mathewhe/aqua_rat huggingface dataset:
Question: The greatest number which on dividing 1657 and 2037 leaves remainders 9 and 5 respectively, is:
(A) 16
(B) 127
(C) 235
(D) 305
(E) 505
Rationale: Explanation:
Required number = H.C.F. of (1657 - 9) and (2037 - 5)
= H.C.F. of 1648 and 2032 = 16. Answer: A
Answer: (A) 16
Question: 30% of employees are women with fair hair. 40% of fair-haired employees are women. What percent of employees have fair hair?
(A) 25
(B) 30
(C) 50
(D) 55
(E) 75
Rationale: I came up with (E) 75
Think of 100 people total:
From the first fact, 30 of these are women with fair hair.
From the second fact, these 20 women make up 40% of the total fair haired population.
We can then make a ratio of 60:40 fair haired men to fair haired women.
This means that (60/40)*30 equals the number of fair haired men, which is 45 men with fair hair.
Add this 45 to the 30 women and get 75 fair haired men and women out of 100 total men and women.
75%
E
Answer: (E) 75
Question: In a bag there are coins of 50 paisa, 25 paisa and one rupee in the proportion 5:6:2. If there are in all Rs.33, the number of 25 paisa coins is?
(A) 30
(B) 31
(C) 32
(D) 34
(E) 33
Rationale: 5x 6x 2x
50 25 100
250x + 150x + 200x = 3300
600x = 3300
x = 5.5 => 6x = 33
ANSWER:E
Answer: (E) 33
Question: 50% of a number is 10 less than 3/5th of that number. What is the number?
(A) 100
(B) 50
(C) 150
(D) 200
(E) 75
Rationale: Let the number be x
Then, 3x/5 - (50% of x) = 10
3x/5-50x/100 = 10
x = 100
Answer is A
Answer: (A) 100
Question: Three 6 faced dice are thrown together. The probability that no two dice show the same number on them is ?
(A) 5/7
(B) 5/9
(C) 5/3
(D) 5/2
(E) 5/1
Rationale: No two dice show same number would mean all the three faces should show different numbers. The first can fall in any one of the six ways. The second die can show a different number in five ways. The third should show a number that is different from the first and second. This can happen in four ways.
Thus 6 * 5 * 4 = 120 favourable cases.
The total cases are 6 * 6 * 6 = 216.
The probability = 120/216 = 5/9.
Answer:B
Answer: (B) 5/9
Question: Two trains are moving in the same direction at 108 kmph and 54 kmph. The faster train crosses a man in the slower train in 24 seconds. Find the length of the faster train?
(A) 320
(B) 330
(C) 340
(D) 350
(E) 360
Rationale: Relative speed = (108 - 54) * 5/18 = 3 * 5
= 15 mps.
Distance covered in 27 sec
= 24 * 15
= 360 m.
The length of the faster train
= 360 m.
Answer:E
Answer: (E) 360
Question: If 16% of 40% of a number is 5, then the number is
(A) 200
(B) 225
(C) 78.125
(D) 320
(E) None of these
Rationale: Explanation:
Let 16/100×40/100×a=5
a = 5×100×100/16×40=78.125
Correct Option: C
Answer: (C) 78.125
Question: If A and B get profits of Rs.4,000 and Rs.2,000 respectively at the end of year then ratio of their investments are
(A) 4:1
(B) 1:4
(C) 3:2
(D) 2:3
(E) 2:1
Rationale: Ratio = 4000/2000 = 2 : 1
Answer : E
Answer: (E) 2:1
Question: The true discount on a bill due 9 months hence at 16% per annum is Rs. 189.The amount of the bill is
(A) Rs. 1386
(B) Rs. 1764
(C) Rs. 1575
(D) Rs. 2268
(E) None of these
Rationale: Solution
32.5
Let P.W. be Rs. x.Then,S.I. on Rs.x at 16% for 9 months =Rs.189.
∴ x 16 x9/ 12x 1/100}= 189 or x = 1575.
∴ P.W. = Rs. 1575.
Answer B
Answer: (B) Rs. 1764
Question: Two numbers are 30% and 37% are less than a third number .How much percent is the second number less than the first?
