mathewhe/aqua_rat huggingface dataset:
Question: A sum of Rs.96000 is divided into three parts such that the simple interests accrued on them for Eight, two and four years respectively may be equal. Find the amount deposited for 8 years.
(A) 14000
(B) 16000
(C) 12000
(D) 20000
(E) 13000
Rationale: Let the amounts be x, y, z in ascending order of value. As the interest rate and interest accrued are same for 2 years 4 years and 8 years i.e. 2x = 4y = 8z = k.
L.C.M. of 2,4,8 = 8 So x:y:z: = 48000 : 24000 :12000
The amount deposited for 11 years = 12000
ANSWER:C
Answer: (C) 12000
Question: Three cars A,B and C started at same point and time. After A reach 50 km, B and C are backward by 10km and 20 km. When B reach 200km, find the position of A and C?
(A) 240 and 160km
(B) 170 and 230 km
(C) 180 and 240 km
(D) 235 and 165 km
(E) 250 and 150 km
Rationale: Explanation:
A:B = 50 : 40 = 5 : 4
A:C = 50 : 30 = 5 : 3
=>B:C = 4:3
When B covers 40 km , C Covers 30 km
When B covers 200 km , C Covers
=> 150 km
When B covers 40 km , A Covers 50 km
When B covers 200 km , A Covers
=> 250 km
Answer: E
Answer: (E) 250 and 150 km
Question: In an examination, 30% of total students failed in Hindi, 42% failed in English and 28% in both. The percentage of these who passed in both the subjects is :
(A) 23
(B) 37
(C) 56
(D) 40
(E) 81
Rationale: Explanation:
Formula n(aâˆªb) = n(a) + n(b) âˆ’ n(aâˆ©b)
Fail in Hindi or English = 30 + 42 â€“ 28 = 44
Therefore students who passed = 100 â€“ 44 = 56.
Answer: C
Answer: (C) 56
Question: The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
(A) 85 kg
(B) 87 kg
(C) 90 kg
(D) 91 kg
(E) 93 kg
Rationale: Total weight increased = (8 x 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg.
Answer is A
Answer: (A) 85 kg
Question: At a certain university, 66% of the professors are women, and 70% of the professors are tenured. If 90% of the professors are women, tenured, or both, then what percent of the men are tenured?
(A) 25
(B) 37.5
(C) 60
(D) 62.5
(E) 75
Rationale: answer is 75%
total women = 66%
total men = 40%
total tenured = 70% (both men and women)
therefore, women tenured + women professors + men tenured = 90%
men tenured = 24%
but question wants to know the percent of men that are tenured
24%/40% = 60%
C
Answer: (C) 60
Question: There are 4 copies of 5 different pencils. In how many ways can they be arranged on a shelf?
(A) 20!/4!
(B) 20!/5(4!)
(C) 20!/(4!)^5
(D) 20!
(E) 5!
Rationale: There are 4 copies of 5 different pencils.20!/((4!)^5)
Answer - C
Answer: (C) 20!/(4!)^5
Question: What is the greatest number of identical bouquets that can be made out of 21 white and 91 red tulips if no flowers are to be left out? (Two bouquets are identical whenever the number of red tulips in the two bouquets is equal and the number of white tulips in the two bouquets is equal)
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Since no flowers are to be left out, then the number of bouquets must be a factor of both 21 and 91. For example, we cannot have 2 bouquets since we cannot divide 91 red tulips into 2 bouquets without one tulip left over.
Only answer choice which is a factor of 91 is E (7).
Answer: E.
Answer: (E) 7
Question: 25 liters of a mixture is created by mixing Liquid P and Liquid Q in the ratio 3:2. How many liters of Liquid Q must be added to make the ratio 5:4?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Let x be the amount of liquid Q to be added.
(2/5)*25 + x = (4/9)*(25+x)
450 + 45x = 500 + 20x
25x = 50
x = 2
The answer is B.
Answer: (B) 2
Question: What is the place value of 7 in the numeral 2734?
