The moment you put a prime number in the function f(s), notice that all the numbers lesser than s have no divisor clashing with divisor of s since s is prime!!.
For instance f(7)= {6, 5, 4, 3, 2, 1}
Thus for f(p) number of integers falling under this set will be p-1
Answer :- A
Answer: (A) p-1
Question: The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs. 14000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is:
(A) 28
(B) 19
(C) 22
(D) 20
(E) 21
Rationale: Let the total number of workers be x. Then,
8000x = (14000 * 7) + 6000(x - 7)
= 2000x = 56000
= x = 28.
ANSWER:A
Answer: (A) 28
Question: Two teams Arrogant and Overconfident are participating in a cricket tournament. The odds that team Arrogant will be champion is 5 to 3, and the odds that team Overconfident will be the champion is 1 to 4. What are the odds that either Arrogant or team Overconfident will become the champion?
(A) 3 to 2
(B) 5 to 2
(C) 6 to 1
(D) 33 to 7
(E) 3 to 8
Rationale: Explanation :
Odds of winning Arrogant is 5/3, then their probability of winning is 5/ (5+3) i.e 5/8.
Similarly,
Odds of winning Overconfident is 1/4, then their probability of winning is 1/ (1+4) i.e 1/5.
Therefore, the probability of winning of Arrogant or Overconfident is :-
=>(5/8) + (1/5).
=>33/40.
Thus, the required odds will be 33/(40-33) i.e 33/7.
Answer : D
Answer: (D) 33 to 7
Question: The smallest number which when diminished by 3, is divisible by 12, 16, 18, 21 and 28 is
(A) 1008
(B) 1011
(C) 1022
(D) 1032
(E) 1043
Rationale: Required Number = (L.C.M of 12, 16, 18,21,28)+3
= 1008 + 3
= 1011
Answer: B
Answer: (B) 1011
Question: Of the 150 people at a party, 70 were women, and 40 women tried the appetizer. If 50 people did not try the appetizer, what is the total number of men who tried the appetizer?
(A) 40
(B) 50
(C) 60
(D) 70
(E) 80
Rationale: Total people at party=150
Women=70
so Men 150-70=80
No. of pple who tried appetizer=150-50 (given info)=100
No of women who tried appetizer=40
So Remaining ppl(men) who tried the appetizer =100-40=60
Correct Option C
Answer: (C) 60
Question: A and B together have Sterling 1230. If 4/15 of A's amount is equal to 2/5 of B's amount, how much amount does B have?
(A) Sterling 460
(B) Sterling 484
(C) Sterling 550
(D) Sterling 492
(E) None
Rationale: Explanation: 4/15A = 2/5B
A = (2/5 x 15/4)B
A = 3/2 B
A/B = 3/2
A : B = 3 : 2.
B's share = Sterling (1230 x 2/5) = Sterling 492.
Answer: Option D
Answer: (D) Sterling 492
Question: Tom opened a shop investing Rs.20000. Jose joined him 8 months later, investing Rs.35000.What will be Tom's and Jose's share of profit ratio after two years?
(A) 4:9
(B) 6:7
(C) 7:6
(D) 5:8
(E) 8:5
Rationale: SoL = ~s- So Tom's and Jose's share of profit ratio= 20*24:35*16 = 6:7
Answer: B
Answer: (B) 6:7
Question: In how many ways, a committee of 7 members can be selected from 6 men and 5 ladies, consisting of 4 men and 3 ladies?
(A) 180
(B) 150
(C) 200
(D) 310
(E) 250
Rationale: (4 men out 6) and (3 ladies out of 5) are to be chosen
Required number of ways = 6C4*5C3 = 150
Answer is B
Answer: (B) 150
Question: If each of 3 digit code is formed of integers from 1 to 20, inclusively, and each of the digits are different, how many possible codes are there?
(A) 6,040
(B) 6,840
(C) 6,240
(D) 6,340
(E) 8,440
Rationale: Code consists of 3 digits and no digit is repeated.
First digit of the code can have 20 possibilities
Second digit can have 19 possibilities
Third digit can have 18 possibilities
Total number of possible codes = 20*19*18 = 6840
Answer: B
Answer: (B) 6,840
Question: The sum of the first 60 positive even integers is 3,660. What is the sum of the first 60 odd integers?
(A) 3600
(B) 3400
(C) 3300
(D) 3200
(E) 3100
Rationale: Sum of first n even numbers = n(n+1) =3660
Sum of first n odd numbers = n^2 = 60*60 = 3600 (here n=60)
Answer : A
Answer: (A) 3600
Question: A trolley which travels at a constant speed and can cover the platform of length 300m in two minute. How long it will take a train of length 200m and having a speed 60kph to pass the trolley?
