mathewhe/aqua_rat huggingface dataset:
Question: Find the greatest number which, while dividing 19, 83 and 67, gives a remainder of 3 in each case?
(A) 16
(B) 17
(C) 18
(D) 19
(E) 20
Rationale: Subtract the remainder 3 from each of the given numbers: (19-3)=16, (67-3)=64 and (83-3)=80. Now, find the HCF of the results 16, 64 and 80, we get 16. Thus, the greatest number is 16
ANSWER:A
Answer: (A) 16
Question: If two dice are thrown together, the probability of getting prime number on both dice is
(A) 5/9
(B) 1/9
(C) 2/9
(D) 4/9
(E) 7/9
Rationale: The number of exhaustive outcomes is 36.
Let E be the event of getting a prime number on both the dice.
P(E) = 8/36 = 2/9.
C)
Answer: (C) 2/9
Question: If r and s are positive integers and r-s=6, which of the following has the greatest value M?
(A) 2r
(B) 2s
(C) r +s
(D) 2r-s
(E) 2s-r
Rationale: You can answer this question by using Number Properties and logic or by TESTing VALUES.
We're told that R and S are POSITIVE INTEGERS and that R-S = 6. We're asked which of the 5 answers has the GREATEST value.
IF....
R = 8
S = 2
Answer A: 2R = 2(8) = 16
Answer B: 2S = 2(2) = 4
Answer C: R+S = 8+2 = 10
Answer D: 2R-S = 2(8) - 2 = 14
Answer E: 2S-R = 2(2) - 8 = -4
Final Answer:
A
Answer: (A) 2r
Question: There are 10 members from that a total of 6 men & 4 ladies a committee of 3 is to be formed. If Mrs. A is not willing to join the committee in which Mr. B is a member, whereas Mr.B is willing to join the committee only if Mrs C is included, how many such committee are possible?
(A) 87
(B) 89
(C) 90
(D) 91
(E) 95
Rationale: We first count the number of committee in which
(i). Mr. Y is a member
(ii). the ones in which he is not
case (i): As Mr. Y agrees to be in committee only where Mrs. Z is a member.
Now we are left with (6-1) men and (4-2) ladies (Mrs. X is not willing to join).
We can choose 1 more in5+\inline {\color{Blue} 2C_{1}}=7 ways.
case (ii): If Mr. Y is not a member then we left with (6+4-1) people.
we can select 3 from 9 in \inline {\color{Blue} 9C_{3}}=84 ways.
Thus, total number of ways is 7+84= 91 ways.
D
Answer: (D) 91
Question: A and B work at a hospital with 4 other workers. For an internal review, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that A and B will both be chosen?
(A) A)1/3
(B) B)1/4
(C) C)1/15
(D) D)3/8
(E) E)2/3
Rationale: Total number of people = 6
Probability of selecting A first and then B is 1/6∗1/5=1/30
Probability of selecting B first and then A is 1/6∗1/5=1/30
Therefore probability of selecting A and B for the review is 1/30+1/30=1/15
Answer is C
Answer: (C) C)1/15
Question: If x and y are positive odd integers, then which of the following must also be an odd integer?
I. x^(y+2)
II. x(y+2)
III. (y+1)^(x-1) + 1
(A) I only
(B) II only
(C) All options are applicable
(D) III only
(E) II,III only
Rationale: let x= 5, y= 3
I. 5^5 = > Odd
II. 5*5 = > Odd
III. 4^4 +1 = > Odd
Answer : C
Answer: (C) All options are applicable
Question: A certain sum earns simple interest of Rs. 800 in 2 years at a certain rate of interest. If the same sum earns compound interest of Rs. 845 in the same period of 2 years, What must be the rate of interest?
(A) 10% p.a.
(B) 90% p.a.
(C) 30% p.a.
(D) 19% p.a.
(E) 530% p.a.
Rationale: Explanation:
Given: 800 = (P * R * 2) / 100
S.I. For 1 year = Rs. 400
Thus, (840 – 800) = S.I. on Rs. 400 for 1 year
40 = (400 * R * 1) / 100
R = 10% p.a.
ANSWER: A
Answer: (A) 10% p.a.