(A) 600
(B) 650
(C) 700
(D) 800
(E) 850
Rationale: Option 'C'
7 * 100 = 700
Answer: (C) 700
Question: A rope of which a calf is tied is increased from 12 m to 18 m, how much additional grassy ground shall it graze?
(A) 1217
(B) 1219
(C) 1210
(D) 565.7
(E) 1312
Rationale: π (182 – 122) = 565.7
Answer:D
Answer: (D) 565.7
Question: Lali builds a tower using only red, green, and blue toy bricks in a ratio of 4:3:1. She then removes 1/2 of the green bricks and adds 1/3 more blue bricks, reducing the size of the tower by 14 bricks. How many red bricks will she need to add in order to double the total number of bricks used to build the original tower?
(A) 82
(B) 96
(C) 110
(D) 120
(E) 192
Rationale: Lali want to double the original amount of blocks, not just the red blocks
the original tower had 96 bricks, the new tower has 82 bricks and the question is asking how many extra red blocks are needed to build a tower of 192 bricks (double the original: 96*2).
192-82 = 110
so 110 bricks need to be added to the new 82 brick tower to double the original.
They worded the question ashow many red bricks need to be addedbut really it could be any colour just that 110 more bricks need to be there to equal 192=E
Answer: (E) 192
Question: The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:
(A) 276
(B) 299
(C) 322
(D) 345
(E) 390
Rationale: the numbers are (23 x 13) and (23 x 14).
Larger number = (23 x 14) = 322.
Answer: Option C
Answer: (C) 322
Question: In a recent election, Ms. Robbins received 7,000 votes cast by independent voters, that is, voters not registered with a specific political party. She also received 20 percent of the votes cast by those voters registered with a political party. If N is the total number of votes cast in the election and 50 percent of the votes cast were cast by independent voters, which of the following represents the number of votes that Ms. Robbins received?
(A) 0.06N + 3,200
(B) 0.1N + 7,000
(C) 0.4N + 7,200
(D) 0.1N + 8,000
(E) 0.06N + 8,000
Rationale: I will go with option B
According to question 50 percent of total votes (N) cas were cast by independent voters. This implies 50 percent of N are voters that belong to political party. And she received 7000 votes from independent voters and 20 percent from registered voters (i.e 0.2 * 0.5 * N = 0.1N). Hence total votes = 7000 + 0.1N ....option B
Answer: (B) 0.1N + 7,000
Question: A and B enter into partnership with capital as 7:9. At the end of 8 months, A withdraws. If they receive the profits in the ratio of 8:9 find how long B's capital was used?
(A) 5
(B) 4
(C) 6
(D) 7
(E) 9
Rationale: 7 * 8 : 9 * x = 8:9 => x= 7
Answer: D
Answer: (D) 7
Question: Calculate the amount that an investor needs to be invest to earn $460 in interest in 12 months if the investor plans to invest x dollars in a savings account that pays interest at an annual rate of 9% compounded semi-annually?
(A) 7,000
(B) 4,000
(C) 6,000
(D) 5,000
(E) 8,000
Rationale: the approach is substitution,
our interest requirement is 460 after 12 months, 2 compounding period.
calculate the compound interest on each option and find out the one that yields 460 in 12 months
5,000 yielded $460
using the formula
A = P(1 + r/n)nt
hence answer is D
Answer: (D) 5,000
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 15 kmph, then the speed in downstream is?
(A) 30 kmph
(B) 5 kmph
(C) 20 kmph
(D) 22 kmph
(E) 25 kmph
Rationale: M = 15
S = 15
DS = 15 + 15 = 30
ANSWER:A
Answer: (A) 30 kmph
Question: 562Ã—99=?
(A) 55684
(B) 55432
(C) 55638
(D) 44530
(E) 44538
Rationale: 562Ã—(100-1)
56200-562=55638
answer C
Answer: (C) 55638
Question: Divide Rs.116000 among three persons A, B and C such that the ratio of the shares of A and B is 3:4 and that of B:C is 5:6.find the share of A?
(A) 29491
(B) 28491
(C) 39491
(D) 49491
(E) 59491
Rationale: Compound ratio of A:B:C
A:B = 3:4
B:C = 5:6
----------
A:B:C = 15:20:24
We can divide Rs.116000 in this ratio.
