mathewhe/aqua_rat huggingface dataset:
Question: A bank issued credit card numbers and the corresponding PIN (Personal Identification Number). Both are 3-digit numbers up to 996. Pinaki was the last to get the credit card and so he had the last possible credit card number.
He was afraid of forgetting his PIN. He wrote down the number 123 in his diary to remember his PIN. He also wrote out the way to calculate 123 : "Multiply the card number by PIN. Divide the product by 997. The remainder is 123".
Once, Prafull saw his diary in which Pinaki wrote this number 123. Prafull did a lot of purchasing, as he now knows Pinaki's PIN. What is Pinaki's PIN?
(A) 874
(B) 875
(C) 876
(D) 877
(E) None
Rationale: Explanation :
Let, the PIN is x.
According to the question,
The card number =996 and Remainder =123.
Thus, (996 × x)/997=123.
=>x= 874.
Answer : A
Answer: (A) 874
Question: A candidate who gets 40% of the marks fails by 40 marks. But another candidate who gets 60% marks gets 20 marks more than necessary for passing. Find the number of marks for passing?
(A) 100 Marks
(B) 200 Marks
(C) 160 Marks
(D) 371 Marks
(E) 827 Marks
Rationale: 40% ------------ 40
60% ------------ 20
----------------------
20% ------------- 60
40% -------------- ?
120 + 40 = 160 Marks
Answer:C
Answer: (C) 160 Marks
Question: If a and b are odd numbers, then which of the following is even ?
(A) a + b
(B) a + b + 1
(C) ab
(D) ab + 2
(E) None of these
Rationale: The sum of two odd number is even. So, a + b is even.
Answer: Option A
Answer: (A) a + b
Question: In a group of dogs and peacocks, the number of legs are 18 less than four times the number of heads How many peacocks are there in that group?
(A) 9
(B) 8
(C) 7
(D) 6
(E) 5
Rationale: Let the number of dogs be 'x' and the number of peacocks by 'y'. Then, number of legs in the group = 4x + 2y. Number of heads in the group = x+y So, 4x+2y = 4(x+y) – 18 ⇒ 2y = 18 ⇒ y = 9 Number of peacocks in that group = 9.
Answer:A
Answer: (A) 9
Question: Convert the following unit:
8 hectares in mÂ²
(A) 60000 mÂ²
(B) 70000 mÂ²
(C) 80000 mÂ²
(D) 85000 mÂ²
(E) 90000 mÂ²
Rationale: 8 hectares in mÂ²
1 hectare = 10000 mÂ²
Therefore, 8 hectares = 8 Ã— 10000 mÂ²
= 80000 mÂ²
ANSWER : OPTION C
Answer: (C) 80000 mÂ²
Question: A man can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit his target?
(A) 451/784
(B) 561/784
(C) 175/256
(D) 362/785
(E) 634/563
Rationale: The man will hit the target if he hits it once or twice or thrice or all four times in the four shots that he takes.
So, the only possibility when the man will not hit the target is when he fails to hit the target in even one of the four shots that he takes.
The event of not hitting the target even once is the complement of the event of hitting the target at least once.
The probability that he will not hit the target in any given shot = 1 – 1/4 = ¾
Therefore, the probability that he will not hit the target in any of the four shots =3/4*3/4*3/4*3/4=81/256
The probability that he will hit the target at least in one of the four shots=1-81/256
=175/256
Ans: C
Answer: (C) 175/256
Question: A man buy a book in Rs50 & sale it Rs50. What is the rate of profit ???
(A) 10%
(B) 0%
(C) 30%
(D) 25%
(E) 28%
Rationale: cp=50
sp=50
profit=50-50=0
%=0/50*100=0%
ANSWER:B
Answer: (B) 0%
Question: Tough and Tricky questions: Combinations.
eight contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?
(A) 6
(B) 7
(C) 12
(D) 16
(E) 24
Rationale: eight contestants representing four different countries advance to the finals of a fencing championship. Assuming all competitors have an equal chance of winning, how many possibilities are there with respect to how a first-place and second-place medal can be awarded?