Question: Steve traveled the first 2 hours of his journey at 60 mph and the remaining 3 hours of his journey at 80 mph. What is his average speed for the entire journey?
(A) 60 mph
(B) 72 mph
(C) 53.33 mph
(D) 64 mph
(E) 66.67 mph
Rationale: Distance traveled in 2 hours = 2 * 60 = 120 m
Distance traveled in 3 hours = 3 * 80 = 240m
Total distance covered = 240 + 120 = 360m
Total time = 2 + 3 =5 h
Hence avg speed = total distance covered / total time taken
= 360/5 = 72mph
Answer: B
Answer: (B) 72 mph
Question: There are 16 stations between Mumbai and Chennai. How many second class tickets have to be printed, so that a passenger can travel from any station to any other station?
(A) 316
(B) 306
(C) 326
(D) 336
(E) 356
Rationale: The total number of stations = 18
From 18 stations we have to choose any two stations and the direction of travel (i.e., Mumbai to Chennai is different from Chennai to Mumbai) in 18P2 ways.
18P2= 18 * 17 = 306
ANSWER: B
Answer: (B) 306
Question: How many seconds will a train 100 meters long take to cross a bridge 150 meters long if the speed of the train is 36 kmph?
(A) 22 sec
(B) 27 sec
(C) 25 sec
(D) 24 sec
(E) 11 sec
Rationale: Explanation:
D = 100 + 150 = 250
S = 36 * 5/18 = 10 mps
T = 250/10 = 25 sec
Answer: Option C
Answer: (C) 25 sec
Question: Without any stoppages a person travels a certain distance at an average speed of 40 km/hr and with stoppages he covers the same distance at an average of 20 km/hr. How many minutes per hour does he stop?
(A) 15
(B) 20
(C) 30
(D) 45
(E) None of above
Rationale: speed = 40km and with stoppages it covers only 20 kmso to travel 20 km at original speed i.e. 20 = 40*t, so t = 1/2 hour = 30minutes Answer : C
Answer: (C) 30
Question: What is the sum of all 3 digit numbers that leave a remainder of '2' when divided by 6?
(A) 82,650
(B) 64,850
(C) 64,749
(D) 49,700
(E) 56,720
Rationale: Find the number , Upon Sum of 3 Digits of a number Gives a Reminder 2 when it is Divided by 6
Seeing the Options After Dividing an Finding the Reminder of 2
My Answer was A
Answer: (A) 82,650
Question: David can divide his herd into 5 equal parts and also to 6 equal parts, but not to 9 equal parts. What could be the number of cows David has in his herd?
(A) 180
(B) 120
(C) 155
(D) 336
(E) 456
Rationale: On first look D, C,E are not divisible either by 5 or 6 - ruled out.
A,B divisible by both 5,6, but 180 is divisible by 9.
Answer : B
Answer: (B) 120
Question: Rajeev' age after 15 years will be 5 times his age 5 years back . What is the present age of Rajeev ?
(A) 8 years
(B) 10 years
(C) 12 years
(D) 14 years
(E) 16 years
Rationale: Explanation :
Dol. Let Rajeev's presen age be xx years , Then
Rajeev's ae after 15 years = (x+15)(x+15)years
Rajeev's age 5 years back = (xâˆ’5)(x-5) years
âˆ´âˆ´ x+15=5(xâˆ’5)x+15=5(x-5)
â‡” x+15=5xâˆ’25â‡” x+15=5x-25
â‡” 4x=40â‡” 4x=40
â‡” x=10â‡” x=10
Hence , Rajeev's present age = 10 years.
ANSWER IS B
Answer: (B) 10 years
Question: After decreasing 24% in the price of an article costs Rs.1216. Find the actual cost of an article?
(A) 1667
(B) 6789
(C) 1200
(D) 1600
(E) 1421
Rationale: CP* (76/100)
= 1216
CP= 16 * 100 => CP
= 1600
Answer: D
Answer: (D) 1600
Question: A sphere is inscribed in a cube with an edge of 10. What is the shortest possible distance from one of the vertices of the cube to the surface of the sphere?
