mathewhe/aqua_rat huggingface dataset:
Question: In a 1000 m race, A beats B by 50 m and B beats C by 10 m. In the same race, by how many meters does A beat C?
(A) A)60m
(B) B)829m
(C) C)822m
(D) D)929m
(E) E)132mj
Rationale: By the time A covers 1000 m, B covers (1000 - 50) = 950 m.
By the time B covers 1000 m, C covers (1000 - 10) = 990 m.
So, the ratio of speeds of A and C =
1000/950 * 1000/990 = 1000/940 So, by the time A covers 1000 m, C covers 940 m.
So in 1000 m race A beats C by 1000 - 940 = 60 m.
Answer:A
Answer: (A) A)60m
Question: A man goes from A to B at a speed of 21 kmph and comes back to A at a speed of 21 kmph. Find his average speed for the entire journey?
(A) 23.3 kmph
(B) 25.3 kmph
(C) 22.5 kmph
(D) 22.3 kmph
(E) 22.9 kmph
Rationale: Distance from A and B be 'd'
Average Speed = total distance/total time
Average Speed = (2d)/[(d/21) + (d/24]
= (2d)/[15d/168) => 22.3 kmph.
Answer:D
Answer: (D) 22.3 kmph
Question: A and B starts a business with Rs.8000 each, and after 4 months, B withdraws half of his capital . How should they share the profits at the end of the 18 months?
(A) 18:11
(B) 18:18
(C) 18:22
(D) 18:39
(E) 18:39
Rationale: Explanation:
A invests Rs.8000 for 18 months, but B invests Rs.8000 for the first 4 months and then withdraws Rs.4000. So, the investment of B for remaining 14 months is Rs.4000 only.
A : B
8000*18 : (8000*4) + (4000*14)
14400 : 88000
A:B = 18:11
Answer:A
Answer: (A) 18:11
Question: For four days of work, a clerk had daily earnings of $140, $130, $140, and $140 respectively. In which of the following intervals does the standard deviation of the daily earnings lie?
(A) Between $10 and $100
(B) Between $10 and $50
(C) Between $0 and $10
(D) Between $10 and $70
(E) Between $10 and $90
Rationale: The standard deviation is between 0 and 10.
The reason is that none of the numbers in the set is further away from the mean than 10(or rather Abs(130-(140*3+130)/4)). I am not fully sure how to calculate the standard deviation(I simply remember that there were some formula for calculating the average of the squared distances from the mean for all items in the set from statistics classes - variation), but I believe this will suffice for any GMAT question related to standard deviation.
Answer : C
Answer: (C) Between $0 and $10
Question: If a large pizza has a radius that is 20% larger that that of a medium pizza, what is the percent increase in area between a medium and a large pizza?
(A) 20%
(B) 36%
(C) 44%
(D) 50%
(E) 64%
Rationale: Let the radius of medium pizza be r. Then the radius of large pizza is 1.2r.
The area of the medium pizza is pi*r^2
The area of the large pizza is pi*(1.2*r)^2 = 1.44*pi*r^2, an increase of 44%.
The answer is C.
Answer: (C) 44%
Question: The ratio of the radius of two circles is 3: 4, and then the ratio of their areas is?
(A) 1:7
(B) 9:16
(C) 1:9
(D) 3:7
(E) 3:4
Rationale: r1: r2 = 3:4
Î r1^2: Î r2^2
r1^2: r2^2 = 9:16
Answer: B
Answer: (B) 9:16
Question: A person can row at 9 kmph and still water. He takes 4 1/2 hours to row from A to B and back. What is the distance between A and B if the speed of the stream is 1 kmph?
(A) 33
(B) 20
(C) 99
(D) 78
(E) 61
Rationale: Let the distance between A and B be x km.
Total time = x/(9 + 1) + x/(9 - 1) = 4.5
=> x/10 + x/8 = 9/2 => (4x + 5x)/40 = 9/2 => x = 20 km.
Answer:B
Answer: (B) 20
Question: The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
(A) 4 years
(B) 5 years
(C) 6 years
(D) 7 years
(E) None
Rationale: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
5x = 20
x = 4.