Share of A = 15/59 * 116000 = 29491
ANSWER:A
Answer: (A) 29491
Question: What will be the CI on a sum of Rs. 25,000 after 3 years at the rate of 12 per year?
(A) Rs. 10110.20
(B) Rs. 10120
(C) Rs. 10123.20
(D) Rs. 10124
(E) Rs. 10125.12
Rationale: Amount
= Rs. 25000 x 1 +	12 3
100
= Rs. 25000 x	28	x	28	x	28
25	25	25
= Rs. 35123.20
C.I. = Rs. (35123.20 - 25000) = Rs. 10123.20
C
Answer: (C) Rs. 10123.20
Question: The average age of 12 men is increased by years when two of them whose ages are 21 years and 23 years are replaced by two new men. The average age of the two new men is
(A) 22
(B) 30
(C) 34
(D) 38
(E) 27
Rationale: total age increased = (12 * 2) years = 24 years.
Sum of ages of two new men = (21 + 23 + 24) years = 68 years
Average age of two new men = (68/2) years = 34 years.
Answer: C
Answer: (C) 34
Question: If a survey shows that 50 citizens out of a sample of 200 support a particular Senate bill, what percent of the sample does not support the bill?
(A) 56%
(B) 64%
(C) 75%
(D) 82%
(E) 86%
Rationale: Those who support = 50.
% of those who don't support it is (200-50)/ 200 = 75%
Answer C
Answer: (C) 75%
Question: What percent is 2 gm of 1 kg?
(A) 0.5 %
(B) 0.2%
(C) 1.5%
(D) 2%
(E) 3%
Rationale: 1 kg = 1000 gm
2/1000 × 100 = 200/1000
=1/5 = 0.2 %
B)
Answer: (B) 0.2%
Question: what is the value of (2)^-3?
(A) 1/6
(B) 1/5
(C) 1/8
(D) 1/9
(E) 1/7
Rationale: 2^-3= 1/(2)^3= 1/8
ANSWER:C
Answer: (C) 1/8
Question: A man can row upstream at 6km/hr and down stream at 11km/hr find mans rate in still water ?
(A) 2.9km/hr
(B) 8.5km/hr
(C) 7.8km/hr
(D) 85.4km/hr
(E) 6.6km/hr
Rationale: given upstream(u) =6km/hr
down stream (v)= 11km/hr rate in still water =1/2(u+v)=1/2(6+11)=8.5km/hr Answer is (B)
Answer: (B) 8.5km/hr
Question: If a card is drawn from a well shuffled deck of cards, what is the probability of drawing a black card or a face card?
(A) 7/13
(B) 15/26
(C) 9/12
(D) 8/13
(E) 29/52
Rationale: P(Bá´œF) = P(B) + P(F) - P(Bâˆ©F), where B denotes black cards and F denotes face cards.
P(Bá´œF) = 26/52 + 12/52 - 6/52
= 8/13
Answer: D
Answer: (D) 8/13
Question: The sum of 3 consecutive numbers is definitely
(A) Positive.
(B) Divisible by 3.
(C) Divisible by 2.
(D) Divisible by 4.
(E) Divisible by 5.
Rationale: If 1st term is x:
x+(x+1)+(x+2)=3x+3--->Always divisible by 3
If 2nd term is x:
(x-1)+x+(x+1)=3x--->Always divisible by 3
If 3rd term is x:
(x-2)+(x-1)+x=3x-3--->Always divisible by 3
Answer: B
Answer: (B) Divisible by 3.
Question: If w, x, and y are consecutive even positive integers and w < x < y, which of the following could be equal to y - x - w ?
(A) -4
(B) -2
(C) -1
(D) 0
(E) 3
Rationale: Since W, X and Y are CONSECUTIVE EVEN POSITIVE INTEGERS and W < X < Y, we can start with the easiest set of values that comes to mind:
W = 2
X = 4
Y = 6
The question asks for what COULD be the value of Y - X - W.
In this case, the value would be...