(A) 10(√3-1)
(B) 5
(C) 10(√2-1)
(D) 5(√3-1)
(E) 5(√2-1)
Rationale: As sphere is inscribed in cube then
=>the edge of the cube equals to the diameter of a sphere --> Diameter=10
Diagonal of a cube equals to Diagonal=square_root(10^2+10^2+10^2)=10√3.
half of Diagonal-Diameter is gap between the vertex of a cube and the surface of the sphere = (10√3-10)/2
=5(√3-1)
ANSWER:D
Answer: (D) 5(√3-1)
Question: In how many ways can a committee consisting of three boys and four girls be formed from a group of six boys and seven girls?
(A) ⁶C₄ ⁷C₃
(B) (⁷C₄)(⁶C₃)
(C) ⁶C₃ ⁷C₅
(D) ⁷C₅ ⁶C₄
(E) ⁶C₃ ⁷C₃
Rationale: The group contain six boys and seven girls
Three boys can be selected from six boys in ⁶C₃ ways.
Four girls can be selected from seven girls in ⁷C₄ ways.
Total number of ways = (⁷C₄)(⁶C₃)
B
Answer: (B) (⁷C₄)(⁶C₃)
Question: A canteen requires 13 dozen bananas per day. How
many bananas will it require for 9 weeks?
(A) 728
(B) 9828
(C) 1404
(D) 9882
(E) None
Rationale: Requirement of bananas for 1 day in the canteen
= 13 dozens
∴ Requirement of bananas for 9 weeks i.e. 63 days
= 63 × 13 dozens
= 63 × 13 × 12 = 9828.
Answer D
Answer: (D) 9882
Question: A couple decides to have 3 children. If they succeed in having 4 children and each child is equally likely to be a boy or a girl, What is the probability that they will have exactly 2 girls and 1 boy?
(A) 1
(B) 2
(C) 3
(D) 5/8
(E) 4
Rationale: Sample space = 2^3 = 8.
Favourable events = {bgg}, {bgb}, {bbb}, {ggg}, {gbg}
Probability = 5/8 = 5/8.
Ans (D).
Answer: (D) 5/8
Question: Ramu bought an old car for Rs. 42000. He spent Rs. 10000 on repairs and sold it for Rs. 64900. What is his profit percent?
(A) 17%
(B) 19%
(C) 24.8%
(D) 14%
(E) 16%
Rationale: Total CP = Rs. 42000 + Rs. 10000
= Rs. 52000 and SP
= Rs. 64900
Profit(%) = (64900 - 52000)/52000 * 100
= 24.8%
Answer: C
Answer: (C) 24.8%
Question: 01-Jan-2007 was Monday. What day of the week lies on 01-Jan-2008?
(A) Wednesday
(B) Sunday
(C) Friday
(D) Tuesday
(E) Thursday
Rationale: Explanation:
Given that January 1, 2007 was Monday.
Odd days in 2007 = 1 (we have taken the complete year 2007 because we need to find out the odd days from 01-Jan-2007 to 31-Dec-2007, that is the whole year 2007)
Hence January 1, 2008 = (Monday + 1 Odd day) = Tuesday
Answer: Option D
Answer: (D) Tuesday
Question: The ratio between the number of sheep and the number of horses at the Stewar farm is 7 to 7. If each of horse is fed 230 ounces of horse food per day and the farm needs a total 12880 ounces of horse food per day. what is number sheep in the form??
(A) 18
(B) 28
(C) 32
(D) 56
(E) 58
Rationale: et no of sheep and horses are 7k and 7k
no of horses= 12880/230=56
now 7K=56 and k=8
no of sheep=(7*8) =56
ANSWER:D
Answer: (D) 56
Question: 2,500 has how many positive divisors?
(A) 10
(B) 12
(C) 15
(D) 20
(E) 25
Rationale: By factorization, we can write 2500 as 2500=2^2*5^4.
The number of factors is (2+1)(4+1) = 15
The answer is C.
Answer: (C) 15
Question: On dividing a number by 357, we get 40 as remainder.On dividing the same number by 17, what will be the remainder ?
(A) 6
(B) 5
(C) 8
(D) 7
(E) 2
Rationale: Let x be the number and y be the quotient.Then,
x=357*y+40
=(17*21*y)+(17*2)+6
=17*(21y+2)+6.
Required number =6.
Answer is A
Answer: (A) 6
Question: Five years ago the average of the ages of A and B was 40 years and now the average of the ages of B and C is 48 years. What will be the age of the B ten years hence?