(A) 11.21
(B) 14.11
(C) 16.32
(D) 18.35
(E) 20.45
Rationale: Speed of the trolley= 300/120= 2.5m/s
Speed of the train = 60kph = 16.67m/s
Relative speed of train with respect to trolley=16.67-2.5 = 14.17m/s
Time taken by the train to pass the trolley= 200/14.17=14.11s
Answer: B
Answer: (B) 14.11
Question: The sector of a circle has radius of 21 cm and central angle 270o. Find its perimeter?
(A) 91.5
(B) 92
(C) 93
(D) 141
(E) 95
Rationale: Perimeter of the sector = length of the arc + 2(radius)
= (270/360 * 2 * 22/7 * 21) + 2(21)
= 141 cm
Answer: Option D
Answer: (D) 141
Question: A sum of Rs.100 is lent at simple interest of 3% p.a. for the first month, 9% p.a. for the second month, 27% p.a. for the third month and so on. What is the total amount of interest earned at the end of the year approximately
(A) Rs.797160
(B) Rs.791160
(C) Rs.65930
(D) Rs.66430
(E) Rs.67430
Rationale: Total amount of Interest is
I = P/100 * 1[3/12 + 9/12 +27/12…. 312/12
Where P = 100; I = 1/12 (3+9+…..312)
I = 1/12(3(312-1))/3-1
= 531440* 3/12*2 =Rs.66430
ANSWER:D
Answer: (D) Rs.66430
Question: A bill is discounted at 10% per annum. If banker's discount is allowed, at what rate percent should the proceeds be invested so that nothing will be lost?
(A) 91/9%
(B) 100/9%
(C) 11
(D) 92/9%
(E) None of these
Rationale: Explanation :
Let the amount = Rs.100
Then BD = Rs.10 (∵ banker's discount, BD is the simple Interest on the face value of the bill for unexpired time and bill is discounted at 10% per annum)
Proceeds = Rs.100 – Rs.10 = Rs.90
Hence we should get Rs.10 as the interest of Rs.90 for 1 year so that nothing will be lost
⇒ 10 = (90 × 1 × R)/100
⇒ R = (10 × 100)/90 = 100/9 Answer : Option B
Answer: (B) 100/9%
Question: If 1/a^2 + a^2 represents the diameter of circle O and 1/a + 4a = 3, which of the following best approximates the circumference of circle O?
(A) 28
(B) 22
(C) 20
(D) 16
(E) 12
Rationale: Given that (1/a)+a =3
Square both sides of the equation:
We get,
[(1/a)^2 + a^2 + 2*(1/a)*a] = 9
=> (1/a)^2 + a^2 + 2 = 9
=> (1/a)^2 + a^2 = 7 ----------------- (1)
Diameter D = (1/a)^2 + a^2
= 7 (From (1))
So Radius = D/2 = 7/2
Circumference = 2*Pi*r
= 2*(22/7)*(7/2)
=12
So the answer should be E.
Answer: (E) 12
Question: A man invested Rs. 1552 in a stock at 97 to obtain an income of Rs. 300. The dividend from the stock is :
(A) 7.5 %
(B) 18.75 %
(C) 9.75 %
(D) None of these
(E) Cannot be determined
Rationale: Solution
By investing Rs. 1552,income = Rs. 128.
By investing Rs. 97, income = Rs. (300/1552x97)= Rs 18.75
âˆ´ Dividend =1 8.75%.
Answer B
Answer: (B) 18.75 %
Question: A person travelled from his house to office at 10km/hr and office to house at 90km/hr. Then find the average speed?
(A) 15km/hr
(B) 18km/hr
(C) 25km/hr
(D) 28km/hr
(E) 33km/hr
Rationale: Average speed = (2*10*90)/(10+90)= 18km/hrAnswer is B
Answer: (B) 18km/hr
Question: Peter can cover a certain distance in 1 hr. 24 min. by covering two-third of the distance at 4 kmph and the
rest at 5 kmph. Find the total distance.
(A) 4 km
(B) 5 km
(C) 6 km
(D) 7 km
(E) 8 km
Rationale: time=distance/speed
let total distance travelled be x in 84/60 hrs
2/3 rd of x travelled in 4 km/hr
1/3 rd of distance travelled in 5 km/hr
2x/(3*4)+x/(3*5)=84/60
x=6 km
ANSWER:C
Answer: (C) 6 km
Question: A goods train runs at the speed of 72 kmph and crosses a 270 m long platform in 26 seconds. What is the length of the goods train?