Age of the youngest child = x = 4 years
A)
Answer: (A) 4 years
Question: In a year N, the 259th day of the year is a Saturday. In the year N+l, the 222th day of the year is also a Saturday. What is the 119th day of the year N-l?
(A) Thursday
(B) Saturday
(C) Friday
(D) Tuesday
(E) Monday
Rationale: as 259th day of year N and 222th day of year N+1 is same i.e saturday, so number of day between above 2 day is must be divided by 7..
no. of days btwn dis 2 day may b (366-259)+222=329----(1) or (365-259)+222=328------(2)
as 329 is divided by 7 so year N is leap year son Year N-1 is not a leap year....
now number of day btwn 119th of N-1 and 259th of N is (365-119)+259 =505
now 505/7 gives remainder 1 , so 504 is divided by 7, so 120th day of N-1 is saturday...so 119th day of N-1 is Friday
ANSWER:C
Answer: (C) Friday
Question: A train which has 410 m long, is running 45 kmph. In what time will it cross a person moving at 9 kmph in same direction ?
(A) 56 sec
(B) 41 sec
(C) 36 sec
(D) 29 sec.
(E) 19 sec.
Rationale: Time taken to cross a moving person = length of train/ relative speed
Time taken = 410/((45-9) (5/18)
= 410/ 36*(5/18)
= 410/10
= 41 sec
ANSWER:B
Answer: (B) 41 sec
Question: Two trains running in opposite directions cross a man standing on the platform in 27 seconds and 17 seconds respectively . If they cross each other in 23 seconds, what is the ratio of their speeds?
(A) Insufficient data
(B) 3 : 2
(C) 3 : 1
(D) 1 : 3
(E) 1 : 2
Rationale: Explanation:
Let the speed of the trains be x and y respectively
length of train1 = 27x
length of train2 = 17y
Relative speed= x+ y
Time taken to cross each other = 23 s
=> (27x + 17 y)/(x+y) = 23
=> (27x + 17 y)/ = 23(x+y)
=> 4x = 6y
=> x/y = 6/4 = 3/2
Answer: Option B
Answer: (B) 3 : 2
Question: For a certain exam,a score of 58 was 2 standard deviations below mean and a score of 98 was 3 standard deviations above mean.What was the mean score Q for the exam?
(A) 74
(B) 76
(C) 78
(D) 80
(E) 82
Rationale: A score of 58 was 2 standard deviations below the mean --> 58 = Mean - 2d
A score of 98 was 3 standard deviations above the mean --> 98 = Mean + 3d
Solving above for Mean Q= 74.
Answer: A.
Answer: (A) 74
Question: Excluding stoppages, the speed of a bus is 75 kmph and including stoppages, it is 45 kmph. For how many minutes does the bus stop per hour?
(A) 15
(B) 24
(C) 17
(D) 19
(E) None of these
Rationale: Due to stoppages, it covers 30 km less.
Time taken to cover 30 km = ((30/75)Ã—60) = 24 min.
Option(B) is correct
Answer: (B) 24
Question: In traveling from a dormitory to a certain city, a student went 1/4 of the way by foot, 1/2 of the way by bus, and the remaining 10 kilometers by car. What is the distance, in kilometers, from the dormitory to the city?
(A) 10
(B) 45
(C) 30
(D) 20
(E) 40
Rationale: Whole trip = distance by foot + distance by bus + distance by car
x = 1/4x + 1/2x + 10
x - 1/4x - 1/2x = 10
X = 40km
Option: E
Answer: (E) 40
Question: Chris age after 9years will be 5 times his age 5years back. what is the present age of Chris?
(A) A)20
(B) B)25
(C) C)15
(D) D)22
(E) E)16
Rationale: Chris present age= x
after 9years = x+9
5years back = x-5
x+9= 5(x-5)
x=16
Answer is E
Answer: (E) E)16
Question: 38, 56, 22,64, 31,47, 13, 82
Which of the following numbers is greater than three-fourth of the numbers but less than one-fourth of the numbers in the list above?