(A) 16 years
(B) 15 years
(C) 56 years
(D) Data inadequate
(E) 17 years
Rationale: Let the present ages of A, B and C be a, b and c respectively.
Given, [(a - 5) + (b - 5)] / 2 = 40 => a + b = 90 --- (1)
(b + c)/2 = 48 => b + c = 96 --- (2)
From (1) and (2), we cannot find b.
Answer:D
Answer: (D) Data inadequate
Question: the square of two digit number(ab) divided by half of itself resultant added by 18 then divided by 2 then we get reverse of original number(ba). how many combination of ab exist
(A) 9
(B) 8
(C) 7
(D) 6
(E) 5
Rationale: (((10a+b)^2)/(10a+b/2)+18)/2=10b+a.
Simplify the above equation.
The final equation will be a-b=-1
There will be 8 combinations of a &b which will satisfy this equation.
i.e.
a=1,b=2
a=2,b=3
a=3,b=4
a=4,b=5
a=5,b=6
a=6,b=7
a=7,b=8
a=8,b=9
ANSWER:A
Answer: (A) 9
Question: If p and q are integers, such that p < 1 < q, and s is a nonnegative integer, which of the following must be true?
(A) p^2 < q^2
(B) p + q = 0
(C) sp < sq
(D) sp ≠ sq
(E) p/q < s
Rationale: We're told that P < 0 < Q and that S is a NON-NEGATIVE INTEGER. We're asked which of the following MUST be true.
P = -2
Q = 1
S = 0
Answer A: P^2 < Q^2.... 4 < 5 is TRUE
Answer B: P+Q=0... -2+1 = -1 NOT TRUE
Answer C: SP < SQ... 0 < 0 NOT TRUE
Answer D: SP ≠ SQ... 0 = 0 NOT TRUE
Answer E: P/Q < S... -2/1 < 0 not TRUE
A
Answer: (A) p^2 < q^2
Question: An meeting has 6 employees; there are 5 female employees and 1 male employee. In how many ways can a 3-person committee be created if the committee must include the male employee?
(A) 10
(B) 12
(C) 15
(D) 24
(E) 30
Rationale: An meeting has 6 employees;for male 1C1 = 1 ........ A
foe female = 5C2 = 10.........B
total = 10*1
= 10 - answer=A
Answer: (A) 10
Question: A women walking at 7 Kmph reaches her office 8 minutes late. If she walks at 9 Kmph, she reaches there 8 minutes earlier. How far is the office from her house?
(A) 2 1/5 Km
(B) 3 2/5 Km
(C) 4 1/3 Km
(D) 8 Km
(E) 8 2/5 Km
Rationale: Formula = S1*S2/S2-S1 * T1+T2/60
= 7*9/2 * 16/60
= 63/2 * 16/60
= 8 * 2/5
E
Answer: (E) 8 2/5 Km
Question: A rectangular field has to be fenced on three sides leaving a side of 20 feet uncovered. If the area of the field is 680 sq. feet, how many feet of fencing will be required?
(A) 95
(B) 92
(C) 88
(D) 82
(E) 90
Rationale: Area of the field =680 sq. feet.
Length of the adjacent sides are
20 feet and 680/20=34 feet.
Required length of the fencing
=20+34+34=88 feet Answer: Option C
Answer: (C) 88
Question: The total age of A and B is 11 years more than the total age of B and C. C is how many year younger than
(A) 14 years
(B) 12 years
(C) 56 years
(D) 66 years
(E) 11 years
Rationale: Given that A+B = 11 + B + C
=> A â€“ C = 11 + B â€“ B = 11
=> C is younger than A by 11 years
Answer:E
Answer: (E) 11 years
Question: Latha has 10 candies, ramu has 20 candies. Totally how many candies they have in all?
(A) 10
(B) 20
(C) 50
(D) 30
(E) 5
Rationale: 10+20=30. Answer is D
Answer: (D) 30
Question: If x and y are positive integers such that x < y and z=x/y, which of the following must be true?
