mathewhe/aqua_rat huggingface dataset:
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) 7 years
(B) 10 years
(C) 12 years
(D) 13 years
(E) 14 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: A, B and C start a business each investing 20,000. After 5 months A withdrew 5000, B withdrew 4000 and C invests 6000 more. At the end of the year, a total profit of 69,900 was recorded. Find the share of B
(A) 20,000
(B) 21,200
(C) 28,200
(D) 20,500
(E) None of these
Rationale: Ratio of the capitals of A, B and C
= 20000 × 5 + 15000 × 7 : 20000 × 5 + 16000 × 7 : 20000 × 5 + 26000 × 7
= 205000 : 212000 : 282000 = 205 : 212 : 282.
B’s share = (69900 × 212⁄699) = 21200;
Answer C
Answer: (C) 28,200
Question: If x is an integer such that 1 < x < 9, 2 < x < 15, 7 > x > –1, 4 > x > 0, and x + 1 < 5, then x is
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: 1 < x < 9,
2 < x < 15,
-1< x < 7
0< x< 4
x+1<5
From above: 2< x < 4 --> x = 3.
Answer: A.
Answer: (A) 3
Question: If a 3-member subcommittee is to be formed from a certain 9-member committee, how many different such subcommittee are possible?
(A) 6
(B) 18
(C) 20
(D) 84
(E) 216
Rationale: Another way:
1st member can be selected in 9 ways
2nd can be selected in 8 ways
3rd can be selected in 7 ways
So total ways : 504
But to avoid the similar scenarios 504/3!=84
D
Answer: (D) 84
Question: The average (arithmetic mean) of 20, 40, and 60 is 7 more than the average of 10, 70, and what number?
(A) 19
(B) 25
(C) 35
(D) 45
(E) 55
Rationale: a1 = 120/3 = 40
a2 = a1 -7 = 33
sum of second list = 33*3 = 99
therefore the number = 99 -80 = 19
ANSWER:A
Answer: (A) 19
Question: In a neighborhood having 90 households, 11 did not have either a car or a bike. If 22 households had a both a car and a bike and 44 had a car, how many had bike only?
(A) 30
(B) 35
(C) 20
(D) 18
(E) 10
Rationale: {Total}={Car}+{Bike}-{Both}+{Neither} --> 90=44+{Bike}-22+11 --> {Bike}=57 --> # those who have bike only is {Bike}-{Both}=57-22=35.
Answer: B.
Answer: (B) 35
Question: Country X imposes a two-tiered tax on imported cars: the first tier imposes a tax of 30% of the car's price up to a certain price level. If the car's price is higher than the first tier's level, the tax on the portion of the price that exceeds this value is 20%. If Ron imported a $50,000 imported car and ended up paying $12000 in taxes, what is the first tier's price level?
(A) $22000
(B) $20000
(C) $23000
(D) $24000
(E) $25000
Rationale: Let T be the tier price, P be total price = 50000
Per the given conditions:
0.30T + 0.20(P-T) = 12000
0.30T+0.20*50000-0.20T =12000
0.10T +10000 =12000
0.10T =12000-10000 = 2000
T = 2000/0.10 =20000
Answer B
Answer: (B) $20000
Question: The difference between a two digit number and the number obtained by interchanging the positions of its digits is 36. What is the difference between the two digits of that number?
(A) 2
(B) 3
(C) four
(D) 8
(E) 9
Rationale: Solution
Let the ten's digit be x and units digit be y.
Then, (10x+y) - (10y+x)= 36	‹=›9(x - y) = 36
‹=›x - y = 4.
Answer C
Answer: (C) four
Question: A train 800 m long is running at a speed of 78 km/hr. If it crosses a tunnel in 1 min, then the length of the tunnel is?
(A) 992
(B) 389
(C) 500
(D) 277
(E) 781
Rationale: Speed = 78 * 5/18 = 65/3 m/sec.
Time = 1 min = 60 sec.
Let the length of the train be x meters.
Then, (800 + x)/60 = 65/3
x = 500 m.
Answer:C
Answer: (C) 500
Question: The sum of the ages of 5 children born at the intervals of 3 year each is 40 year. what is the age of the youngest child ?