We have 2 slots to be filled using 8 contestants:8 options for slot1*3 option for slot2
= 8* 3
= 24
Ans. E) 24
Answer: (E) 24
Question: Three female friendsthree male friends will be pictured in a advertising photo. If the photographer wants to line them up in one row, with menwomen alternating. How many possible arrangements may she chose?
(A) 40320
(B) 1680
(C) 1152
(D) 576
(E) 72
Rationale: now any of the alternate 3 places can be filled by 3 male or female in 3!
similarily,
other 3 alternate places can be filled in 3!
hence required probability= 2*3!*3!=72
hence E
Answer: (E) 72
Question: A man buys a cycle for Rs. 1400 and sells it at a loss of 15%. What is the selling price of the cycle?
(A) Rs 970
(B) Rs 1075
(C) Rs 1190
(D) Rs 1210
(E) Rs 1810
Rationale: S.P. = 85% of Rs. 1400 = Rs.85/100x 1400	= Rs. 1190
ANSWER : C
Answer: (C) Rs 1190
Question: An bus covers a certain distance at a speed of 280 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of?
(A) 600 km/hr
(B) 720 km/hr
(C) 730 km/hr
(D) 840 km/hr
(E) 760 km/hr
Rationale: Distance = (280 x 5) = 1400 km.
Speed = Distance/Time
Speed = 1400/(5/3) km/hr. [We can write 1 hours as 5/3 hours]
Required speed = 1400 x 3 km/hr = 840 km/hr.
D
Answer: (D) 840 km/hr
Question: Ten different letters of alphabet are given, words with 5 letters are formed from these given letters. Then, the number of words which have at least one letter repeated is:
(A) 69760
(B) 30240
(C) 99748
(D) 42386
(E) None
Rationale: Solution:
Number of words which have at least one letter replaced,
= Total number of words - total number of words in which no letter is repeated.
=> 105 – 16P5.
=> 100000 − 30240 = 69760.
Answer: Option A
Answer: (A) 69760
Question: In a survey of political preferences, 78% of those asked were in favour of at least one of the proposals: I, II and III. 50% of those asked favoured proposal I, 30% favoured proposal II, and 20% favoured proposal III. If 5% of those asked favoured all three of the proposals, what W percentage of those asked favoured more than one of the 3 proposals.
(A)  10
(B)  12
(C)  17
(D)  22
(E)  30
Rationale: Bunuel, my answer for exactly 2 people was 17 and this was my approach:
100%=(A+B+C)-(AnB+AnC+BnC)-5%+22% which leads me to
W=100%=(50+30+20)-(at least 2 people)-5%+22%.C
Answer: (C)  17
Question: A shopkeeper loses 15%,if an article is sold for Rs. 187. What should be the selling price of the article to gain 20%?
(A) s.247
(B) s.248
(C) s.264
(D) s.329
(E) s.412
Rationale: Given that SP = Rs. 187 and loss = 15%
CP = [100(SP)]/(100 - l%) = (100 * 187)/85 = 20 * 6
= Rs. 220.
To get 20% profit, New SP = [(100 + p%)CP]/100
= (220 * 120)/100
= Rs.264
Answer:C
Answer: (C) s.264
Question: Every year an amount increases by 1/8th of itself. How much will it be after two years if its present value is Rs.65000?
(A) 81000
(B) 81007
(C) 81008
(D) 81066
(E) 82265.6
Rationale: 65000* 9/8 * 9/8 = 82265.6
Answer:E
Answer: (E) 82265.6
Question: The average of first four prime numbers greater than 30 is?
(A) 38
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: 31 + 37 + 41 + 43 = 152/4 = 38
ANSWER:A
Answer: (A) 38
Question: 1/3, 1/2, 1/4, 2 1/3, 3 1/2, 4 1/4, 4 1/3, 6 1/2, ?
(A) 8 1/4
(B) 9 1/4
(C) 8 1/2
(D) 8 1/3
(E) 6 1/4
Rationale: there are 3 series---
1/3,2 1/3,4 1/3.
1/2,3 1/2,6 1/2.