I. z>(x − 1)/(y − 1)
II. z<(x − 1)/(y − 1)
III. z>(x + 1)/(y + 1)
(A) I only
(B) I and II
(C) II and III
(D) II only
(E) I and III
Rationale: x < y --> Let x = 2 and y = 3 --> z = 2/3
I. z>(x − 1)/(y − 1) --> 2/3 > 1/2 --> True
II. z<(x − 1)/(y − 1) --> 2/3 < 1/2 --> False
III. z>(x + 1)/(y + 1) --> 2/3 > 3/4 --> False
Answer: A
Answer: (A) I only
Question: The speed of a boat in still water is 60kmph and the speed of the current is 20kmph. Find the speed downstream and upstream?
(A) 80,70 kmph
(B) 87,40 kmph
(C) 80,40 kmph
(D) 70,40 kmph
(E) 80,44 kmph
Rationale: Speed downstream = 60 + 20 = 80 kmph
Speed upstream = 60 - 20 = 40 kmph
Answer: C
Answer: (C) 80,40 kmph
Question: The angle between the minute hand and the hour hand of a clock when the time is 7.30, is
(A) 35°
(B) 65°
(C) 55°
(D) 45°
(E) 95°
Rationale: Angle between hands of a clock
When the minute hand is behind the hour hand, the angle between the two hands at M minutes past H 'o clock
=30(H−M/5)+M/2 degree
When the minute hand is ahead of the hour hand, the angle between the two hands at M minutes past H 'o clock
=30(M/5−H)−M/2 degree
Here H = 7, M = 30 and minute hand is behind the hour hand.
Hence the angle
=30(H−M/5)+M/2
=30(7−30/5)+30/2
=30(7−6)+15
=30×1+15 =45°
Answer is D.
Answer: (D) 45°
Question: What will $1000 amount to in three years if it is invested at 20% per year compound interest, with the interest being compounded annually?
(A) $1596
(B) $1624
(C) $1728
(D) $1832
(E) $1958
Rationale: After one year: 1.2 * $1000
After two years: (1.2)^2 * $1000
After three years: (1.2)^3 * $1000 = $1728
The answer is C.
Answer: (C) $1728
Question: 12. What is the dividend. divisor 17, the quotient is 9 and the remainder is 5.
(A) 150
(B) 152
(C) 154
(D) 158
(E) 144
Rationale: D = d * Q + R
D = 17 * 9 + 5
D = 153 + 5
D = 158
Answer: (D) 158
Question: Can you find the missing number in the sequence given below?
10 15 20 11 16 ? 12 17 22 13 18 23
(A) 25
(B) 23
(C) 21
(D) 18
(E) 19
Rationale: Let's break the given series as below:
10 15 20
11 16 ?
12 17 22
13 18 23
Now read the number from left hand side from top to bottom as :
So the number that will replace '?' is 21
Answer : C
Answer: (C) 21
Question: Each shelf of a bookcase contained 12 books. If the librarian took out 19 books and rearranged the remaining books so that all shelves but one contained 8 books and the last shelf contained 9 books, how many shelves does the bookcase have?
(A) 7
(B) 6
(C) 5
(D) 8
(E) 9
Rationale: Let x be the number of shelves.
No of books in the beginning =12*x
After taking out 21 books No of remaining books = 12x -19
when the remaining books are rearranged, each shelf except the last shelf has 8 books and the last shelf has 11 books. So No of remaining books is also equal to 8*(x-1)+9
12x-19=8(x-1)+9
4x=20
x=5. Answer C
Answer: (C) 5
Question: If it is assumed that 60 percent of those who receive a questionnaire by mail will respond and 210 responses are needed, what is the minimum number of questionnaires that should be mailed?
(A) 290
(B) 320
(C) 350
(D) 380
(E) 410
Rationale: Let x be the minimum number of questionnaires to be mailed.
0.6x = 210
x = 350
The answer is C.
Answer: (C) 350
Question: Two trains of equal lengths take 10 sec and 15 sec respectively to cross a telegraph post. If the length of each train be 140 m, in what time will they cross other travelling in opposite direction?
(A) 17 sec
(B) 12 sec
(C) 16 sec
(D) 14 sec
(E) 18 sec
Rationale: Speed of the first train = 120/10 = 12 m/sec.
Speed of the second train = 120/5 = 8 m/sec.
Relative speed = 12 + 8 = 20 m/sec.