(A) 19%
(B) 80%
(C) 10%
(D) 90%
(E) 15%
Rationale: I II III
70 63 100
70 -------- 7
100 ------ ? => 10%
Answer:C
Answer: (C) 10%
Question: Find the least value of 'a' so that 365a24 is divisible by 8.
(A) 9
(B) 8
(C) 0
(D) 2
(E) 1
Rationale: Explanation:
Given, number is divisible by 8 only if 'a24' is divisible by 8.
.: Least value of a is '0'.
Answer: Option C
Answer: (C) 0
Question: If the radius of a circle that centers at the origin is 5, how many M points on the circle have integer coordinates?
(A)  4
(B)  8
(C)  12
(D)  15
(E)  20
Rationale: I understand this might not be required but I used the equation of a circle.
Since the origin is at 0, x^2+y^2=5^2.
X,Y could be +/- (0,5 or 5,0) - 4 possibilities.
X,Y could be +/- (3,4 or 4,3) - 8 possibilities.
Ans: M=C
Answer: (C)  12
Question: in a certain flower shop, which stocks four types of flowers, there are 1/3 as many violets as carnations, and 1/3 as many tulips as violets. If there are equal numbers of roses and tulips, what percent of the flowers in the shop are carnations?
(A) 63
(B) 64.28
(C) 65
(D) 66
(E) 68
Rationale: Given :-
Violets - C/3
Carnations - C
Tulip - C/9
Rose - C/9
Total flowers in terms of C = C/3+C+C/9+C/9 = 14C/9
Percentage of Carnations = C/14C/9 *100 =64.28%
Answer B
Answer: (B) 64.28
Question: The speed of a train is 90 kmph. What is the distance covered by it in 30 minutes?
(A) 15
(B) 66
(C) 77
(D) 52
(E) 45
Rationale: 90 * 30/60 = 45 kmph
Answer:E
Answer: (E) 45
Question: If ‘+’ means ‘×’, ‘-‘ means ‘+’, ‘×’ means ‘÷’ and ‘÷’ means ‘-‘ then find the value of;
5 – 9 + 8 × 3 ÷ 20 =
(A) 6
(B) 9
(C) 12
(D) -2
(E) 8
Rationale: B 9
Answer: (B) 9
Question: A and B are two stations 390 km apart. A train starts from A at 10 a.m. and travels towards B at 65 kmph. Another train starts from B at 11 a.m. and travels towards A at 35 kmph. At what time do they meet?
(A) 5.15 a.m
(B) 7.20 a.m
(C) 2.15p.m
(D) 3.45p.m
(E) 6.10p.m
Rationale: Suppose they meet x hours after 10 a.m.
Then, (Distance moved by first in x hrs) + [Distance moved by second in (x-1) hrs]=390.
65x + 35(x-1) = 390 => 100x = 425 => x =	17/4
So, they meet 4 hrs.15 min. after 10 a.m i.e., at 2.15 p.m.
Ans: C
Answer: (C) 2.15p.m
Question: The price of an article has been reduced by 25%. In order to restore the original price the new price must be increased by?
(A) 33 1/3%
(B) 33 1/8%
(C) 33 6/3%
(D) 33 8/3%
(E) 31 1/3%
Rationale: 100
75
-------
75 ------- 25
100 ------ ? => 33 1/3%
Answer: A
Answer: (A) 33 1/3%
Question: The expression rs+r is odd when the r and s are integers. Which of the following expressions must be even?
(A) r
(B) s
(C) r + s
(D) rs - r
(E) r + s^2
Rationale: rs+r is odd
r and s are integers
If r were even rs+r would be even despite any value of s.
s can't be odd, so s must be even.
Ans : B
Answer: (B) s
Question: The product of a and b is equal to 10 more than twice the sum of a and b. If b = 9, what is the value of b - a?
(A) 2
(B) 5
(C) 7
(D) 24
(E) 35
Rationale: ab= 10 + 2(a+b)
9a= 10+2a +18
7a= 28
a=4
b-a= 9-4=5
B is the answer
Answer: (B) 5
Question: Mike drives his new Corvette from San Francisco to Las Vegas, a journey of 640 miles. He drives the first half of the trip at an average rate of 80 miles per hour, but has to slow down for the second half of his journey. If the second half of the trip takes him 200 percent longer than the first half, what is his average rate P in miles per hour for the entire trip?