(A) 230 m
(B) 250m
(C) 643m
(D) 832m
(E) 270m
Rationale: Speed =	(72 x	5/18)m/sec	= 20 m/sec.
Time = 26 sec.
Let the length of the train be x metres.
Then,	x + 270/26	= 20
x + 270 = 520
x = 250.
Answer:B
Answer: (B) 250m
Question: A straight line in the xy- plane has y-intercept of 10 . On this line the x-coordinate of the point is 100 and y-coordinate is 1000 then what is the slope of the line?
(A) 2
(B) 5.5
(C) 6.5
(D) 3.2
(E) 9.9
Rationale: Eq of line = Y = MX +C
C= 10
X=100
Y=100M + 10,
Substitute Y by 1000 as given in question.
1000=100M+10 , M =9.9.
correct option is E
Answer: (E) 9.9
Question: Two trains start from A & B and travel towards each other at
speed of 50kmph and 60kmph resp. At the time of the meeting the
second train has traveled 120km more than the first.the distance
between them.
(A) 1300 km
(B) 1310 km
(C) 1320 km
(D) 1330 km
(E) 1340 km
Rationale: Let the distance traveled by the first train be x km
then distance covered by the second train is x + 120km
x/50 = x+120 / 60
x= 600
so the distance between A & B is x + x + 120 = 1320 km
Answer is C.
Answer: (C) 1320 km
Question: The pilot of a small aircraft with a 40-gallon fuel tank wants to fly to Cleveland, which is 480 miles away. The pilot recognizes that the current engine, which can fly only 8 miles per gallon, will not get him there. By how many miles per gallon must the aircraft’s fuel efficiency be improved to make the flight to Cleveland possible?
(A) 2
(B) 4
(C) 12
(D) 40
(E) 160
Rationale: Actual miles/gallon is = 480/4 = 12 miles/gallon.
Current engine miles/gallon is 8 miles/gallon.
Additional 4 miles/gallon is required to match the actual mileage.
ANSWER:B
Answer: (B) 4
Question: A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present
(A) 33
(B) 37
(C) 39
(D) 40
(E) 82
Rationale: Explanation:
Let the mother's present age be x years.
Then, the person's present age = years.
2(2x + 40) = 5(x + 8)
x = 40
Answer: D) 40
Answer: (D) 40
Question: A number consists of two digits. If the digits interchange places and the new number is added to the original number, then the resulting number will be divisible by:
(A) 3
(B) 5
(C) 9
(D) 11
(E) 13
Rationale: Let the ten's digit be x and unit's digit be y.
Then, number 10x + y.
Number obtained by interchanging the digits = 10y + x.
(10x + y) + (10y + x) = 11(x + y)
which is divisible by 1
ANSWER:D
Answer: (D) 11
Question: {150, 260, 250, n}
Which of the following could be the median of the 4 integers listed above?
I. 175
II. 215
III. 235
(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III
Rationale: If 175 is the median, (n+250) / 2 = 175. Then n = 100. But n < 150, so 175 can not be the median.
If 215 is the median, (n+250) / 2 = 215. Then n = 180. Thus 215 can be the median.
If 235 is the median, (n+250) / 2 = 235. Then n = 220. Thus 235 can be the median.
The answer is D.
Answer: (D) II and III only
Question: A boat can move upstream at 15 kmph and downstream at 35 kmph, then the speed of the current is?
(A) 5
(B) 6
(C) 10
(D) 8
(E) 9
Rationale: US = 15
DS = 35
M = (35 - 15)/2 = 10
Answer: C
Answer: (C) 10
Question: What number should replace the question mark? 10, 30, 14, 25, 18, 20, ---?
(A) 19
(B) 21
(C) 25
(D) 22
(E) 20
Rationale: Answer: D
10, 30, 14, 25, 18, 20, 22?
There are two alternate sequences: +4 and -5.
Answer: (D) 22
Question: 3 men or 6 women can do a piece of work in 20 days. In how many days will 12 men and 8 women do the same work?
(A) 12/9 days
(B) 15/4 days
(C) 82/8 days
(D) 22/76 days
(E) 22/2 days
Rationale: 3M = 6W ---- 20 days
12M + 8W -----?
24W + 8 W = 32W ---?
6W ---- 20 32 -----?
6 * 20 = 32 * x => x = 15/4 days
Answer:B
Answer: (B) 15/4 days
Question: A man purchases 8 pens for Rs.9 and sells 9 pens for Rs.8, how much profit or loss does he make?