6 - 4 - 2 = 0
0 IS among the answer choices, so we're done.
D
Answer: (D) 0
Question: If C.P. of 24 books is equal to S.P of 30 books , then your gain or loss is ?
(A) 23 1/3 gain %
(B) 30 10/23 loss %
(C) 20% loss %
(D) 30 1/3 loss %
(E) 40 1/3 loss %
Rationale: Say the cost price of 24 books is $24 so $1 for a book.
The cost of 30 books would be $30, and the selling price of 30 books would be 24$, hence the loss = ($30 - $24)/$30 = 20%.
Answer: C.
Answer: (C) 20% loss %
Question: 75% of a number when added to 75 is equal to the number. The number is ?
(A) 150
(B) 200
(C) 225
(D) 300
(E) None
Rationale: Answer
75 + 75% of N = N
⇒ N -3N/4 = 75
⇒ N/4 = 75
∴ N = (75 x 4) = 300
Correct Option: D
Answer: (D) 300
Question: Given two sets A = {1,1,6,6,7,7} and B = {0,1}, if one number is chosen from each set at random, what is the probability that the sum of both numbers is an even number
(A) 1/4
(B) 1/6
(C) 1/2
(D) 1/3
(E) 1/5
Rationale: One way to look at it:
The number from set A can be ANYTHING.
The number selected from set B will determine whether the sum is odd or even.
For example, if a 6 is selected from set A, we need a 0 from set B to get an even sum.
If a 7 is selected from set A, we need a 1 from set B to get an even sum.
And so on.
So, P(sum is even) = P(select ANY number from set AANDselect the number from set B that makes the sum even)
= P(select ANY number from set A)xP(select the number from set B that makes the sum even)
= 1x1/2
= 1/2
= C
Answer: (C) 1/2
Question: A, B and C invests Rs.2000, Rs.3000 and Rs.4000 in a business. After one year A removed his money; B and C continued the business for one more year. If the net profit after 2 years be Rs.3200, then A's share in the profit is?
(A) 238
(B) 288
(C) 237
(D) 400
(E) 281
Rationale: Explanation:
2*12 : 3*12 : 4*24
1: 3: 4
1/8 * 3200 = 400
Answer: D
Answer: (D) 400
Question: An outlet pipe empties a tank which is full in 5 hours. If the inlet pipe is kept open, which lets water in at the rate of 4 litres/min then outlet pipe would take 3 hours longer. Find the capacity of the tank.
(A) 8600 litres
(B) 3200 litres
(C) 12800 litres
(D) 11200 litres
(E) 13200 litres
Rationale: Let the rate of outlet pipe be x liters/hour;
Rate of inlet pipe is 8 litres/min, or 4*60 = 240 liters/hour;
Net outflow rate when both pipes operate would be x-240 liters/hour.
Capacity of the tank = x*5 hours = (x-240)*(5+3) hours
5x=(x-240)*8 --> x=640 --> capacity = 5x = 3200 liters.
Answer: B.
Answer: (B) 3200 litres
Question: Some persons can do a piece of work in 20 days. Two times the number of these people will do half of that work in?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
Rationale: 20/ (2 * 2) = 5 days
Answer:C
Answer: (C) 5
Question: If log	(a/b)+log(b/a)	= log (a + b), then:
(A) a=b
(B) a+b=0
(C) a-b=1
(D) a+b=1
(E) a-b = 0
Rationale: log(a/b)+ log(b/a)	= log (a + b)
log (a + b) = log{(a/b)x(b/a)}	= log 1.
So, a + b = 1.
Answer is D
Answer: (D) a+b=1
Question: 1. Internet: $90, with no sales tax, plus $10 shipping fee
2. Store X: $90, a 10% discount, plus 30% tax on discounted price
3. Store Y: $100, no tax
4. Store Z: $90, a 20% sales tax, and $10 rebate after tax
Isaac can purchase a certain item in four different ways, as shown in the table. What is the lowest price for which he can purchase this item?
(A) 88.1
(B) 89.0
(C) 89.1
(D) 89.5
(E) 98.0
Rationale: Option 2 = (90 - 9) + 0.3 * 81
=105.3
Option 4 = 90 + 0.2 * 90 - 10
= 98
So the OA is correct - E
Answer: (E) 98.0
Question: A man can row with a speed of 15 kmph in still water. If the stream flows at 5 kmph, then the speed in downstream is?