(A) a- 60
(B) b- 68
(C) c- 69
(D) d- 71
(E) e- 73
Rationale: Important:- Arrange the numbers in ascending order first.
13, 22, 31, 38, 47, 56, 64, 82
3/4th of the number list represents- 56 (6th number)
remaining 1/4th list represents 64 (7 th number)
60 fits in between above 2
Answer:- A
Answer: (A) a- 60
Question: Company KW is being sold, and both Company A and Company B were considering the purchase. The price of Company KW is 40% more than Company A has in assets, and this same price is also 100% more than Company B has in assets. If Companies A and B were to merge and combine their assets, the price of Company KW would be approximately what percent of these combined assets?
(A) 66%
(B) 75%
(C) 82%
(D) 116%
(E) 150%
Rationale: Let the price of Company A's assets be 100
Price of assets of KW is 40% more than company A's assets which is 140
Price of assets of KW is 100% more than company B's assets which means price of Company B's assets is half the price of KW = 70
A+B = 170
KW = 140
KW/(A+B)*100 = 140/170*100 = 82.35% or 82%
C
Answer: (C) 82%
Question: What is the next number in the given series
4,18,100,294,....?
(A) 1210
(B) 1220
(C) 1230
(D) 1240
(E) 1250
Rationale: The given series is difference of cubes and squares of consecutive prime numbers.
2*2*2-2*2=4,
3*3*3-3*3=18,
5*5*5-5*5=100,
7*7*7-7*7=294,
11*11*11-11*11=1210
ANSWER:A
Answer: (A) 1210
Question: A palindrome is a number that reads the same front-to-back as it does back-to-front (e.g. 202, 575, 1991, etc.) p is the smallest integer greater than 200 that is both a prime and a palindrome. What is the sum of the digits of p?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
Rationale: Given that p is smallest integer greater than 200 - assume there is a 3-digit that satisfies the above conditions. Let the number be xyx ; question asks us the values of 2x+y
We can straight away cross out options A) and D) - sum of digits 3 or 6 implies it is divisible by 3 ---> we know that p is a prime number
Coming to option B) 2x + y = 4 --> only x = 2 and y = 0 satisfy this equation ( x> 2 will never give sum of digits = 4) ; but 202 is divisible by 2 ; we know that p is a prime number
Similarly option C) 2x+y = 5 --> only x = 2 and y = 1 satisfy this equation ( x> 2 will never give sum of digits = 5) ; but 212 is divisible by 2 ; we know that p is a prime number
Therefore answer option should be E ---> can be verified by taking 2x+y = 7 ---> x = 3 and y = 1 ; gives 313
ANSWER:E
Answer: (E) 7
Question: The average of 7 consecutive numbers is 20. The largest of these numbers is :
(A) 21
(B) 25
(C) 31
(D) 23
(E) 29
Rationale: Let the numbers be x, x + 1, x + 2, x + 3, x + 4, x + 5 and x + 6,Then (x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6)) / 7 = 20.or 7x + 21 = 140 or 7x = 119 or x =17.Latest number = x + 6 = 23. Answer : D
Answer: (D) 23
Question: The smallest number when increased by " 1 " is exactly divisible by 12, 18, 24, 32 and 40 is:
(A) 1439
(B) 1440
(C) 1459
(D) 1449
(E) 1549
Rationale: LCM = 1440
1440 - 1 = 1439
ANSWER:A
Answer: (A) 1439
Question: What is the next number of the following sequence
2,5,10,50,500,?
(A) 24000
(B) 20000
(C) 30000
(D) 25000
(E) 40000
Rationale: 2*5=10
5*10=50
10*50=500
50*500=25000
therefore next no. is 25000
ANSWER:D
Answer: (D) 25000
Question: Let p be a prime number greater than 2 and let N = 14p. How many even numbers divide N?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: Answer: A. There is exactly one. The prime factorization of 14 is 14 = 2*7, so N = 2*7*p = 7*2*p = 7*2p, so 2p is the only even number that divides N.
Answer: (A) 1
Question: A train 150 m long running at 72 kmph crosses a platform in 25 sec. What is the length of the platform?
