divelab/Sys2Bench huggingface dataset:
Question: In an increasing sequence of 6 consecutive integers, the sum of the first 4 integers is 570. What is the sum of the last 2 integers in the sequence?
Options:
A) 291
B) 290
C) 274
D) 270
E) 265
Rationale: Solution:
In solving this problem we must first remember that when we have 6 consecutive integers we can display them in terms of just 1 variable. Thus, we have the following:
Integer 1: x
Integer 2: x + 1
Integer 3: x + 2
Integer 4: x + 3
Integer 5: x + 4
Integer 6: x + 5
We are given that the sum of the first 4 integers is 570. This means that:
x + x+1 + x+2 + x+3 = 570
4x + 6 = 570
4x = 564
x = 141
The sum of the last 2 integers can be expressed and simplified as:
x+4 + x+5 = 2x + 9
Substituting 141 for x yields:
(2)(141) + 9 = 291
Answer: A
Answer: A
Question: Sandy can do a job in 15 days and Molly can do the same job in 30 days. If they work together, in how many days will they complete the job?
Options:
A)8
B)9
C)10
D)11
E)12
Rationale: Sandy can do 1/15 of the job each day.
Molly can do 1/30 of the job each day.
The combined rate is 1/15 + 1/30 = 1/10 of the job each day.
The job will take 10 days.
The answer is C.
Answer: C
Question: How many 5 letter combinations can be made from the letters of the word VERMONT if the first letter has to be a vowel and the last letter has to be a consonant, and repetition is allowed?
Options:
A)3441
B)3433
C)3333
D)3430
E)3773
Rationale: Vowel: E O
Consonants: V R M N T
First letter can be filled in 2 Ways ( As the question states that first letter has to be a vowel)
Fifth letter can be filled in 5 Ways ( As the question states that the last letter has to be a consonant)
Second letter can be filled in 7 Ways
Third letter can be filled in 7 Ways
Fourth letter can be filled in 7 Ways
So, Total number of ways = 2 Ways x 7 Ways x 7 ways x 7 ways x 5 ways = 3430
Answer D
Answer: D
Question: 5, 9, 17, 29, 45, ?
Options:
A)49
B)87
C)60
D)65
E)44
Rationale: D
65
The pattern is + 4, + 8, + 12, + 16, ....
Answer: D
Question: The present ages of A,B & C are in proportions 4:7:9. 8 years ago, the sum of their ages was 56. What are their present ages?
Options:
A)10,20 and 36
B)16,22 and 36
C)16,28 and 36
D)14,18 and 36
E)None
Rationale: Let present age of A,B and C be 4x,7x and 9x respectively.
(4x−8)+(7x−8)+(9x−8)=56⇒20x=80⇒x=4
Hence present age of A, B and C are
4×4, 7×4 and 9×4 respectively.
i.e., 16,28 and 36 respectively.
C
Answer: C
Question: A train 300m long takes 10 sec to cross a man walking at 5kmph in a direction opposite to that of the train. Find the speed of the train?
Options:
A)A)175kmph
B)B)113kmph
C)C)162kmph
D)D)145kmph
E)E)100kmph
Rationale: Let the speed of the train be x kmph
Speed of the train relative to man = x+5 = (x+5)*5/18 m/sec
300/[(x+5)*5/18] = 10
10(x+5) = 60*18
x = 175kmph
Answer is B
Answer: B
Question: A train 250 m long passed a pole in 10 sec. How long will it take to pass a platform 1250 m long?
Options:
A)60 sec
B)90 sec
C)120 sec
D)150 sec
E)180 sec
Rationale: Speed = 250/10 = 25 m/sec.
Required time = (250 + 1250)/25 = 60 sec
Answer:A
Answer: A
Question: Two horses begin running on an oval course at the same time. One runs each lap in 4 minutes; the other takes 16 minutes to run each lap. How Many minutes after the start will the faster horse have a one lap lead?
Options:
A)36
B)12
C)16/3
D)4
E)3
Rationale: The rate of the faster horse is 1/4 lap/minute;
The rate of the slower horse is 1/16 lap/minute;
Their relative rate is 1/4-1/16=3/16 lap/minute;
The faster horse to gain one full lap will need time=distance/rate=1/(3/16)=16/3 minutes.
Answer: C
Answer: C
Question: Two tailors x and y are paid a total of $100 per week by their employer. If x is paid 150% of the sum paid to y. How much is y paid per week?
Options:
A)28.6
B)15.9
C)36.3
D)45.5
E)19.2
Rationale: Let the sum paid to y per week be $z
then, z+150% of z = 100
z+(150/100)z = 100
z = 28.6
Answer is A
Answer: A
Question: 1100 boys and 700 girls are examined in a test; 45% of the boys and 30% of the girls pass. The percentage of the total who failed is ?
Options:
A)A)63.3%
B)B)60.8%
C)C)81.2%
D)D)75.4%
E)E)69.1%
Rationale: Total number of students = 1100+700 = 1800
Number of students passed = (45% of 1100+30% of 700) = 495+210 = 705
number of failures = 1095*100/1800 = 60.8%
Answer is B
Answer: B
Question: If A:B = 1/7: 1/3 B:C = 1/2:1/3 then A:B:C?
Options:
A)9:6:6
B)9:6:8
C)9:6:2
D)9:6:4
E)9:21:14
Rationale: A:B = 1/7:1/3 = 3:7
B:C = 1/2:1/3 = 3:2
--------------------
A:B:C = 9:21:14
Answer:E
Answer: E
Question: z, b, and c are positive integers. If z, b, and c are assembled into the six-digit number zbczbc, which one of the following must be a factor of zbczbc?