(A) 2 year
(B) 8 year
(C) 10 year
(D) None of these
(E) 9 year
Rationale: Solution
let the ages of the children be x,(x + 3),(x + 6),(x + 9) and (x + 12) year.
then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 40 â‡” 5 x = 10 â‡” x= 2.
âˆ´ Age of the youngest child = x = 2 years. Answer A
Answer: (A) 2 year
Question: If a particular player is always chosen, in how many ways can a cricket-be chosen out of 15 players?
(A) 1224
(B) 1234
(C) 1350
(D) 1358
(E) 1365
Rationale: A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players.
=. Required number of ways = 14C10 = 14C4
= 14!/4!x19! = 1365
E
Answer: (E) 1365
Question: If a and b are odd integers, which of the following must be an even integer?
(A) a(b – 2)
(B) ab + 4
(C) (a + 2)(b – 4)
(D) 3a + 5b
(E) a(a + 6)
Rationale: 3a+5b==0dd*odd + odd*odd =odd+odd = even.
ANSWER:D
Answer: (D) 3a + 5b
Question: Rs.3150 is divided so that 5 times the first share, thrice the 2nd share and six times the third share amount to the same. What is the value of the third share?
(A) s529
(B) s527
(C) s570
(D) s750
(E) s507
Rationale: A+B+C = 3150
5A = 2B = 6C = x
A:B:C = 1/5:1/2:1/6 = 6:15:5
5/21 * 3150=Rs750
Answer:D
Answer: (D) s750
Question: At a restaurant, glasses are stored in two different-sized boxes. One box contains 12 glasses, and the other contains 16 glasses. If the average number of glasses per box is 15, and there are 16 more of the larger boxes, what is the total number of glasses at the restaurant? (Assume that all boxes are filled to capacity.)
(A) 96
(B) 240
(C) 56
(D) 384
(E) 480
Rationale: 1 small box and 17 large boxes = 1(12) + 17(16) = 12 + 272 = 284 glasses at the MINIMUM
Since the question asks for the total number of glasses, we can now eliminate Answers A, B and C....
The difference in the number of boxes MUST be 16 though, so we could have....
2 small boxes and 18 large boxes
3 small boxes and 19 large boxes
etc.
With every additional small box + large box that we add, we add 12+16= 28 MORE glasses. Thus, we can just "add 28s" until we hit the correct answer....
284+28 = 312
312+28 = 340
340+28 = 368
368+28 = 396
At this point, we've 'gone past' Answer D, so the correct answer MUST be Answer E.....But here's the proof....
396+28 = 424
424+28 = 452
452+28 = 480
Final Answer:E
Answer: (E) 480
Question: For 600km journey it will take 8hrs, if 120 km is done by bus and the rest by car. It takes 20 minutes more, if 200 km is done by bus and the rest bycar. The ratio of the speed of the train to that of the cars is?
(A) 1:3
(B) 3:4
(C) 2:5
(D) 3:7
(E) 3:11
Rationale: Let the speed of the train be x km/hr and that of the car be y km/hr.
Then, 120 + 480 = 8 1 + 4 = 1 ....(i)
x y x y 15
And, 200 + 400 = 25 1 + 2 = 1 ....(ii)
x y 3 x y 24
Solving (i) and (ii), we get: x = 60 and y = 80.
Ratio of speeds = 60 : 80 = 3:4.
B
Answer: (B) 3:4
Question: 9 - 3 ÷ 1/3 + 3 = ?
(A) 1
(B) 3
(C) 6
(D) 9
(E) 12
Rationale: 9 - 3 1/3 + 3
=9-3÷1/3+3
=9-(3X3) +3
=9-9+3
=3
CORRECT ANSWER : B
Answer: (B) 3
Question: Alok ordered 16 chapatis, 5 plates of rice, 7 plates of mixed vegetable and 6 ice-cream cups. The cost of each chapati is Rs.6, that of each plate of rice is Rs.45 and that of mixed vegetable is Rs.70. The amount that Alok paid the cashier was Rs.1051. Find the cost of each ice-cream cup?