(A) 287
(B) 288
(C) 350
(D) 278
(E) 728
Rationale: D = 72 * 5/18 = 25 = 500 – 150
= 350
Answer: C
Answer: (C) 350
Question: What is the value of X, if
1/(log442/441 X) + 1/(log443/442 X) + 1/(log444/443 X) +…+ 1/(log899/898 X) +1/(log900/899 X) = 2?
(A) 2/21
(B) 1
(C) 7/100
(D) 10/7
(E) None of these
Rationale: The given equation
= 1/(log442/441 X) = (log442/441)/logX = logX 442/441.
= logX 442/441 + logX 443/442 + logX 444/443 +......+ logX 899/898 + logX 900/899 = 2.
= logX 900/441 = 2
=>X2 = 900/441
=>X = 30/21 = 10/7.
ANSWER:D
Answer: (D) 10/7
Question: A person is traveling at 75 km/hr and reached his destiny in 4hr then find the distance?
(A) 300 km
(B) 200 km
(C) 250 km
(D) 400 km
(E) 220 km
Rationale: T = 4 hrs
D= T*S = 75*4 = 300KM
Answer is A
Answer: (A) 300 km
Question: Two children want to walk together to visit their aunt, who lives exactly 7 blocks north and 5 blocks east of their current location. If they travel only along streets and do not travel diagonally, the shortest possible route connecting the two points is exactly 12 blocks. How many different 12-block routes may they take to travel the shortest possible distance to their aunt’s house?
(A) 12!/(7*5)
(B) 19!/(12!)
(C) 12!/(7!5!)
(D) 12!*7!*5!
(E) 7!*5!
Rationale: If they need to walk 7 blocks north and 5 blocks east, we can express this route as NNNNNNNEEEEE. The question thus asks us how many ways we can arrange those letters.
The number of arrangements of 12 things is 12!
We then divide by the repetitions of N's and E's, which are 7! and 5! respectively.
The number of walking routes is 12!/(7!5!).
The answer is C.
Answer: (C) 12!/(7!5!)
Question: There is a 30% increase in the price of an article in the first year, a 20% decrease in the second year and a 10% increase in the next year. If the final price of the article is Rs. 2288, then what was the price of the article initially?
(A) 2009
(B) 6000
(C) 2000
(D) 7000
(E) 1000
Rationale: Let the price of the article, four years age be Rs. 100 in the 1st year, price of the article
= 100 + 30 = Rs. 130. In the 2nd year, price = 130 - 20% of 130
= 130 - 26 = Rs. 104.
In the 3rd year, price = 104 + 10% of 104
= 104 + 10.4 = Rs. 114.40.
But present price of the article is Rs. 2288
for 114.4 ---> 100 ; 2288 ---> ?
Required price = (2288 * 100)/114.4 = 20 * 100 = Rs.2000.
Answer:C
Answer: (C) 2000
Question: The length of a rectangle is twice its breadth. If its length is decreased by 5 cm and breadth is increased by 5 cm, the area of the rectangle is increased by 75 sq.cm. Find the length of the rectangle?
(A) 10 cm
(B) 20 cm
(C) 30 cm
(D) 40 cm
(E) 50 cm
Rationale: Solution
Let the breadth = x	Then length =2x
= [(2x-5)(x+5)-2x ] x [x=75]
x =20.
Length of the rectangle=20cm.
Answer B
Answer: (B) 20 cm
Question: If c is 20% of a and 10% of b, what percent of a is b?
(A)  2.5%
(B)  15%
(C)  25%
(D)  35%
(E)  200%
Rationale: Answer = E
20a/100 = 10b/100
b = 20a/10 = 200a/100 = 200%
Answer: (E)  200%
Question: A babysitter is paid a regular rate of $16 per hour for any number of hours that does not exceed 30 hours per week. For any overtime hours worked in excess of 30 hours per week, the babysitter is paid a rate that is 75% higher than his regular rate. If last week the babysitter earned $760, how many total hours did she work that week?