(A) 40.98% loss
(B) 20.98% loss
(C) 60.98% loss
(D) 50.98% loss
(E) 10.98% loss
Rationale: Explanation:
81 ---- 17
100 ----- ? Ã¨ 20.98%loss
Answer:B
Answer: (B) 20.98% loss
Question: Mother,her daughter and her grand child weighs 110 kg. daughter and her daughter(child) weighs 60 kg. child is 1/5th of her grand mother. What is the age of the daughter?
(A) 46
(B) 47
(C) 48
(D) 49
(E) 50
Rationale: mother + daughter + child = 110kg
daughter + child = 60kg
mother = 110 - 60 = 50kg
child = 1/5th of mother = (1/5)*50 = 10kg
So now daughter = 110 -(mother + child) = 110 - (50+10) = 50kg
ANSWER:E
Answer: (E) 50
Question: If m is an integer, which of the following must be an even integer?
(A) m^2-m-1
(B) m^2-4m+6
(C) m^2-5m+5
(D) m^2+3m+8
(E) m^2+2m+10
Rationale: Check the options by plugging in some values ( Preferably smaller integers like 1 and 2 )
A: m^2-m-1 = -1 { If m = 1 }
B: m^2-4m+6 = 3 { If m = 1 }
C: m^2-5m+5 = 1 { If m = 1 }
D: m^2+3m+8 = 12 { If m = 1 }m^2+3m+8 = 18 { If m = 2 }
E: m^2+2m+10 = 13 { If m = 1 ]
Thus the only possible answer is (D)
Answer: (D) m^2+3m+8
Question: The ratio of 2 numbers is 2:8 and their H.C.F. is 40. Their L.C.M. is ?
(A) 400
(B) 120
(C) 80
(D) 320
(E) 40
Rationale: Let the numbers be 2x and 8x
Their H.C.F. = 40
so the numbers are 2*40 , 8*40 = 80, 320
L.C.M. = 320
Answer is D
Answer: (D) 320
Question: The diagonals of a rhombus are 10 cm and 15 cm. Find its area?
(A) 75
(B) 129
(C) 150
(D) 123
(E) 117
Rationale: 1/2 * 10 * 15 = 75
Answer:A
Answer: (A) 75
Question: A board of length L feet is cut into two pieces such that the length of piece A is 2 feet less than three times the length of piece B. Which of the following is the length, in feet, of piece A?
(A) (L - 2)/4
(B) (3L - 2)/4
(C) (L + 2)/3
(D) (3L + 2)/3
(E) (2L - 1)/4
Rationale: A+B = L so we know that B = L - A.
A = 3B-2
A = 3(L-A) - 2
4A = 3L - 2
A = (3L-2) / 4
The answer is B.
Answer: (B) (3L - 2)/4
Question: When 50% of one number is added to a second number,the second number increases to its four-thirds. What is the ratio between the first number and the second number?
(A) 3 : 2
(B) 3 : 4
(C) 2 : 3
(D) Data inadequate
(E) None of these
Rationale: Let the numbers be y and x respectively
x + 50% of y = 4x⁄3 or, y⁄2 = 4x⁄3 - x
or, y⁄2 = x⁄3
or, y⁄x = 2⁄3
Answer C
Answer: (C) 2 : 3
Question: Equal amount of water were poured into two empty jars of different capacities, which made one jar 1/8 full and other jar 1/6 full. If the water in the jar with lesser capacity is then poured into the jar with greater capacity, what fraction of the larger jar will be filled with water?
(A) 1/7
(B) 2/7
(C) 1/2
(D) 7/12
(E) 1/4
Rationale: Same amount of water made bigger jar 1/8 full, then the same amount of water(stored for a while in smaller jar) were added to bigger jar, so bigger jar is 1/8+1/8=1/4 full.
Answer: E.
Answer: (E) 1/4
Question: If a/x = 2/3 and a/y =1/ 2, then (x + y) =
(A) A)2a
(B) B)7a/2
(C) C)6a
(D) D)7a
(E) E)9a
Rationale: Ratio 1:
3a = 2x
Ratio 2:
4a = 2y
x+y = 7a/2
Answer is B
Answer: (B) B)7a/2
Question: A train running at 1/5 of its own speed reached a place in 20 hours. How much time could be saved if the train would have run at its own speed?
(A) 8hrs
(B) 10hrs
(C) 12hrs
(D) 16 hrs
(E) 6hrs
Rationale: time taken if run its own speed = 1/5*20 = 4 hrs
Time saved = 20 - 4 = 16 hrs
Answer : D
Answer: (D) 16 hrs