1/4,4 1/4,?
ans 8 1/4
ANSWER:A
Answer: (A) 8 1/4
Question: A wheel that has 6 cogs is meshed with a larger wheel of 14 cogs. When the larger wheel has made 24 revolutions, then the number of revolutions made by the smaller wheel is:
(A) 52
(B) 24
(C) 48
(D) 56
(E) 43
Rationale: D
56
Let the required number of revolutions made by larger wheel be x.
Then, less cogs, more revolutions (Indirect Proportion)
6 : 14:: 24: x <-> 6 x X = 14 x 24
x = (14 x 24)/6
x = 56
Answer: (D) 56
Question: Two family reunions are happening at the Leela hotel, the Oates reunion and the Hall reunion. All 100 guests at the hotel attend at least one of the reunions. If 50 people attend the Oates reunion and 62 people attend the Hall reunion, how many people attend both reunions?
(A)  2
(B)  5
(C)  12
(D)  16
(E)  22
Rationale: No of people in Oates reunion=50
No of people in Hall reunion=62
Attending both=x
All guests attend at least one.
Therefore, 100=50+62-(Both)
Both=12
Answer C
Answer: (C)  12
Question: The average price of three items of furniture is Rs. 15000. If their prices are in the ratio 3:5:7, the price of the cheapest item is
(A) 4888
(B) 2090
(C) 9028
(D) 9000
(E) 9202
Rationale: Explanation:
Let their prices be 3x, 5x and 7x.
Then, 3x + 5x + 7x = (15000 * 3) or x = 3000.
Cost of cheapest item = 3x = Rs. 9000.
Answer: D
Answer: (D) 9000
Question: Rose is two years older than Bruce who is twice as old as Chris. If the total of the age of Rose, B and Chris be 27 years, then how old is Bruce ?
(A) 8 years
(B) 10 years
(C) 12 years
(D) 14 years
(E) 16 years
Rationale: Let Chris's age be x years. Then, Bruce's age = 2x years.Rose's age = (2x + 2) years.
(2x + 2) + 2x + x = 27
5x = 25
x = 5.
Hence, Bruce's age = 2x = 10 years.
B
Answer: (B) 10 years
Question: The average marks of a class of 25 students is 40 and that of another class of 30 students is 60. Find the average marks of all the students?
(A) 52.6
(B) 52.4
(C) 52.1
(D) 50.9
(E) 52.9
Rationale: Sum of the marks for the class of 25 students = 25 * 40 = 1000
Sum of the marks for the class of 30 students = 30 * 60 = 1800
Sum of the marks for the class of 55 students =
1000 + 1800 = 2800
Average marks of all the students = 2800/55 = 50.9.Answer: D
Answer: (D) 50.9
Question: If x and y are positive integers, and 1 is the greatest common divisor of x and y, what is the greatest common divisor F of 2x and 3y?
(A) F=1
(B) F=Cannot be determined
(C) F=2
(D) 5
(E) 6
Rationale: My explanation: from question stem we know that nothing is common between X and Y , X and Y are two prime numbers eg: X=2, Y=3 and their GCD(2,3) =1 and so 2X and 3Y will have a GCD (2X,3Y) = 1 . what if either X or Y was 1, eg: X=1,Y=4 then GCD(1,4) =1 , but GCD(2,12) = 2.
and hence answer B
Answer: (B) F=Cannot be determined
Question: What is the value of (log2 3)(log3 4)(log4 5)...(log63 64)?
(A) 1/6
(B) 2
(C) 5/2
(D) 6
(E) 32
Rationale: Using the identity (loga b)(logb c) = loga c repeatedly, we obtain
(log2 3)(log3 4)(log4 5)...(log63 64) = log2 64 = 6
correct answer D
Answer: (D) 6
Question: The sum of the first 50 positive even integers is 2550. What is the sum E of even integers from 102 to 200 inclusive?