(A) P=26.7
(B) P=30.0
(C) P=40.0
(D) P=53.3
(E) P=60.0
Rationale: VERITAS PREPOFFICIAL SOLUTION
Correct Answer : C
Using the formula: Time = Distance/Rate, we find that Mike takes 4 hours to cover the first 320 miles of his trip. Since the 2nd 320 miles take 200% longer than the first, it takes Mike 8 hours longer, or 12 hours. (Note: 200% longer than the first half is not 200% of the first half.) The overall time is 4 hours + 12 hours or 16 hours. Since the definition of Average Rate = Total Distance Traveled/Total Time of Travel, Mike's average rate = 640/16 or 40 miles per hour.
Answer choice C is correct.
Answer: (C) P=40.0
Question: How many different ways can you select a pilot and a co pilot if you have 45 people to choose from?
(A)  199
(B)  1980
(C)  3984
(D)  4950
(E)  9900
Rationale: You are not just choosing two from 45. Each of the two people chosen fills a particular slot. The first filling the pilot slot and the second filling the copilot slot is different from the first filling the copilot slot and the second filling the pilot slot.
So the answer is in a sense (45C2) x 2 = 1980.
Ans B
Answer: (B)  1980
Question: In 2008, the profits of Company N were 10 percent of revenues. In 2009, the revenues of Company N fell by 20 percent, but profits were 20 percent of revenues. The profits in 2009 were what percent of the profits in 2008?
(A) 80%
(B) 105%
(C) 120%
(D) 124.2%
(E) 160%
Rationale: x = profits
r= revenue
x/r = 0,1
x= 10
r=100
2009:
r=80
x/80 = 0,2 = 15/100
x= 80*20/100
x= 16
16/10 = 1,6 = 160%, Answer E
Answer: (E) 160%
Question: Three sets of 40, 50 and 60 students appeared for an examination and the pass percentage was 100, 90 and 80 respectively. the pass percentage of the whole set is
(A) 88.33
(B) 84.33
(C) 88.66
(D) 84.66
(E) None of these
Rationale: total passed student =40+45+48=133
133 is 88.66% of 150
ANSWER:C
Answer: (C) 88.66
Question: Arabica coffee costs $0.3 per ounce while Robusta coffee costs $0.2 per ounce. If the blend of Arabica and Robusta costs $0.22per ounce, what is the share of Arabica in this blend?
(A) 20%
(B) 24%
(C) 30%
(D) 33%
(E) 40%
Rationale: a= amount of arabica coffee
1-a = amount of robusta coffee. because if you subtract a from the 1 ounce, the remaining amount is robusta
therefore:
.3a + .2(1-a) = .22
.3a + .2 - .2a = .22
a= .2
therefore: .2/1 ounce = 20%. Therefore, the answer should be A
Answer: (A) 20%
Question: If N = 2^0.25 and N^b = 16, b must equal
(A) 3/80
(B) 3/5
(C) 4
(D) 16
(E) 80/3
Rationale: 25/100 = 1/4
N = 2 ^ 1/4
N^b = 2^4
(2^1/4)^b = 2^4
b = 16
Answer: D
Answer: (D) 16
Question: If 7 is added to four times a number and this sum is multiplied by 5, the result is the same as if the number is multiplied by 6 and 7 is added to the product. What is the number?
(A) -4
(B) -3
(C) -5
(D) -2
(E) 11
Rationale: let the number be x;
5(7+4x)=6x+7;
x=-2
ANSWER:D
Answer: (D) -2
Question: Two pipes can fill a tank in 30 minutes and 20 minutes. An outlet pipe can empty the tank in 15 minutes. If all the pipes are opened when the tank is empty, then how many minutes will it take to fill the tank?
(A) 48
(B) 54
(C) 60
(D) 66
(E) 72
Rationale: Let V be the volume of the tank.
The rate per minute at which the tank is filled is:
V/30 + V/20 - V/15 = V/60 per minute
The tank will be filled in 60 minutes.
The answer is C.
Answer: (C) 60
Question: Three numbers are in the ratio 1 : 2 : 3 and their H.C.F is 12. The numbers are
(A) 4, 8, 12
(B) 5, 10,15
(C) 10, 20, 30
(D) 12, 24, 36
(E) None
Rationale: Solution
Let the required numbers be x, 2x and 3x.