Required time = (140 + 140)/20 = 14 sec.
Answer:D
Answer: (D) 14 sec
Question: A batsman makes a score of 74 runs in the 17th inning and thus increases his averages by 3. What is his average after 17th inning?
(A) 25
(B) 31
(C) 26
(D) 29
(E) 39
Rationale: Let the average after 17 innings = x
Total runs scored in 17 innings = 17x
Average after 16 innings = (x-3)
Total runs scored in 16 innings = 16(x-3)
Total runs scored in 16 innings + 74 = Total runs scored in 17 innings
=> 16(x-3) + 74 = 17x
=> 16x - 48 + 74 = 17x
=> x = 26
Answer is C
Answer: (C) 26
Question: Sakshi can do a piece of work in 15 days.Tanya is 25% more efficient than Sakshi. The number of days taken by Tanya to do the same piece of work :
(A) 15
(B) 16
(C) 18
(D) 12
(E) 10
Rationale: Solution
Ratio of times taken by Sakshi and Tanya = 125 : 100 = 5 : 4 .
Suppose Tanya taken x days to do the work.
5 : 4 : : 15 : x ⇒ x = (15x4/5) ⇒ x = 12 days.
Hence,Tanya takes 16 days is complete the work.
Answer D
Answer: (D) 12
Question: Find the number of factors of 9321?
(A) 3
(B) 6
(C) 8
(D) 16
(E) 32
Rationale: 9321 = 3 x 13 x 239 = 31 x 13 1 x 239 1 ; add one to all the powers i.e.,
(1+1) x (1+1) x (1+1)= 8 ;
we get eight factors 1, 3, 13, 39, 239, 717, 3107, 9321
ANSWER:C
Answer: (C) 8
Question: If P and Q are non-zero integers, and P/Q > 1, then which of the following must be true?
(A) P > Q
(B) 2P >Q
(C) P^2< Q^2
(D) PQ > P
(E) P^3 < Q^3
Rationale: D
Answer: (D) PQ > P
Question: If each participant of a chess tournament plays exactly one game with each of the remaining participants, then 136 games will be played during the tournament. Find the number of participants.
(A) 15
(B) 16
(C) 17
(D) 18
(E) 19
Rationale: Let P be the number of participants.
PC2 = 136
(P)(P-1) = 272 = 17*16
P = 17
The answer is C.
Answer: (C) 17
Question: If 25^5 × 5^(-1) = (125)^x , then what is the value of x?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: 25^5 × 5^(-1) = (125)^x
(5^2)^5 × 5^(-1) = 5^3x
5^10 x 5^(-1) = 5^3x; Since all of the bases are the same now, we can equate the exponents in the next step
10-1 = 3x
9=3x
x=3
Ans. B)3
Answer: (B) 3
Question: If p#q denotes the least common multiple of p and q, then Q=((12#16)#(18#24)) = ?
(A)  216
(B)  180
(C)  144
(D)  108
(E)  72
Rationale: There are several ways to find the Least Common Multiple of two numbers. In this case, the most efficient method is to use the Greatest Common Factor: (A * B) / (GCF AB) = LCM AB
The greatest common factor of 12 and 16 is 4. So, 12#16 = 12*16/4 = 48.
The greatest common factor of 18 and 24 is 6. So, 18#24 = 18*24/6 = 72
Finally, the greatest common factor of 48 and 72 is 24. So,Q= ((12#16)#(18#24)) = 48#72 = (48*72)/24 = 2*72 = 144
The correct answer is C.
Answer: (C)  144
Question: A certain fruit stand sold apples for $0.70 each and bananas for $0.60 each. If a customer purchased both apples and bananas from the stand for a total of $5.60, what total number of apples and bananas did the customer purchase?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12
Rationale: Let's start with 1 apple for $0.70.
Let's subtract $0.70 from $5.60 until we get a multiple of $0.60.
$5.60, $4.90, $4.20 = 7*$0.60
The customer purchased 7 bananas and 2 apples.
The answer is B.
Answer: (B) 9
Question: An article is bought for Rs.675 and sold for Rs.810, find the gain percent?