(A) 5100
(B) 7550
(C) 10100
(D) 15500
(E) 20100
Rationale: My solution is:
First 50 even integers:
2
4
6
8
<...>
Integers from 102 to 200
102
104
106
108
<...>
We notice that each integer from the second set is 100 more than the respective integer in the first set. Since we have 50 even integers from 102 to 200, then:
E=2550+(100*50)=7550.B
Answer: (B) 7550
Question: A father said to his son, "I was as old as you are at the present at the time of your birth". If the father's age is 68 years now, the son's age five years back was:
(A) 14
(B) 17
(C) 19
(D) 29
(E) 24
Rationale: Let the son's present age be x years. Then, (68 - x) = x
2x = 68.
x = 34.
Son's age 5 years back (34 - 5) = 29 years.
answer :D
Answer: (D) 29
Question: Each of X alarm tolls at regular intervals. All of them tolls together twelve times a day. No two alarm at equal intervals of time. If each alarm tolls after a whole number of minutes, what is the maximum possible value of X?
(A) 14
(B) 16
(C) 18
(D) 20
(E) 22
Rationale: Explanation :
The alarm tolls together twelves times a day. Therefore, they toll together once every 2 hours i.e in 120 minutes.
Since, no two alarms toll at equal intervals of time, the total number of distinct factors of 120, including 1 and 120 itself =23×3×5.
The number of factors =(3+1)×2×2=16.
Hence, the maximum value of X is 16.
Answer : B
Answer: (B) 16
Question: The winning relay team in a high school sports competition clocked 48 minutes for a distance of 13.2 km. Its runners A, B, C and D maintained speeds of 16 kmph, 17 kmph, 18 kmph, and 19 kmph respectively. What is the ratio of the time taken by B to than taken by D?
(A) 5:16
(B) 19:17
(C) 9:8
(D) 8:9
(E) None of these
Rationale: Explanation :
Since it is a relay race, all the runners ran the same distance.
Hence for a same distance, (ratio of times) = 1/(ratio of speeds).
Hence ratio of times taken by B t& D = 19 : 17
Answer : B
Answer: (B) 19:17
Question: A and B entered into a partnership investing Rs.25000 and Rs.30000 respectively. After 4 months C also joined the business with an investment of Rs.35000. What is the share of C in an annual profit of Rs.47000?
(A) 1687
(B) 1478
(C) 1480
(D) 14000
(E) 1500
Rationale: 25*12: 30*12: 35*8
15:18:14
14/47 * 47000 = 14000
Answer: D
Answer: (D) 14000
Question: A, B and C are partners. A receives 2/3 of profits, B and C dividing the remainder equally. A's income is increased by Rs.200 when the rate to profit rises from 5 to 7 percent. Find the Capital of B?
(A) Rs.2450
(B) Rs.3600
(C) Rs.2500
(D) Rs.3100
(E) Rs.2100
Rationale: A:B:C = 2/3:1/6:1/6 = 4:1:1
x * 2/100 * 2/3 = 200
B capital = 15000*1/6 = 2500
ANSWER:C
Answer: (C) Rs.2500
Question: A town's oldest inhabitant is x years older than the sum of the ages of the Lee triplets. If the oldest inhabitants is now J years old, how old will one of the triplets F be in 20 years?
J-X-40/3 is my answers.
J = X + L + L + L is the initial situation
After 20 years
J + 20 = X + L + L + L + 60 ...20 years for each triplet so 60 years totally.
J - X - 40/ 3 = L is my answer.
What wrong am i doing ? Since the age asked is after 20 years i also consider adding 20 years to J .
(A) (J - 50)/3
(B) 3(J + 20)/x
(C) (J + x - 50)/3
(D) (J - x + 60)/3
(E) (J + x - 20)/3
Rationale: here it goes:
Oldest inhabitant = sum of age of triplets + X
J = 3L + X so L = (J - X)/3
After 20 years = L + 20
F= (J - X)/3 + 20
= (J - X + 60)/3=D
Answer: (D) (J - x + 60)/3
Question: A 3" cube is painted in all its faces and then it is cut down into 1" blocks. How many 1" blocks
are there even without a single face being painted?
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
Rationale: The unpainted blocks are the interior blocks.
This block forms a 1" cube on the inside.
The answer is B.
Answer: (B) 1
Question: What are the number of ways to select 3 men and 2 women such that one man and one woman are always selected?