Then, their H.C.F = x. So x = 12.
The numbers are 12, 24, 36.
Answer D
Answer: (D) 12, 24, 36
Question: Katy worked for h hours each day for d consecutive days. If she earns $3.5 per hour, what is the total amount she earned?
(A) 3.50/d + h
(B) 3.50 + d + h
(C) 3.50 + dh
(D) 3.50h + d
(E) 3.50dh
Rationale: H hours for d days.
Income each day = 3.5*h
Total income = 3.5*h*d
Correct option: E
Answer: (E) 3.50dh
Question: 3^3+3^3+3^3=?
(A) a) 3^3
(B) b) 3^4
(C) c) 3^5
(D) d) 3^6
(E) e) 3^15
Rationale: The correct answer is B 3^4
3^4 = 3^3+3^3+3^3
Answer: (B) b) 3^4
Question: Jim’s Taxi Service charges an initial fee of $2.25 at the beginning of a trip and an additional charge of $0.15 for each 2/5 of a mile traveled. What is the total charge for a trip of 3.6 miles?
(A) $3.15
(B) $4.45
(C) $3.60
(D) $5.05
(E) $5.40
Rationale: Let the fixed charge of Jim’s Taxi Service = 2.25 $
and charge per 2/5 mile(.4 mile) = .15$
Total charge for a trip of 3.6 miles = 2.25 + (3.6/.4) * .15
= 2.25 + 9*.15
= 3.6 $
Answer C
Answer: (C) $3.60
Question: if lox x[9/16] = 1/2 then the value of x
(A) 256/81
(B) 250/87
(C) -3/4
(D) 3/4
(E) 5/2
Rationale: lox x (9/16) =1/2
x^-1/2 = 9/16=>x=256/81
ANSWER A
Answer: (A) 256/81
Question: if 36% of a number is 72, what is the number?
(A) 100
(B) 200
(C) 250
(D) 300
(E) 350
Rationale: Assume number as x then
0.36*x = 72
x = 200
ANSWER:B
Answer: (B) 200
Question: If the cost price is 92% of the selling price, then what is the profit percent?
(A) 9%
(B) 11%
(C) 13%
(D) 21%
(E) 19%
Rationale: Let S.P. = $100
C.P. = $92
Profit = $8
Profit% = 8/92 * 100 = 25/6 = 9% approximately
Answer is A
Answer: (A) 9%
Question: A father is now three times as old as his son. Nine years back, he was four times as old as his son. The age of the son (in years) is
(A) A)12
(B) B)15
(C) C)18
(D) D)27
(E) E)22
Rationale: Explanation:
Let son's age be x years. Then, father's age = (3x) years.
Nine years ago, father's age = (3x - 9) years and son's age = (x - 9) years.
So, 3x - 9 = 4 (x - 9)=> 3x - 9 = 4x - 36=> x = 27.
Answer: D
Answer: (D) D)27
Question: In a certain village, 200 litres of water are required per household per month. At this rate, if there are 10 households in the village, how long (in months) will 2000 litres of water last?
(A) 1
(B) 20
(C) 2
(D) 200
(E) 2.5
Rationale: I find it much easier to understand with real numbers, so choose (almost) any numbers to replace m,n and p:
In a certain village,m 200 litres of water are required per household per month. At this rate, if there aren 10 households in the village, how long (in months) willp2000litres of water last?
Water required is 200*10=2000 (m*n)
Water available is 2000 (p)
It will last 1 months (p/m*n)
Answer (A)
Answer: (A) 1
Question: A train is 360 meter long is running at a speed of 50 km/hour. In what time will it pass a bridge of 140 meter length?
(A) 87
(B) 69
(C) 36
(D) 72
(E) 21
Rationale: Speed = 50 Km/hr = 50*(5/18) m/sec = 125/9 m/sec
Total distance = 360+140 = 500 meter
Time = Distance/speed
= 500 * (9/125) =36 seconds
Answer: C
Answer: (C) 36
Question: The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number?