(A) 25
(B) 40
(C) 77
(D) 99
(E) 91
Rationale: Let the cost of each ice-cream cup be Rs.x
16(6) + 5(45) + 7(70) + 6(x) = 1051
96 + 225 + 490 + 6x = 1051
6x = 240 => x = 40.
Answer: B
Answer: (B) 40
Question: In a certain city, 60 percent of the registered voters are Democrats and the rest are Republicans. In a mayoral race, if 75 percent of the registered voters who are Democrats and 25 percent of the registered voters who are Republicans are expected to vote for Candidate A, what percent of the registered voters are expected to vote for Candidate A ?
(A) 50%
(B) 53%
(C) 54%
(D) 55%
(E) 57%
Rationale: Say there are total of 100 registered voters in that city. Thus 60 are Democrats and 40 are Republicans.
60*0.75=45 Democrats are expected to vote for Candidate A;
40*0.25=10 Republicans are expected to vote for Candidate A.
Thus total of 45+10=55 registered voters are expected to vote for Candidate A, which is 55% of the total number of registered voters.
Answer: D.
Answer: (D) 55%
Question: Two pipes can fill a tank in 20 and 24 minutes respectively and a waste pipe can empty 6 gallons per minute. All the three pipes working together can fill the tank in 15 minutes. The capacity of the tank is?
(A) 60 gallons
(B) 100 gallons
(C) 240 gallons
(D) 180 gallons
(E) 130 gallons
Rationale: Work done by the waste pipe in 1 minute = 1/15 - (1/20 + 1/24) = - 1/40
Volume of 1/40 part = 6 gallons\
Volume of whole = 6 * 40 = 240 gallons.
ANSWER:C
Answer: (C) 240 gallons
Question: A sum of Rs.4400 is invested at a compound interest for three years, the rate of interest being 10% p.a., 20% p.a. and 25% p.a. for the 1st, 2nd and the 3rd years respectively. Find the interest received at the end of the three years.
(A) Rs.2860
(B) Rs.3120
(C) Rs.3320
(D) Rs.2760
(E) None of these
Rationale: Let A be the amount received at the end of the three years.
A = 4400[1 + 10/100][1 + 20/100][1 + 25/100]
A = (4400 * 11 * 6 * 5)/(10 * 5 * 4)
A = Rs.7260
So the interest = 7260 - 4400 = Rs.2860
ANSWER:A
Answer: (A) Rs.2860
Question: Beth received 1/10 of the votes cast in a certian election. What franction of the other votes cast would she have needed in order to have received 1/2 of the votes cast?
(A) 1/5
(B) 4/7
(C) 3/10
(D) 7/20
(E) 1/2
Rationale: Let the total votes be 10. Beth received 1 votes, other votes 10-1=9. In order to have received 1/2 of the votes she needed 5 votes so 4 more, which is 4/7 of the other votes.
Answer: B.
Answer: (B) 4/7
Question: In a two-digit number, the digit at unit place is 1 more than twice of the digit at tens place. If the digit at unit and tens place be interchanged, then the difference between the new number and original number is less than 1 to that of original number. What is the original number?
(A) 52
(B) 73
(C) 25
(D) 49
(E) 37
Rationale: Let the original number be l0 x + y
y = 2x + 1....(i)
and (l0y + x) – (10x + y) = 10x + y – 1
or, 9y – 9x = l0x + y – 1
or, l9x – 8y = 1 ...(ii)
Putting the value of (i) in equation (ii) we get,
19x – 8(2x + 1) = 1
or, 19x – 16x – 8 = 1
or, 3x = 9 or, x = 3
So, y = 2 × 3 + 1 = 7
Answer E
\ original number = 10 × 3 + 7 = 37
Answer: (E) 37
Question: A, B and C have Rs.500 between them, A and C together have Rs.200 and B and C Rs.310. How much does C have?
(A) 50
(B) 78
(C) 267
(D) 29
(E) 10
Rationale: A+B+C = 500
A+C = 200
B+C = 310
--------------
A+B+2C = 510
A+B+C = 500
----------------
C = 10
Answer: E
Answer: (E) 10
Question: In the formula V = 1/(2r)^2, if r is halved, then V is multiplied by ?