(A) 27
(B) 27
(C) 20
(D) 99
(E) 2
Rationale: M = 15
S = 5
DS = 15 + 5 = 20'
Answer:C
Answer: (C) 20
Question: Aishwarya was first to board to her flight to delhi.
She forgot her seat number and picks a random seat for herself.
After this, every single person who get to the flight sits on his seat if its available else chooses any available seat at random.
Abhishek is last to enter the flight and at that moment 99/100 seats were occupied.
Whats the probability what Abhishek gets to sit in his own seat ?
(A) 1/2
(B) 1/5
(C) 2/9
(D) 4/7
(E) 3/6
Rationale: A
1/2
one of two is the possibility
1. If any of the first 99 people sit in Abhishek seat, Abhishek will not get to sit in his own seat.
2. If any of the first 99 people sit in Aishwarya's seat, Abhishek will get to sit in his seat.
Answer: (A) 1/2
Question: A diagonal of a polygon is an segment between two non-adjacent vertices of the polygon. How many diagonals does a regular 10-sided polygon have?
(A)  875
(B)  35
(C)  1425
(D)  2025
(E)  2500
Rationale: There's a direct formula for this.
Number of diagonals in a regular polygon = [n*(n-3)] / 2, n = number of sides of the regular polygon.
Here, n = 10.
Plugging it in, we get 35 diagonals!
Answer (B).
Answer: (B)  35
Question: The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 9540, what is the length of the plot in metres?
(A) 20
(B) 200
(C) 300
(D) 400
(E) 100
Rationale: Let length of plot = L meters, then breadth = L - 20 meters
and perimeter = 2[L + L - 20] = [4L - 40] meters
[4L - 40] * 26.50 = 9540
[4L - 40] = 9540 / 26.50 = 360
4L = 400
L = 400/4= 100 meters. Answer: E
Answer: (E) 100
Question: To mail a package, the rate is 20 cents for the first pound and 5 cents for each additional pound. Two packages weighing 3 pounds and 5 pounds, respectively can be mailed seperately or combined as one package. Which method is cheaper and how much money is saved?
(A) Combined, with a saving of 5 cents
(B) Separately, with a saving of 5 cents
(C) Combined, with a saving of 15 cents
(D) Separately, with a saving of 10 cents
(E) Combined, with a saving of 10 cents
Rationale: 3 pounds = 1*20+2*5 = 30
5 pounds = 1*20+4*5 =40
total = 70
8 pound = 1*20+7*5 = 55
dif. 15
Answer : C
Answer: (C) Combined, with a saving of 15 cents
Question: Every day Daniel drives 64 miles back from work. On Sunday, Daniel drove all the way back from work at a constant speed of x miles per hour. On Monday, Daniel drove the first 32 miles back from work at (2x) miles per hour, and the rest of the way at (x/2) miles per hour. The time it took Daniel to drive back from work on Monday is longer than the time it took him to drive back from work on Sunday by what percent?
(A) 15%
(B) 25%
(C) 35%
(D) 45%
(E) 55%
Rationale: Let's TEST X = 4....
On Sunday, Daniel drove 64 miles at 4 miles/hour.
D = (R)(T)
64 = (4)(T)
64/4 = 16 = T
It takes 16 hours to drive home
On Monday, Daniel drove the first 32 miles at (2)(4) = 8 miles/hour and the rest of the way (32 miles) at 4/2 = 2 miles/hour
D = (R)(T)
32 = (8)(T)
32/8 = 4 = T
It takes 4 hours for the first part
D = (R)(T)
32 = (2)(T)
32/2 = 16 = T
It takes 16 hours for the second part
Total time to drive home on Monday = 4+16 = 20 hours
We're asked by what percent 20 hours is greater than 16 hours.
20/16 = 1.25, so it is 25% greater.
B
Answer: (B) 25%
Question: Three fifth of the square of a certain number is 126.15. What is the number?