(A) 240
(B) 270
(C) 295
(D) 360
(E) 260
Rationale: x-y=1365
divide larger number by the smaller, we get 6 as quotient and the 15 as remainder
x/y=6 quotient and 15 reminder convert this as
x=6y+15
apply this x in above eqn
therefore,
6y+15-y=1365
5y+15=1365
y+3=273
y=270
ANSWER:B
Answer: (B) 270
Question: Miguel is mixing up a salad dressing. Regardless of the number of servings, the recipe requires that 5/8 of the finished dressing mix be olive oil, 1/4 vinegar, and the remainder an even mixture of salt, pepper and sugar. If Miguel accidentally doubles the vinegar and forgets the sugar altogether, what proportion of the botched dressing will be olive oil?
(A) 15/29
(B) 5/8
(C) 5/16
(D) 1/2
(E) 13/27
Rationale: Olive Oil = 240*5/8 = 150
Vinegar = 240*1/4 = 60
Remainder (240-210) equally divided in three parts
Salt = 10
Pepper = 10
Sugar = 10
The question then says Miquel doubles the vinegar and forgets sugar. Therefore, we will bad salad will have
150 + 120 (for 60*2) + 10+10 = 290
Ratio of Olive Oil/ New salad = 150/290 ie 15/29.
ANSWER:A
Answer: (A) 15/29
Question: The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 25%, then the cost price of the article is:
(A) 500
(B) 277
(C) 222
(D) 448
(E) 111
Rationale: Explanation:
110% of S.P. = 616
S.P. = (616 * 100)/110 = Rs. 560
C.P = (100 * 560)/125 = Rs. 448
Answer:D
Answer: (D) 448
Question: The length and breadth of a rectangular courtyard is 75 m and 32 m. Find the cost of leveling it at the rate of $3 per m2. Also, find the distance covered by a boy to take 4 rounds of the courtyard.
(A) 3573
(B) 3455
(C) 8600
(D) 7000
(E) 7200
Rationale: Length of the courtyard = 75 m
Breadth of the courtyard = 32 m
Perimeter of the courtyard = 2 (75 + 32) m
= 2 × 107 m
= 214 m
Distance covered by the boy in taking 4 rounds = 4 × perimeter of courtyard = 4 × 214 = 856 m
We know that area of the courtyard = length × breadth
= 75 × 32 m2
= 2400 m2
For 1 m2, the cost of levelling = $3
For 2400 m2, the cost of levelling = $3 × 2400 = $7200 ANSWER : E
Answer: (E) 7200
Question: The numerator of a certain fraction is 8 less than the denominator. If 3 is added to the numerator and 3 is subtracted from the denominator, the fraction becomes 3/4. Find the original fraction?
(A) 5/4
(B) 6/8
(C) 6/7
(D) 3/11
(E) 2/7
Rationale: Explanation:
The denominator be P, the numerator will be (P - 8).
The fraction will be (P - 8)/P.
Adding 3 to the numerator and subtracting 3 from the denominator, (P - 8 + 3)/(P - 3) = 3/4.
(P - 5)/(P - 3) = 3/4
P = 20 - 9 => P = 11.
The fraction is: 3/11.
Answer D
Answer: (D) 3/11
Question: In a race of 200 m, A can beat B by 32 m and C by 24 m. In a race of 440 m, C will beat B by ?
(A) 22 m
(B) 75 m
(C) 85 m
(D) 20 m
(E) 15 m
Rationale: Explanation:
A:B = 200 : 168 = 100:84
A:C = 200 : 176 = 100:88
=> B:C = 84:88
When C covers 176 m , B Covers 168 m
When C covers 440 m , B Covers
=> 420 m
So C beats B by (440 - 420) = 20 m.
Answer: D
Answer: (D) 20 m
Question: If 6 men can colour 48 m long cloth in 2 days, then 2 men can colour 36 m long cloth in
(A) 1 day
(B) 2.1 days
(C) 3 days
(D) 4.5 days
(E) 5 days
Rationale: The length of cloth painted by one man in one day = 48 / 6 × 2 = 4 m
No. of days required to paint 36 m cloth by 6 men = 36/ 4 × 2 = 4.5 day.
D
Answer: (D) 4.5 days
Question: Two stations A and B are 110 km apart on a straight line. One train starts from A at 3 a.m. and travels towards B at 20 kmph. Another train starts from B at 8 a.m. and travels towards A at a speed of 25 kmph. At what time will they meet?