(A) 64
(B) 1/8
(C) 1
(D) 4
(E) 1/64
Rationale: Say r=2 => V1 = 1/16
when r=1; V2 = 1/4
V2 = 4*V1.
Answer : D
Answer: (D) 4
Question: A metallic hemisphere is melted and recat in the shape of a cone with the same base radius (R) as that of the hemisphere. If H is the height of the cone, then :
(A) H = 2R
(B) H = 4R
(C) H = √4R
(D) H = 2/3 R
(E) None
Rationale: Sol.
2/3 ∏R³ = 1/3 ∏R²H ⇒ H = 2R.
Answer A
Answer: (A) H = 2R
Question: A train 385 meters long is running with a speed of 60 kmph. In what time will it pass a man who is running at 6 kmph in the direction opposite to that in which the train is going?
(A) 75 sec
(B) 52 sec
(C) 41 sec
(D) 62 sec
(E) 21 sec
Rationale: Speed of train relative to man
= (60 + 6) km/hr
= 66 km/hr
[66 * 5/18] m/sec
= [55/3] m/sec.
Time taken to pass the man
= [385 * 3/55] sec
= 21 sec
Answer:E
Answer: (E) 21 sec
Question: If n is a positive integer, which one of these following numbers must have a remainder of 3 when
divided by any of the numbers 4, 5, and 6?
(A) 125n + 3
(B) 240n + 3
(C) 380n + 3
(D) 590n + 3
(E) 700n + 3
Rationale: The numbers 4, 5, and 6 all divide 240 so they all divide 240n.
When we divide (240n + 3) by 4, 5, or 6, the remainder must be 3.
The answer is B.
Answer: (B) 240n + 3
Question: The fourth proportional to 6, 11, 36 is:
(A) 64
(B) 66
(C) 68
(D) 70
(E) 72
Rationale: Let the fourth proportional to 6, 11, 36 be x.
Then, 6 : 11 : 36 : x
6x = (11 x 36)
x =	(11 x 36)/6
x=396/6 =66
Answer: Option B
Answer: (B) 66
Question: Ratio of the ages of Mahesh and Nilesh is 5:x. Mahesh is 18 years younger to Ramesh. After nine years Ramesh will be 47 years old. If the difference between the ages of Mahesh and Nilesh is same as the age of Ramesh, what is the value of x?
(A) 14.8
(B) 14.4
(C) 14.7
(D) 14.1
(E) 14.5
Rationale: Let the present ages of Mahesh, Nilesh and Ramesh be M, N and R respectively.
M/N = 5/x --- (1)
M = R - 18 --- (2)
R + 9 = 47 --- (3)
M - N = R --- (4)
(3) => R = 47 - 9 = 38 years
(2) => M = 38 - 18 = 20 years
(1) => 20/N = 5/x => N = 4x
(4) => 4x - 20 = 38
=> 4x = 58 => x = 14.5
Answer:E
Answer: (E) 14.5
Question: Rahul will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. The heights of the people within each row must increase from left to right, and each person in the second row must be taller than the person standing in front of him or her. How many such arrangements of the 6 people are possible?
(A) 5
(B) 6
(C) 9
(D) 24
(E) 26
Rationale: Rahul will arrange 6 people of 6 different heights for photograph by placing them in two rows of three so that each person in the first row is standing is standing in front of someone in the second row. person with max height is in the second row, person with min height is in the first row. We need to select 1 person in the middle of each row... In the middle of the first row we can put only 2, 3 or 4. In the middle of the second row we can put only 3, 4, 5. If we select {3 in the sec. row, 2 in the first}, {4,2}, {5,2}, {4,3}, {5,3}, {5,4}. So, there are 0*1 + 1*1 + 2*1 + 1*1 + 1*1 + 0*1 = 5 cases....A
Answer: (A) 5
Question: In a certain egg-processing plant, every egg must be inspected, and is either accepted for processing or rejected. For every 96 eggs accepted for processing, 4 eggs are rejected. If, on a particular day, 12 additional eggs were accepted, but the overall number of eggs inspected remained the same, the ratio of those accepted to those rejected would be 99 to 1. How many R eggs does the plant process per day?