(A) 210.25
(B) 75.69
(C) 14.5
(D) 145
(E) 150
Rationale: Let the number be X
Given, 3/5 X^2 = 126.5
X^2 = 126.15 * 5/3
X^2 = 42.05 * 5 = 210.25
X = 14.5
Answer C.
Answer: (C) 14.5
Question: For any integer k > 1, the term “length of an integer” refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k. For example, if k = 24, the length of k is equal to 4, since 24 = 2 × 2 × 2 × 3. If x and y are positive integers such that x > 1, y > 1, and x + 3y < 980, what is the maximum possible sum of the length of x and the length of y?
(A) 16
(B) 14
(C) 18
(D) 10
(E) 20
Rationale: we know that : x > 1, y > 1, and x + 3y < 980,
and it is given that length means no of factors.
for any value of x and y, the max no of factors can be obtained only if factor is smallest no all factors are equal.
hence, lets start with smallest no 2.
2^1 =2
2^2 =4
2^3=8
2^4=16
2^5=32
2^6=64
2^7=128
2^8=256
2^9=512
2^10 =1024 (it exceeds 1000, so, x can't be 2^10)
so, max value that X can take is 2^9 , for which has length of integer is 9.
now, since x =512 ,x+3y<980
so, 3y<468
==> y<156
so, y can take any value which is less than 162. and to get the maximum no of factors of smallest integer, we can say y=2^7
for 2^7 has length of integer is 7.
SO, combined together : 9+7 = 16.
A
Answer: (A) 16
Question: If |z|/w = 5,which of the following must be true?
(A) z = -5w
(B) z = 5w
(C) z^2 = 25w^2
(D) z^2 = 25w^3
(E) z^3 = 125w^3
Rationale: |z|/w = 5.
|z| = 5w.
Then z = 5w or -5w and so z^2 = 25w^2.
The answer is C.
Answer: (C) z^2 = 25w^2
Question: .3+33+333+33.3=?
(A) 362.33
(B) 399.6
(C) 702.33
(D) 702
(E) None of them
Rationale: .3
33
333
33.3
----------
399.6
----------
Answer is B
Answer: (B) 399.6
Question: Which of the following will divide evenly into 347,406,520?
(A) 4
(B) 11
(C) 9
(D) 3
(E) 13
Rationale: Rule:
4: Last two digits should be divisible by 4
the last two digits are 00, which are divisible by 4
Answer: A
Answer: (A) 4
Question: Integers a, b, c and d, not necessarily distinct, are chosen independently and at random from 0 to 2007, inclusive. What is the probability that ad - bc is even?
(A) 3/8
(B) 7/16
(C) 1/2
(D) 9/16
(E) 5/8
Rationale: First of all notice that half of the numbers from from 0 to 2007, inclusive are odd and half even.
Next, let's find the probability of ad - bc being odd and subtract it from 1.
The difference of two integers to be odd we should have either ODD-EVENOREVEN-ODD:
ODD-EVEN = ad - bc = odd*odd-even*evenorodd*odd-odd*evenorodd*odd-even*odd. Three cases. The probability of each is 1/2^4, so the probability of 3 cases is 3/2^4.
The same for EVEN-ODD: p=3/2^4.
P(even) = 1 - P(odd) = 1 - (3/2^4 + 3/2^4) = 10/16 = 5/8.
Answer: E.
Answer: (E) 5/8
Question: The greatest common factor of positive integers m and n is 12. What is the greatest common factor of (2m^2, 2n^2)?
(A) 2
(B) 12
(C) 24
(D) 144
(E) 288
Rationale: Given : GCD of (m and n) = 12 = 2^2*3
i.e. m and n are both multiples of 2^2*3
i.e. m^2 and n^2 will both be multiples of (2^2*3)^2 = 2^4*3^2
i.e. 2m^2 and 2n^2 will both be multiples of 2(2^2*3)^2 = 2^5*3^2 = 288
Answer: Option E
Answer: (E) 288
Question: (1.1 + 1.1 + 1.1 + 1.1) x 1.1 x 1.1 = ? = ? x 0.121
(A) 54
(B) 33
(C) 44
(D) 22
(E) 26
Rationale: Explanation:
? = (1.1 + 1.1 + 1.1 + 1.1) x 1.1 x 1.1/0.121
= (4.4 x 1.1 x 1.1)/0.121 = 44
Answer: Option C
Answer: (C) 44
Question: Age of Raghav who is 30 years old is 3/5 times of Ram and Ram is older than Mohan by 35 years.If vijay's age is just between the age of Ramesh and and Mohan and Ramesh is 21 years old.What is age of vijay?