(A) 15 ways
(B) 77 ways
(C) 30 ways
(D) 11 ways
(E) 87 ways
Rationale: The number of ways to select three men and two women such that one man and one woman are always selected = Number of ways selecting two men and one woman from men and five women
= ⁴C₂ * ⁵C₁ = (4 * 3)/(2 * 1) * 5
= 30 ways.
Answer: C
Answer: (C) 30 ways
Question: The volume of a sphere with radius r is (4/3)*pi*r^3 and the surface area is 4*pi*r^3. If a sperical balloon has a volume of 36 pi cubic centimeters, what is hte surface area of the balloon in square centimeters?
(A) a. 40
(B) b. 100
(C) c. 400
(D) d. 1,000
(E) e. 10,000
Rationale: The surface area is 4.pi.r^2 (its area remember not volume)
as 4/3.pi.r^3=36pi
r=3
so area = 4.pi.r^2= 36.pi= 36 x 3.14 = 100 (approx)
B
Answer: (B) b. 100
Question: The ratio of men to women in a class is 6 to 5. If 6 men and 6 woman drop out of the class and the ratio of men to women after the drop out is 4 to 3, then how many men are currently in the class?
(A) 10
(B) 11
(C) 14
(D) 15
(E) 12
Rationale: Equation on the basis of question
6x-6/5x-6=4/3
x=3
Original number of men = 6*3=18
Original Number of Women = 5*3=15
Current number of men = 18-6=12 (Answer)
Current number of women = 15-6=9
Ratio = 12/9= 4/3 ( Just to verify)
Ans E
Answer: (E) 12
Question: A dress on sale in a shop is marked at $D. During the discount sale its price is reduced by 15%. Staff are allowed a further 10% reduction on the discounted price. If a staff member buys the dress what will she have to pay in terms of D ?
(A) A)0.75D
(B) B)0.76D
(C) C)0.765D
(D) D)0.775D
(E) E)0.805D
Rationale: Successive doscounts = - a - b +ab/100
Putting the values,
Total discount = -15 - 10 + 150/100 = -25 + 1.5 = 23.5% discount
Hence the final price of the dress = D - 0.235D = 0.765D
Correct Option: C
Answer: (C) C)0.765D
Question: What is the value of 4^4+4^6?
(A)  4^12
(B)  4^35
(C)  17(4^5)
(D)  8^12
(E)  17(4^4)
Rationale: 4^4+4^6
=4^4(1+4^2)
=4^4 * 17
Answer E
Answer: (E)  17(4^4)
Question: 15 men take 21 days of 8 hrs. each to do a piece of work. How many days of 5 hrs. each would it take for 21 women if 3 women do as much work as 2 men?
(A) 30
(B) 20
(C) 16
(D) 26
(E) 36
Rationale: Let 1Man does 1unit/hr of work
15M in 21 days of 8hrs will do (15*21*8) units
3W = 2M
1W=(2/3)units/hr
21W with 6hrs a day will take (15*21*8)/(21*5*(2/3)) days
=> 36 Days
ANSWER:E
Answer: (E) 36
Question: There are 51 people in a certain community who belong to the local golf club, tennis club or both clubs. If twice as many people belong to the tennis club as belong to the golf club, what could be the number of people who belong to both clubs?
(A) 4
(B) 7
(C) 17
(D) 21
(E) 27
Rationale: let's find the range of Both and hence the range of x.
Minimum value of Both: Say there is no overlap in the two sets.
51 = x + 2x
x = 17
In this case Both = 0
Maximum value of Both: Say there is maximum overlap between the two sets. One set has x so it could be a subset of the set 2x.
51 = 2x
But x cannot be a decimal so (x-1) could be the overlap (= Both) and there could be 1 in only the Golf club.
51 = 2 x + x - (x - 1)
x = 25
In this case Both = 25 - 1 = 24
So Both lies between 0 and 24
Only option (D) satisfies this condition.
ANSWER:D
Answer: (D) 21
Question: A certain collage has total of 200 seniors each majoring in exactly one of six subjects. A minimum of 20 seniors major in each six subjects. If three quarter of the seniors major in one of four subjects, what is the greatest possible number of seniors majoring in one of the other two subjects?