(A)  100
(B)  300
(C)  400
(D)  3,000
(E)  4,000
Rationale: Straight pluggin in for me. As usual, I started with C and got the answer.
Lets' back calculate and see what we get
Let us consider eggs processed each day to be 400
So Initial ratio of eggs processed and rejected is 96:4 or 24:1
So out of 400 eggs, there will be 384 eggs processed and 16 rejected.
Now if the no. of eggs inspected remain and 12 more eggs get accepted that means there R=384+12=396 eggs accepted and 4 rejected...and the ratio will be 99:1
Bingo...this is what the questions says....
Its always a good idea to start with C.
Answer: (C)  400
Question: 15 binders can bind 1400 books in 21 days. How many binders will be required to bind 1600 books in 20 days?
(A) 87
(B) 18
(C) 17
(D) 16
(E) 10
Rationale: Binders Books Days
15 1400 21
x 1600 20
x/15 = (1600/1400) * (21/20) => x = 18
Answer:B
Answer: (B) 18
Question: How many multiples of 10 are there between 11 and 1001?
(A) 98
(B) 99
(C) 100
(D) 97
(E) 95
Rationale: 10 * 2 = 20
10 * 100 = 1000
Total multiples = (100 - 2) + 1
= 99
Answer B
Answer: (B) 99
Question: A can do a piece of work in 18 days, B in 27 days, C in 36 days. They start worked together . But only C work till the completion of work. A leaves 4 days and B leaves 6 days before the completion of work. In how many days work be completed?
(A) 12
(B) 11
(C) 99
(D) 27
(E) 99
Rationale: Let the work be completed in x days
(x-4)days of A + (x-6)days of B + x days of C = 1
\inline \Rightarrow \inline \frac{x-4}{18}+\frac{x-6}{27}+\frac{x}{36}=1
\inline \Rightarrow \frac{13x-48}{108}=1
x = 12
\inline \therefore Total time = 12 days
Answer:A
Answer: (A) 12
Question: When positive integer X is divided by positive integer Y, the remainder is 1.44. If X/Y = 96.12, what is the value of Y?
(A) 96
(B) 75
(C) 48
(D) 25
(E) 12
Rationale: When positive integer x is divided by positive integer y, the remainder is 1.44 --> x=qy+1.44;
x/y=96.12 --> x=96y+0.12y (so q above equals to 96);
0.12y=1.44 --> y=12.
Answer: E.
Answer: (E) 12
Question: Two MBA admissions committees are to be formed randomly from 6 second year MBAs with 3 members each. What is the probability R that Jane will be on the same committee as Albert?
(A)  12%
(B)  20%
(C)  33%
(D)  40%
(E)  50%
Rationale: Total number of ways to choose 3 member committee - 6C3=(6!/3!3!)=20
No. of ways Albert n Jane are in same committee:- (4C1 * 2)= 8
Probability R= (8/20) *100 =40%.
+1 for me.. :D
Answer: (D)  40%
Question: On a game show, a contestant spins three different wheels; each wheel is numbered 1 to 10. What is the probability that the contestant will spin all tens?
(A) 1/3
(B) 1/2
(C) 1/50
(D) 1/1,000
(E) 1/100
Rationale: All 10s:
1st wheel = 10 = 1/10
2nd wheel = 10 = 1/10
3rd wheel = 10 = 1/10
(1/10)(1/10)(1/10) = 1/1,000
Answer: D
Answer: (D) 1/1,000
Question: John Purchased 1300 large bottles at $1.89 per bottle and 750 small bottles at $1.38 per bottle. What was the approximate average price paid per bottle?
(A) $1.63
(B) $1.64
(C) $1.68
(D) $1.70
(E) $1.76
Rationale: (1300*1.89+750*1.38)/(1300+750) =~1.70
Option (D)
Answer: (D) $1.70
Question: In 4 years, Raj's father age twice as raj, Two years ago, Raj's mother's age twice as raj. If Raj is 32yrs old in eight yrs from now, what is the age of Raj's mother and father?