(A) 20
(B) 25
(C) 18
(D) 17
(E) 16
Rationale: Solution:
Raghav's age=3/5 Ram's age
=>30=3/5 Ram's age
=>Ram's age=30/3 * 5=50
Ram's age=Mohan's age +35
=>Mohan's age=Ram's age -35
=>Mohan's age=50-35
=>Mohan's age =15
Vijay's age=(Ramesh's age +Mohan's age)/2
=>Vijay's age=(21+15)/2
=>Vijay's age=18 years.
Answer C
Answer: (C) 18
Question: A man walking at the rate of 6km per hour crosses a square field diagonally in 9 seconds the area of the field is
(A) 110sq.m
(B) 111.5aq.m
(C) 112.5sq.m
(D) 114sq.m
(E) None of these
Rationale: Explanation:
Distance covered in 9 seconds = (6×1000/3600)×9 = 15m
Diagonal of square field = 15m
Side of square =a then diagonal of that square= √2 a
Hence area of the square = a2= (152)/2 =112.5 sq.m
Answer: Option C
Answer: (C) 112.5sq.m
Question: A is half good a work man as B and together they finish a job in 26 days. In how many days working alone B finish the job?
(A) 98 days
(B) 21 days
(C) 17 days
(D) 39 days
(E) 19 days
Rationale: WC = 1:2
2x + x = 1/26 => x = 1/78
2x = 1/78 => 39 days
Answer:D
Answer: (D) 39 days
Question: What approximate value should come in place of (x) in the following question?
139.25 + 223.94 / 4.002 = x
(A) 195
(B) 276
(C) 188
(D) 166
(E) 161
Rationale: Explanation:
Given: 139.25 + 223.94 / 4.002 = x
Approximate 139.25 as 140, 223.94 as 224, 4.002 as 4,
we get, x = 140 + 224 / 4 = 140 + 56 = 196 =>195
ANSWER: A
Answer: (A) 195
Question: A and B can do a piece of work in 6 days, B and C in 7 days, C and A in 8 days. How long will C take to do it?
(A) 12.6 days
(B) 14.4 days
(C) 15.2 days
(D) 16.8 days
(E) 18.2 days
Rationale: 2c = 1/7 + 1/8 – 1/6 = 20/168 = 10/84
c = 5/84 => 84/5 = 16.8 days
The answer is D.
Answer: (D) 16.8 days
Question: Two brothers Ram and Ravi appeared for an exam. The probability of selection of Ram is 5/7 and that of Ravi is 1/5. Find the probability that both of them are selected.
(A) 2/35
(B) 2/3
(C) 7/35
(D) 1/7
(E) 7/5
Rationale: Let A be the event that Ram is selected and B is the event that Ravi is selected.
P(A) = 5/7
P(B) = 1/5
Let C be the event that both are selected.
P(C) = P(A) x P(B) as A and B are independent events:
= 5/7 x 1/5 = 1/7
ANSWER:D
Answer: (D) 1/7
Question: Find the wrong number below mentioned series
11,150,280,560,800
(A) 800
(B) 560
(C) 280
(D) 150
(E) 11
Rationale: 11 is the only prime number or odd number in the series.
ANSWER:E
Answer: (E) 11
Question: If XY denotes X is raised to the power Y, Find the last two digits of 19413844+ 19714181
(A) 154
(B) 677
(C) 784
(D) 148
(E) 132
Rationale: 1941^3844
unit digit= 1^4=1
10th digit=4*4=16=2 means last two digit =61
and 1971^4181
unit digit=1
10th digit=7*1=7 mean last two digit= 71
hence,
71+61= 132
Answer: (E) 132