(A) 33 1/9%
(B) 33 8/3%
(C) 20%
(D) 33 2/3%
(E) 33 1/2%
Rationale: 675 ---- 135
100 ---- ? => 20%
Answer: C
Answer: (C) 20%
Question: The average age of a group of 10 persons was decreased by 3 years when one person, whose age was 45 years, was replaced by a new person. Find the age of the new person?
(A) 12
(B) 15
(C) 18
(D) 21
(E) 25
Rationale: Initial average age of the 10 persons be P.
Age of the new person Q.
Sum of the ages of the initial 10 persons = 10P
New average = (P-3)
10(P-3) = 10P - 45 + Q => Q = 15
ANSWER:B
Answer: (B) 15
Question: For my anniversary, I decided to surprise my wife. Since she is a voracious reader, I decided to collect a lot of books for her. On the first day of the month, I bought one book, on the second, I bought two and on the third, I bought three. This process went on till the anniversary and on the day, I had 210 books with me to gift her.
Can you calculate, on which day is our anniversary?
(A) 20
(B) 28
(C) 23
(D) 33
(E) 25
Rationale: A
20rd day
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20 = 210
Thus our anniversary falls on the 20rd day of the month.
You can apply other formulas to shorten the process but that is the simplest way to do it.
Answer: (A) 20
Question: If A, B, C, and D are integers such that A - C + B is even and D + B - A is odd, which of the following expressions is always odd?
(A) A + D
(B) B + D
(C) C + D
(D) A + B
(E) A + C
Rationale: Even matrix method takes more than two mins in this problem since you have to jot down the even and odd values.
Try subtracting the equations
(A - C + B) - (D + B - A) = 2A-(C+D)
Even - Odd = Odd
So 2A-(C+D) is odd
2A is always even , so the subtrahend should always be odd, so C+D is odd.
ANSWER:C
Answer: (C) C + D
Question: The number 311311311311311311311 is
(A) divisible by 3 but not by 11
(B) divisible by 11 but not by 3
(C) divisible by both 3 and 11
(D) neither divisible by 3 nor by 11
(E) None of these
Rationale: Solution
311 is repeated seven times in the number, 311 is not divisible by 3 but 311 repeated twice is not divisible by 3, but divisible by 11.
Similarly 311 repeated thrice is divisible by 3, but not by 11.
As 311 is repeated seven times, which is neither multiple of 2 nor 3.
So, number is not divisible by 3 or 11. Answer D
Answer: (D) neither divisible by 3 nor by 11
Question: The elevator in an eleven-story office building travels at the rate of one floor per 1/4 minute, which allows time for picking up and discharging passengers. At the main floor and at the top floor, the operator stops for 1 minute. How many complete trips will an operator make during a 2-hour period?
(A) 88
(B) 56
(C) 42
(D) 17
(E) 64
Rationale: Complete trip = 10 floors up and 10 floors down = 20 floors = 20*1/4 = 5 minutes plus 2 minutes = 7 minutes.
2 hour = 120 minutes.
In 120 minutes operator can make 120/7=17 trips.
Answer: D.
Answer: (D) 17
Question: If there are 10 peanuts in a box and Mary puts 8 more peanuts inside, how many peanuts are in the box?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 18
Rationale: 10+8=18
correct answer is E)18
Answer: (E) 18
Question: A case of 12 rolls of paper towels sells for $9. The cost of one roll sold individually is $1.What is the percent of savings per roll for the 12-roll package over the cost of 12 rolls purchased individually?
(A) 9%
(B) 11%
(C) 15%
(D) 25%
(E) 90%
Rationale: Cost of 12 paper towels individually = 1*12=12
Cost of a set of 12 paper towels = 9
Cost of one roll = 9/12 = 3/4 = 0.75
Savings per roll = 1-.75 = 0.25
% of savings is = .25/ 1 *100 = 25%
D is the answer.
Answer: (D) 25%
Question: 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) 7/15
(B) 2/8
(C) 7/11
(D) 13/5
(E) 87
Rationale: Explanation:
Drawing two balls of same color from seven green balls can be done in â·Câ‚‚ ways.
Similarly from eight white balls two can be drawn in â¸Câ‚‚ ways.
P = â·Câ‚‚/Â¹âµCâ‚‚ + â¸Câ‚‚/Â¹âµCâ‚‚ = 7/15
A
Answer: (A) 7/15