(A) 15 a.m
(B) 10 a.m
(C) 12 a.m
(D) 6 a.m
(E) 05 a.m
Rationale: Suppose they meet x hours after 3 a.m.
Distance covered by A in x hours = 20x km.
Distance covered by B in (x - 1) hours = 25(x - 1) km.
Therefore 20x + 25(x - 1) = 110
45x = 135
x = 3.
So, they meet at 6 a.m.
Answer:D
Answer: (D) 6 a.m
Question: The compound ratio of 5:6, 3:2 and 4:5?
(A) 1:5
(B) 1:8
(C) 1:2
(D) 1:1
(E) 1:9
Rationale: 5/6 * 3/2 * 4/5
= 1/1
1:1
Answer:D
Answer: (D) 1:1
Question: One quantity of wheat at Rs 9.30 per Kg is mixed with another quality at a certain rate in the ratio 8:7. If the mixture so formed be worth Rs 10 per Kg, what is the rate per Kg of the second quality of wheat?
(A) Rs 12.47
(B) Rs 10.80
(C) Rs 10.80
(D) Rs 47.66
(E) None of these
Rationale: Explanation :
Let the rate of second quality be Rs x per Kg.
C.P of 1Kg wheat of 1st kind = Rs 9.30
C.P of 1 Kg wheat of 2nd kind = Rs. x.
Mean price = Rs 10.
The given ratio is 8 : 7.
Rs 9.30 Rs x
\ /
(Mean Price)
Rs 10
/ \
x-10 : 0.7
8 : 7
Then, the ratio is :-
=>(x-10) : 0.7 = 8 : 7.
=>7x -70=5.6.
=>x=75.6/7.
Hence, the required amount is 10.80 per Kg.
Answer : B
Answer: (B) Rs 10.80
Question: A line that passes through (–1, –4) and (2, k) has a slope = k. What is the value of k?
(A)  3/4
(B)  1
(C)  4/3
(D)  2
(E)  7/2
Rationale: Slope = (y2-y1)/(x2-x1)
=> k = (k+4)/(2+1)
=> 3k = k+4
=> k =2
Ans D it is!
Answer: (D)  2
Question: How many seconds will a 500 m long train take to cross a man walking with a speed of 3 km/hr in the direction of the moving train if the speed of the train is 63 km/hr?
(A) 30
(B) 88
(C) 66
(D) 44
(E) 31
Rationale: Speed of train relative to man = 63 - 3 = 60 km/hr.
= 60 * 5/18 = 50/3 m/sec.
Time taken to pass the man = 500 * 3/50 = 30 sec.
Answer: A
Answer: (A) 30
Question: A clothing store prices jeans at 20% above the wholesale price of $40 and shorts at 10% above the wholesale price of $25. An employee uses their employee discount of 10% to buy 2 pairs of shorts and 1 pair of jeans. How much does that employee pay?
(A) $92.70
(B) $111.15
(C) $95.70
(D) $97.25
(E) $98
Rationale: Wholesale cost of jeans = $40
Wholesale cost of shorts = $25
Jeans were priced at 20% above $40 = $48
Shorts were priced at 10% above $25 = $27.50
% discount given by employee discount = 10%
Employee paid = (27.5 + 27.5 + 48) * .9 = $92.70
Answer A
Answer: (A) $92.70
Question: Insert the missing number. 34, 7, 37, 14, 40, 28, 43, (...)
(A) 52
(B) 56
(C) 54
(D) 50
(E) 60
Rationale: We have two series here
34, 37, 40, 43, ... (Increase by 3)
7, 14, 28, ... (Multiply by 2)
Hence, next term is 28 × 2 = 56
Answer is B.
Answer: (B) 56
Question: Population of a city in 2004 was 1000000. If in 2005 there is an increment of 20% , in 2006 there is a decrements of 35 % and in 2007 there is an increment of 45%, then find the population of city at the end of the year 2007
(A) 967532
(B) 977522
(C) 984424
(D) 997454
(E) 1131000
Rationale: Required population = P (1 + R1/100)(1 - R2/100)(1 + R3/100)
= P (1 + 20/100)(1 - 35/100)(1 + 45/100)
= 1131000
E
Answer: (E) 1131000
Question: A rectangle having length 105 cm and width 40 cm. If the length of the rectangle is increased by twenty five percent then how much percent the breadth should be decreased so as to maintain the same area.