(A) 27
(B) 36
(C) 28
(D) 46
(E) 91
Rationale: Raj present age = 32 - 8 = 24.
After 4 years Raj's age is 28. and Raj's fathers age is 28 x 2 = 56, and his present age is 52.
Two years ago, Raj's age is 22. and his mother's age is 22 x 2 = 44. His mother's present age = 46
Answer:C
Answer: (C) 28
Question: In a college, the ratio of the number of boys to girls is 8 : 5. If there are 160 girls, the total number of students in the college is
(A) 100
(B) 250
(C) 260
(D) 416
(E) None of these
Rationale: Explanation:
Let the number of boys and girls be 8x and 5x.
Total number of students = 13x = 13 × 32 = 416.
Answer: D
Answer: (D) 416
Question: R-R-G-G-G-Y-Y-B-R-R-G-G-G-Y-Y-B… B-R-R
The preceding is a representation of the different colored beads on a string. The beads follow a repeating pattern and the colors Red, Green, Yellow, and Blue are represented by R, G, Y, and B respectively. Which of the following is a possible number of beads in the missing section of the string represented above?
(A) 63
(B) 64
(C) 65
(D) 66
(E) 67
Rationale: The repeated pattern R-R-G-G-G-Y-Y-B has 8 beads.
But the missing section includes R-R-G-G-G-Y-Y at the end.
Thus the number of beads in the missing section has the form 8k + 7.
The answer is A.
Answer: (A) 63
Question: The average of 13 numbers is 60. Average of the first 7 of them is 57 and that of the last 7 is 61. Find the 8th number?
(A) 46
(B) 82
(C) 45
(D) 43
(E) 53
Rationale: Sum of all the 13 numbers = 13 * 60 = 780
Sum of the first 7 of them = 7 * 57 = 399
Sum of the last 7 of them = 7 * 61 = 427
So, the 8th number = 427 + 399 - 780 = 46.
Answer:A
Answer: (A) 46
Question: Which of the following CANNOT be the least common multiple of two positive integers x and y
(A) xy
(B) x
(C) x - xy
(D) y
(E) x + y
Rationale: The least common multiple of two positive integers cannot be less than either of them. Therefore, since x - xy is less than x, it cannot be the LCM of a x and y.
Answer: C
Answer: (C) x - xy
Question: I chose a number and divide it by 8. Then I subtracted 160 from the result and got 12. What was the number I chose?
(A) 1376
(B) 1800
(C) 1400
(D) 2500
(E) 100
Rationale: Let x be the number I chose, then
x/8−160=12
x/8=172
x=1376
Answer is A.
Answer: (A) 1376
Question: Raman's salary was decreased by 50% and subsequently increased by 50%. How much percent does he loss
(A) 75
(B) 65
(C) 45
(D) 25
(E) 35
Rationale: Explanation:
Let the origianl salary = Rs. 100
It will be 150% of (50% of 100)
= (150/100) * (50/100) * 100 = 75
So New salary is 75, It means his loss is 25%
Answer: Option D
Answer: (D) 25
Question: Donald plans to invest x dollars in a savings account that pays interest at an annual rate of 8% compounded quarterly. Approximately what amount is the minimum that Donald will need to invest to earn over $100 in interest within 6 months?
(A) $1500
(B) $1750
(C) $2000
(D) $2500
(E) $3000
Rationale: Solution:
r = Rate = 8% compounded quarterly.. = 2% per quarter
t = 6 months = 2 quarters
So A = P (1+0.02)^2
=> A = P * 1.0404
Substitute, P for 1500, 1700, 2000.. The A-P should be greater than 100 (since Interest = Amount - principal).
For 2500, interest is 101...
Hence, D
Answer: (D) $2500
Question: An article is bought for Rs.675 and sold for Rs.1080, find the gain percent?