(A) 100
(B) 80
(C) 25
(D) 60
(E) 50
Rationale: Answer C
200 = 150 + 20 + x => x = 25
= 3/4 * 200 in 4 subjects + 20 min for 5th subject + x = 200
Answer: (C) 25
Question: Look at this series: 1.5, 2.3, 3.1, 3.9, ... What number should come next?
(A) 4.7
(B) 4.5
(C) 6.7
(D) 8.9
(E) 9.2
Rationale: In this simple addition series, each number increases by 0.8.
ANSWER A
Answer: (A) 4.7
Question: If n is an integer and n^4 is divisible by 5, which of the following could be the remainder when n is divided by 5?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: option 1
Remainder 1 means 5+1=6
n^4= 6^4= 6*6*6*6/5 is not an integer
option 2
Remainder 2 means 5+2=7
n^4= 7^4=7*7*7*7/5 is not an integer
option 3
Remainder 3 means 5+3=8
n^4= 8^4=8*8*8*8/5 is not an integer
option 4
Remainder 4 means 5+4=9
n^4= 9^4=9*9*9*9/5 is not an integer
option 5
Remainder 5 means 5+5=10
n^4= 10*10*10*10/5 is an integer means n^4 is divisible by 5 if we take n=5
so E is correct
Answer: (E) 5
Question: The price of a bushel of corn is currently $3.20, and the price of a peck of wheat is $8.80. The price of corn is increasing at a constant rate of 5x cents per day while the price of wheat is decreasing at a constant rate of x(2^1/2) - x cents per day. What is the approximate price when a bushel of corn costs the same amount as a peck of wheat?
(A) $8.40
(B) $5.10
(C) $5.30
(D) $5.50
(E) $5.60
Rationale: I Tried using Time/Rate approach:-
Initial Price Difference = 8.80 - 3.20 = 5.60
Price of Corn increasing by 5x
Price of Wheat decreasing by x(1.4)-x = .4x
Since both the quantities are moving towards reducing the Price Gap hence:-
Relative Increase = 5x +.4x
Let T be the Time by which GAP is filled so,
5.6 = T(5.4x) -> T= (5.6)/5.4X
Final Price = 3.20 + 5X * T -> 3.20 + 5*5.6/5.4 = 8.4
Answer A.
Answer: (A) $8.40
Question: A train 132 m long pass a telegraph pole in 6 seconds. Find the speed of the train
(A) 66 km/hr
(B) 68.4 km/hr
(C) 72 km/hr
(D) 79.2 km/hr
(E) None
Rationale: Sol.
Speed = [132/6] m/sec = [22 * 18/5] km/hr = 79.2 km/hr.
Answer D
Answer: (D) 79.2 km/hr
Question: If a boat goes 7 km upstream in 42 minutes and the speed of the stream is 3 kmph, then the speed of the boat in still water is :
(A) 2.5 km/hr
(B) 4.2 km/hr
(C) 5 km/hr
(D) 10.5 km/hr
(E) None of these
Rationale: Solution
Speed of stream = 1/2 (13-8) km/hr= 2.5kmph . Answer A
Answer: (A) 2.5 km/hr
Question: A man walks at a speed of 3 km/hr and runs at a speed of 7 km/hr. How much time will the man require to cover a distance of 10 1/2 km, if he completes half of the distance, i.e., (5 1/4) km on foot and the other half by running?
(A) 2 1/7 hours
(B) 2 1/2 hours
(C) 2 7/2 hours
(D) 4 1/2 hours
(E) 2 1/5 hours
Rationale: Required time = (5 1/4)/3 + (5 1/4)/7
= 2 1/2 hours.
Answer:B
Answer: (B) 2 1/2 hours
Question: Consider the sequence of numbers beginning 23, 27, 28, 32, 33... It continues in such a way that by adding 5 to the nth term, one obtains the (n + 2)th term. What is the sum of the first 16 members of this sequence?
(A) 878
(B) 680
(C) 788
(D) 928
(E) 1022
Rationale: I would split them up like this.