(A) 40
(B) 30
(C) 35
(D) 25
(E) 45
Rationale: For 30 hrs = 30*16=480
Excess = 760-480=280
For extra hours =.75(16)=12 in addition to $16. Thus, 12+16=28
Number of extra hrs =280/28=10
Total hrs =30+10=40
Answer A 40
Answer: (A) 40
Question: In a race of 4Kms A beats B by 100m or 25 seconds, then time taken by A is
(A) 8 min 15 sec
(B) 10 min 17 sec
(C) 15 min 8 sec
(D) 16 min 15 sec
(E) 17 min 15 sec
Rationale: B covers 100m in 25 seconds
B take time =(4000*25)/100=1000 sec=16 min 40 sec.
A takes time =1000 sec-25sec=975 sec= 16 min 25 sec.
ANSWER:D
Answer: (D) 16 min 15 sec
Question: A , B , and C started a partnership business by investing $27,000 , $72,000 , and $81,000 respectively. At the end of the year , the profit was distributed among them. If C's share of profit is $18,000, what is the total profit?
(A) $24,000
(B) $32,000
(C) $40,000
(D) $48,000
(E) $56,000
Rationale: A:B:C = 27000:72000:81000 which is a ratio of 3:8:9.
Let the total profit be x.
x * 9/20 = 18000
x = 18000*20/9 = 40,000.
The answer is C.
Answer: (C) $40,000
Question: An article is bought for Rs.605 and sold for Rs.900, find the gain percent?
(A) 30 1/3%
(B) 33 1/3%
(C) 48 92/121%
(D) 35 1/3%
(E) 29 1/3%
Rationale: C
48 92/121%
605 ---- 295
100 ---- ? => 48 92/121%
Answer: (C) 48 92/121%
Question: A box has exactly 100 balls, and each ball is either red, blue, or white. If the box has 10 more blue balls than white balls, and thrice as many red balls as blue balls, how many white balls does The box has ?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Rationale: x = the number of red balls
y = the number of blue balls
z = the number of white balls
From the first sentence we have
Equation #1: x + y + z = 100
...the box has 10 more blue balls than white balls...
Equation #2: y = 10 + z
...thrice as many red balls as blue balls...
Equation #3: x = 3y
Solve equation #2 for z: z = y - 10
Now, we can replace both x and z with y in Equation #1
3y + y + (y - 10) = 100
5y - 10 = 100
5y = 110
y = 22
There are 22 blue balls. This is 10 more than the number of white balls, so z = 12. That's the answer. Just as a check, x = 66, and 66 + 22 + 12 = 100.
Answer = 12,(C)
Answer: (C) 12
Question: which of the following is correct formula for divisor rule ?
(A) dividend = divisor * quotient + remainder
(B) quotient = divisor * dividend + remainder
(C) dividend = divisor * quotient - remainder
(D) dividend = divisor * remainder + quotient
(E) dividend = divisor * remainder - quotient
Rationale: option A is correct
Answer: (A) dividend = divisor * quotient + remainder
Question: The length of a rectangular plot is 20 metres more than its breadth. If the cost of fencing the plot @ Rs. 26.50 per metre is Rs. 7420, what is the length of the plot in metres?
(A) 20
(B) 200
(C) 300
(D) 400
(E) 80
Rationale: Let length of plot = L meters, then breadth = L - 20 meters
and perimeter = 2[L + L - 20] = [4L - 40] meters
[4L - 40] * 26.50 = 7420
[4L - 40] = 7420 / 26.50 = 280
4L = 320
L = 320/4= 80 meters. Answer: E
Answer: (E) 80
Question: The number of people at Ovations Bar in the hour from 12 p.m. to 1 p.m. was 20% greater than the number of people there from 11 a.m. to 12 p.m. The number of the people at the bar from 11 a.m. to 12 p.m. was 10% more than the number there from 10 a.m. to 11 a.m. If 242 people were at the bar from 11 a.m. to 1 p.m., which of the following is the number of people in the bar from 10 a.m. to 11 a.m.?
(A) 100
(B) 20
(C) 30
(D) 40
(E) 50
Rationale: No of people from 10 - 11 is x
No of people from 11 - 12 is 11x/10
No of people from 12 to 1 is (6/5)(11x/10)
Given that 11x/10 + (6/5)(11x/10) = 121x / 50 = 242
Then x = 100
A
Answer: (A) 100
Question: A train running at the speed of 60 km/hr crosses a pole in 12 sec. What is the length of the train?