(A) 33 1/9%
(B) 60%
(C) 33 1/3%
(D) 33 2/3%
(E) 33 1/2%
Rationale: 675 ---- 405
100 ---- ? => 60%
Answer: B
Answer: (B) 60%
Question: Two numbers are in the ratio 3:5. If 9 be subtracted from each, they are in the ratio of 2:3. The first number is:
(A) A)27
(B) B)98
(C) C)34
(D) D)35
(E) E)62
Rationale: (3x-9):(5x-9) = 2:3
x = 9 => 3x = 27
Answer:A
Answer: (A) A)27
Question: The mean of 30 values was 150. It was detected on rechecking that one value 165 was wrongly copied as 135 for the computation of the mean. Find the correct mean.
(A) 151
(B) 149
(C) 152
(D) 148
(E) None of the above
Rationale: Corrected mean = 150×30−135+165/30
= 4500−135+165/30
=4530/30=151
Answer A
Answer: (A) 151
Question: A set of data consists of the following 7 numbers: 0, 2, 4, 6, and 8. Which two numbers, if added to create a set of 7 numbers, will result in a new standard deviation that is close to the standard deviation for the original 5 numbers?
(A) -1 and 9
(B) 4 and 4
(C) 3 and 5
(D) 2 and 6
(E) 0 and 8
Rationale: If you are in for some calculations , this is how I got to it
mean = 4
sd = \sqrt{8} = 2.8
Expected values for the SD to not change are - One value below SD from mean is (4 - 2.8) = 1.2 , and one value above SD is (4 + 2.8) = 6.8
This would mean , adding 1.2 ans 6.8 would have no impact on the SD . SD remains the same when these two numbers are added. Now for SD to change the least , we need to add two values that are closest to these two values.
Hence any two values that are closest to 1.2 and 6.8 would change the SD , the least.
1. -1 , 9
distance between (1,9) and (1.2 and 6.8) is 2.2 and 2.2
2. 4 , 4
distance etween (4,4) and (1.2 , 6.8) is 2.8 and 2.8
3. 3 , 5
Distance is - 1.8 and 1.8
4. 2 , 6
Distance is - 0.8 and 0.8
5. 0 , 8
Distnace is - 1.2 and 1.2
Hence from above , we see that adding 3 and 5 , results in a value that would change the SD to the least. Hence C
Answer: (C) 3 and 5
Question: If A + B means A is the brother of B; A - B means A is the sister of B and A x B means A is the father of B. Which of the following means that C is the son of M?
(A) M - N x C + F
(B) F - C + N x M
(C) N + M - F x C
(D) M x N - C + F
(E) none
Rationale: M is the father of N and N is the sister of C.C is brother of F..
so,N and c and F are siblings.
ANSWER:D
Answer: (D) M x N - C + F
Question: Louie takes out a three-month loan of $1000. The lender charges him 20% interest per month compounded monthly. The terms of the loan state that Louie must repay the loan in three equal monthly payments. To the nearest dollar, how much does Louie have to pay each month?
(A) A)333
(B) B)383
(C) C)402
(D) D)438
(E) E)478
Rationale: Here's the calculation for that case, assume monthly payment is X.
After 1st month: (1000)(1.2)-X = 1200-X
After 2nd month: (1200-X)(1.2)-X = 1440-2.21X
After 3rd month: (1440-2.21X)(1.2)-X = 1584-3.31X
Now, the amount after the last payment in 3rd month must bring the total to 0. Hence:
1584-3.31X = 0
X = 1584/3.31 = 478.54
Answer E
Answer: (E) E)478
Question: Calculate the area of a triangle, if the sides of are 39 cm, 36 cm and 15 cm, what is its area?
(A) 570 cm2
(B) 370 cm2
(C) 170 cm2
(D) 271 cm2
(E) 270 cm2
Rationale: The triangle with sides 39 cm, 36 cm and 15 is right angled, where the hypotenuse is 39 cm.
Area of the triangle = 1/2 * 36 * 15 = 270 cm2
Answer: E
Answer: (E) 270 cm2
Question: A person can swim in still water at 12 km/h. If the speed of water 10 km/h, how many hours will the man take to swim back against the current for 12km?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: M = 12
S = 10
US = 12 - 10 = 2
D = 12
T = 12/2 = 6 Answer:D
Answer: (D) 6