23 28 33 and so on (8 terms)....the 10th term = 23+7*5 = 58
27 32 37 and so on (8 terms)......the 9th term = 27+7*5 = 62
Since the distance between any two numbers is the same we can use arithmetics
first+last/2 times no of numbers = the sum
(23+58)/2 * 8 = 324
(27+62)/2 * 8= 356
= 680
B
Answer: (B) 680
Question: If a number between 10 and 60 (inclusive) at random. What is the probability that the tens digit is greater than ones digit?
(A) 31/41
(B) 1041
(C) 14/41
(D) 16/51
(E) 11/41
Rationale: If tens digi is 6 ---> ones digit : 0
If tens digi is 5 ---> ones digit : 0, 1, 2, 3, 4
If tens digi is 4 ---> ones digit : 0, 1, 2, 3
If tens digi is 3 ---> ones digit : 0, 1, 2
If tens digi is 2 ---> ones digit : 0, 1
If tens digi is 1 ---> ones digit : 0
So the number of numbers whose tens digit is greater than ones digit is 11.
The total number is 60-10+1=51.
So the probability is 16/51. The answer is (D).
Answer: (D) 16/51
Question: When x is divided by y, the quotient is s with remainder r. Which of the following is y in terms of r, x, and s? (Assume both y and s are nonzero.)
(A) x – r –s
(B) (x+r)/s
(C) x/s−r
(D) (x−r)/s
(E) xr – s
Rationale: Given that when x is divided y, the quotient is s and remainder is r. This implies x-r is divisible by y and ys=(x-r) or y = (x-r)/s.
Answer D.
Answer: (D) (x−r)/s
Question: The original price of a camera was displayed as a whole dollar amount. After adding sales tax of 10 percent, the final price was also a whole dollar amount. Which of the following could be the final price of the camera?
(A) $207
(B) $209
(C) $211
(D) $213
(E) $215
Rationale: let original price be 100
Price after sales tax will be 110
Thus whatever be the final amount it will be divisible by 11
check the options , only 209 is divisible by 11 without leaving any remainder , hence this is our answer !!
ANSWER:B
Answer: (B) $209
Question: Given that a “12-inch pizza” means circular pizza with a diameter of 12 inches, changing from an 4-inch pizza to a 12-inch pizza gives you approximately what percent increase in the total amount of pizza?
(A) 330
(B) 500
(C) 670
(D) 800
(E) 125
Rationale: area of 4 inch pizza= 2*2*pi=4 pi
area of 12 inch pizza =6*6*pi=36 pi
32/4*100= 800% increase
hence answer is D
Answer: (D) 800
Question: A clock loses a minute every three hours for 4 days and gains 1% in the subsequent 6 days. If it was set right on Friday at 10 AM, what will be the time at the end of 10 days?
(A) 10:54:24 AM
(B) 10:56:24 AM
(C) 11:16:40 AM
(D) 10:54:40 AM
(E) 11:06:36 AM
Rationale: Loses 8 minutes each day.
so total loss = 4×8 = 32min
subsequent 6 days = 6×24×60 minutes
1% gain = ( 6×24×60)/100 = 86.4 minutes
so, total gain = 86.4 - 32 = 54.4 min = 54 + 0.4 min = 54 minutes + 0.4 × 60 seconds = 54min + 24seconds
10 days later the clock should be 54 min and 24seconds fast.
so time , 10:54:24 am (Answer A)
Answer: (A) 10:54:24 AM
Question: A train 125 m long passes a man, running at 3 km/hr in the same direction in which the train is going, in 10 sec. The speed of the train is?
(A) 65 km/hr
(B) 17 km/hr
(C) 76 km/hr
(D) 50 km/hr
(E) 48 km/hr
Rationale: Speed of the train relative to man = 125/10 = 25/2 m/sec.
= 25/2 * 18/5 = 45 km/hr
Let the speed of the train be x km/hr. Then, relative speed = (x - 3) km/hr.
x - 3 = 45 => x = 48 km/hr.
Answer: E
Answer: (E) 48 km/hr