(A) 120 m
(B) 180 m
(C) 200 m
(D) Cannot be determined
(E) None of these
Rationale: Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 12 = 200 m
ANSWER:C
Answer: (C) 200 m
Question: An inspector rejects 0.0008% of the meters as defective. How many will be examine to project ?
(A) 2000
(B) 2300
(C) 2700
(D) 250000
(E) 250
Rationale: Let the number of meters to be examined be x.
Then, 0.0008% of x =2
[(8/10000)*(1/100)*x] = 2
x = [(2*100*10000)/8] = 250000
Answer is D.
Answer: (D) 250000
Question: If 4 men can color 48 m long cloth in 2 days, then 6 men can color 36 m long cloth in?
(A) 1 day
(B) 2 days
(C) 3 days
(D) 4 days
(E) 5 days
Rationale: The length of cloth painted by one man in one day = 48 / 4 × 2 = 6 m
No. of days required to paint 36 m cloth by 6 men = 36/ 6 × 6 = 1 day
A)
Answer: (A) 1 day
Question: The greatest common factor of two positive integers is L. The least common multiple of these two integers is Y. If one of the integers is Z, what is the other?
(A) LY⁄Z
(B) XZ + YZ
(C) X⁄Z + Y
(D) X + Y⁄Z
(E) X + Z⁄Y
Rationale: Say other integer is W
Formula
GCF(WZ)*LCM(WZ) = W*Z
L*Y = W*Z
So W= LY/Z
Answer A
Answer: (A) LY⁄Z
Question: The slant height of a cone is 10 cm and radius of the base is 5 cm, find the curved surface of the cone.
(A) 250
(B) 170
(C) 148
(D) 157
(E) 150
Rationale: π * 5* 10=157
Answer:D
Answer: (D) 157
Question: if the ratio of two number is 2:3 and LCM of the number is 120 then what is the number.
(A) 15
(B) 20
(C) 25
(D) 30
(E) 35
Rationale: product of two no = lcm *hcf
2x*3x=120*x
x=20
ANSWER:B
Answer: (B) 20
Question: A car travels at a speed of 65 miles per hour. How far will it travel in 5 hours?
(A) 255 miles
(B) 325 miles
(C) 645 miles
(D) 121 miles
(E) 333 miles
Rationale: During each hour, the car travels 65 miles. For 5 hours it will travel
65 + 65 + 65 + 65 + 65 = 5 * 65 = 325 miles
correct answer B
Answer: (B) 325 miles
Question: Of the 75 house in a development, 50 have a two-car garage, 40 have an in-the-ground swimming pool, and 35 have both a two-car garage and an in-the-ground swimming pool. How many houses in the development have neither a two-car garage nor an in-the-ground swimming pool?
(A) 10
(B) 15
(C) 20
(D) 25
(E) 30
Rationale: Neither Car nor Garage
= Total - Garage - (Swim - Common)
= 75 - 50 - (40-35) = 75-55 = 20
Answer C
Answer: (C) 20
Question: The average of 40 results is 30 and the average of other 30 results is 40 . what is the average of all the results?
(A) 34
(B) 25
(C) 48
(D) 50
(E) None
Rationale: Answer
Sum of 70 result = sum of 40 result + sum of 30 result.
= 40 x 30 + 30 x 40
= 2400/70
Correct Option: A
Answer: (A) 34
Question: The price of a book is increased from $300 to $450. What is the % of increase in its price?
(A) 10%
(B) 20%
(C) 40%
(D) 50%
(E) 60%
Rationale: Explanation: Change in the price = Rs 450 â€“ Rs 300
= Rs 150
Percentage of increase = Change in the price Initial Price
* 100.
Percentage increase in price =( 150 300
) *100 = 50%
D
Answer: (D) 50%
Question: From a salary of an officer, 10% is deducted as house rent, 15% of the rest he spend on children's education and 10% of the balance he spends on clothes. Then, he is left with Rs. 4131. Find his total salary?