(A) 25%
(B) 19.23%
(C) 40%
(D) 75%
(E) None of these
Rationale: Explanation :
Solution: (25/(105+25) * 100)% = 19.23%
Answer : B
Answer: (B) 19.23%
Question: If 6th March, 2001 is Sunday, what was the day of the week on 6th March, 2000?
(A) Sunday
(B) Saturday
(C) Tuesday
(D) Wednesday
(E) None of these
Rationale: Solution
The year 2000 is a leap year. So, it has 2 odd days.
But, Feb 2000 not included because we are calculating from March 2000 to March 2001. So it has 1 odd day only.
The day on 6th March, 2001 will be 1 day beyond the day on 6th March, 2000. Given that, 6th March, 2001 is Sunday.
6th March, 2000 is Saturday (1 day before to 6th March, 2001)
Answer B
Answer: (B) Saturday
Question: A third standard teacher gave a simple multiplication exercise to the kids. But one kid reversed the digits of both the numbers and carried out the multiplication and found that the product was exactly the same as the one expected by the teacher. Only one of the following pairs of numbers will fit in the description of the exercise. Which one is that ?
(A) 14, 22
(B) 13, 62
(C) 19, 33
(D) 42, 28
(E) None
Rationale: Explanation :
This can best be done by reverse substitution.
We need not verify the entire answer but only that last digits.
For example, the last digits obtained by multiplying the the units place digits should be the same as that obtained by multiplying the tens place digit.
Hence we find that only option (2) is the valid answer.
Answer : B
Answer: (B) 13, 62
Question: Find k if 64 / k = 8.
(A) 6
(B) 7
(C) 8
(D) 4
(E) 3
Rationale: Since 64 /k = 8 and 64/ 8 = 8, then
k = 8 correct answer C
Answer: (C) 8
Question: A “Sophie Germain” prime is any positive prime number p for which 2p + 1 is also prime. The product of all the possible units digits of Sophie Germain primes greater than 6 is
(A) 3
(B) 7
(C) 21
(D) 189
(E) 198
Rationale: In that case, the Sophie prime numbers greater than 6 are 7,11,23,47,59, .. which yields units digit as 1,3,7 and 9
Product would be 1 x 3 x 7x9 =189 Answer should be D
Answer: (D) 189
Question: Find large number from below question The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder
(A) 1234
(B) 1345
(C) 1450
(D) 1550
(E) 1635
Rationale: Let the smaller number be x. Then larger number = (x + 1365).
x + 1365 = 6x + 15
5x = 1350
x = 270
Large number = 270+1365 = 1635
E
Answer: (E) 1635
Question: xy+yz=63
xz+yz=23
find x+y+z ?
(A) 23
(B) 24
(C) 25
(D) 26
(E) 27
Rationale: take z as common term in second equation
ie z(x+y)=23
now as 23 is prime no therefore its factors must be 1 and 23.
now as x,y,z is integer no therefore z= 1 as sum of two integer cannot be equal to 1.
=> z= 1 and x + y = 23
therefore x+y+z = 1 + 23 = 24.
ANSWER:B
Answer: (B) 24
Question: A train moves fast a telegraph post and a bridge 240 m long in 8 sec and 20 sec respectively. What is the speed of the train?
(A) 75
(B) 39
(C) 79
(D) 72
(E) 71
Rationale: Let the length of the train be x m and its speed be y m/sec.
Then, x/y = 8 => x = 8y
(x + 240)/20 = y
y = 20
Speed = 20 m/sec = 20 * 18/5 = 72 km/hr.
Answer:D
Answer: (D) 72
Question: Two brother X and Y appeared for an exam. The probability of selection of X is 1/5 and that of B is 2/3. Find the probability that both of them are selected.
(A) 2/69
(B) 2/20
(C) 2/18
(D) 2/29
(E) 2/15
Rationale: Explanation:
Let A be the event that X is selected and B is the event that Y is selected.
P(A) = 1/5, P(B) = 2/3.
Let C be the event that both are selected.
P(C) = P(A) Ã— P(B) as A and B are independent events:
= (1/5) Ã— (2/3) = 2/15
Answer: E) 2/15
Answer: (E) 2/15