(A) 6000
(B) 3788
(C) 9009
(D) 6788
(E) 2772
Rationale: Suppose his total salary be Rs.x, then
90% of 85% of 90% of x = 4131
\inline \Rightarrow \frac{90}{100}\times \frac{85}{100}\times \frac{90}{100}\times x=4131
\inline \therefore x=\frac{4131\times 100\times 100\times 100}{90\times 85\times 90}=6000
Hence , the salary of the officer is Rs.6000
Answer:A
Answer: (A) 6000
Question: What is the largest integral value of 'k' for which the quadratic equation x2 - 6x + k = 0 will have two real and distinct roots?
(A) 9
(B) 7
(C) 3
(D) 8
(E) 12
Rationale: Explanatory Answer
Any quadratic equation will have real and distinct roots if the discriminant D > 0
The discriminant 'D' of a quadratic equation ax2 + bx + c = 0 is given by b2 - 4ac
In this question, the value of D = 62 - 4 * 1 * k
If D > 0, then 36 > 4k or k < 9.
Therefore, the highest integral value that k can take is 8.
correct choice is (D)
Answer: (D) 8
Question: The factorial expression 12!/6! is not divisible by which of the following integers?
(A) 3
(B) 5
(C) 13
(D) 10
(E) 9
Rationale: 12!/6! => 12 x 11 x 10 x 9 x 8 x 7
(A) 3 Can divide 12 or 9
(B) 5 Can divide 10
(C) 13 None of the Multiplicands present
(D) 10 Can divide 10
(E) 9 Can divide 9
Hence answer will be (C)
Answer: (C) 13
Question: An amount of Rs.1560 was divided among A, B and C, in the ratio 1/2 : 1/3 : 1/4. Find the share of C?
(A) 272
(B) 276
(C) 360
(D) 277
(E) 261
Rationale: Let the shares of A, B and C be a, b and c respectively.
a : b : c = 1/2 : 1/3 : 1/4
Let us express each term with a common denominator which is the last number divisible by the denominators of each term i.e., 12.
a : b : c = 6/12 : 4/12 : 3/12 = 6 : 4 : 3.
Share of C = 3/13 * 1560 = Rs. 360.
Answer: D
Answer: (D) 277
Question: Find the odd man out
125, 106, 88, 76, 65, 58, 53
(A) 125
(B) 106
(C) 88
(D) 76
(E) 57
Rationale: Add series of prime numbers starting from 5 to get the next number
53+5 =58
58+7= 65
65+11=76
76+13 =89
89+17=106
106+19 = 125
ANSWER:C
Answer: (C) 88
Question: How many integerskgreater than 100 and less than 700 are there such that if the hundreds and the units digits ofkare reversed, the resulting integer is k+99?
(A) 50
(B) 60
(C) 70
(D) 80
(E) 90
Rationale: Numbers will be like 102 => 201 = 102 + 99
203 => 302 = 103 + 99
so the hundereth digit and units digit are consecutive where unit digit is bigger than hundred digit.
There will be five pairs of such numbers
for every pair there will 10 numbers like for 12 => 102, 112,132,142,152, 162,172,182,192.
Total = 5 *10 = 50 hence A.
Answer: (A) 50
Question: If a and b are both prime numbers greater than 12, which of the following CANNOT be true?
I. ab is an even number.
II. The difference between a and b equals 117.
III. The sum of a and b is even.
(A)  I only
(B)  I and III only
(C)  I and II only
(D)  II and III only
(E)  I, II and III
Rationale: MANHATTAN GMATOFFICIAL SOLUTION:
Since a and b are both prime numbers greater than 10, they must both be odd. Therefore ab must be an odd number, so Statement I cannot be true. Similarly, if a and b are both odd, then a - b cannot equal 117 (an odd number). This difference must be even. Therefore, Statement II cannot be true. Finally, since a and b are both odd, a + b must be even, so Statement III will always be true. Since Statements I and II CANNOT be true, but Statement III IS true,the correct answer is (C).
Answer : C
Answer: (C)  I and II only