Options:
A) 16
B) 13
C) 5
D) 3
E) none of the above
Rationale: Plug in some values and check -
zbczbc = 123123
Not divisible by 16 and 5
let zbczbc = 125125
Not divisible by 3
Only option (B) and (E) is left in both the cases...
Check once more to marke (B) as correct answer
let zbczbc = 135135
Again divisible by 13
So, mark answer as (B) 13
Answer: B
Question: A company recently conducted a survey and found that 25,000 of its customers live in rural areas. If the number of customers who live in urban areas is 120 percent greater than the number of customers who live in rural areas, how many customers live in urban areas?
Options:
A)50,000
B)55,000
C)60,000
D)65,000
E)70,000
Rationale: The number of customers in urban areas is 25,000+1.2*25,000=55,000.
The answer is B.
Answer: B
Question: The lenght of a room is 5.5 m and width is 4 m. Find the cost of paving the floor by slabs at the rate of Rs. 900 per sq. metre.
Options:
A)s. 19,800
B)s. 15,600
C)s. 16,500
D)s. 17,600
E)s. 17,900
Rationale: Area of the floor = (5.5 Ã— 4) m2 = 22 m2.
Cost of paving = Rs. (900 Ã— 22) = Rs. 19800
Answer: Option A
Answer: A
Question: In a class of 40 students, 2 students did not borrow any books from the library, 12 students each borrowed 1 book, 12 students each borrowed 2 books, and the rest borrowed at least 3 books. If the average number of books per student was 2, what is the maximum number of books any single student could have borrowed?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: The class borrowed a total of 40*2 = 80 books.
The 26 students who borrowed 0, 1, or 2 books borrowed a total of 12 + 12*2 = 36.
To maximize the number of books borrowed by 1 student, let's assume that 13 students borrowed 3 books and 1 student borrowed the rest.
80 - 36 - 3*13 = 5
The maximum number of books borrowed by any student is 5.
The answer is C.
Answer: C
Question: A sum of money deposited at C.I. amounts to Rs.2420 in 2 years and to Rs.2662 in 3 years. Find the rate percent?
Options:
A)12%
B)10%
C)90%
D)80%
E)20%
Rationale: 2420 --- 242
100 --- ? => 10%
Answer: B
Answer: B
Question: Rs.1690 is divided so that 4 times the first share, thrice the 2nd share and twice the third share amount to the same. What is the value of the third share?
Options:
A)s.528
B)s.542
C)s.780
D)s.540
E)s.549
Rationale: A+B+C = 1690
4A = 3B = 2C = x
A:B:C = 1/4:1/3:1/2 = 3:4:6
6/13 * 1690 = Rs.780
Answer: C
Answer: C
Question: Three unbiased coins are tossed. What is the probability of getting at most two heads?
Options:
A)3/4
B)7/8
C)3/8
D)5/6
E)9/11
Rationale: Here S = {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}
Let E = event of getting at most two heads.
Then E = {TTT, TTH, THT, HTT, THH, HTH, HHT}.
P(E)=n(E)/n(S)
=7/8
The answer should be B
Answer: B
Question: A test has a mean of 110 and a standard deviation of 5, find the corresponding x score for: a) a test score of 116?
Options:
A)A)6/5
B)B)2.4
C)C)5
D)D)5.6
E)E)7
Rationale: A test has a mean of 110 and a standard deviation of 5,
find the corresponding x score for:
a) a test score of 116,
x(116) = (116-110)/5= 6/5
Option A
Answer: A
Question: 8, 19, 30, 41, 52, ….
Given the sequence above, what is the sum of the 13th and the 20th terms?
Options:
A)324
B)335
C)346
D)357
E)368
Rationale: The first term is 8 = 11 – 3. The second term is 19 = 22 – 3, the third term is 30 = 3 × 11 – 3, the fourth term is 41 = 4 × 11 – 3, etc.
Thus, 11n – 3 describes the values in the sequence where n is the number of the term.
The 13th term is 13 × 11 – 3 = 140
The 20th term is 20 × 11 – 3 = 220 – 3 = 217.
The sum of these two values is 357
The correct answer is choice (D).
Answer: D
Question: The perimeter of a triangle is 40 cm and the inradius of the triangle is 2.5 cm. What is the area of the triangle?
Options:
A)76 cm2
B)56 cm2
C)18 cm2
D)98 cm2
E)50 cm2
Rationale: Area of a triangle = r * s
Where r is the inradius and s is the semi perimeter of the triangle.
Area of triangle
= 2.5 * 40/2
= 50 cm2
Answer:E
Answer: E
Question: A train 440 meters long is running with a speed of 54 kmph. The time taken by it to cross a tunnel 180 meters long is?
Options:
A)40.33 sec
B)41.33 sec
C)42.33 sec
D)40 sec
E)44.33 sec
Rationale: D = 440 + 180 =620
S = 54 * 5/18 = 15 mps
T = 620/15 = 41.33 sec
ANSWER:B
Answer: B
Question: The area of a triangle will be when a = 5m, b = 7m, c = 8m, a, b, c being lengths of respective sides?
Options:
A)3
B)6
C)4
D)9
E)10
Rationale: S = (5 + 7 + 8)/2= E Answer:E
Answer: E
Question: If p and q are two different prime numbers, which of the following cannot be true?
Options:
A)pq is odd.
B)p + q is even.
C)p + q is odd.
D)pq is even.
E)p/q is an integer
Rationale: A prime number is a positive integer with exactly two distinct positive divisors: 1 and itself. So, a prime number cannot be a multiple of another prime number. Which makes option E not possible (p/q=integer means that p is a multiple of q).
Answer: E.
All other options are possible:
A. pq is odd --> p=3 and q=5;
B. p + q is even --> p=3 and q=5;
C. p + q is odd --> p=2 and q=3;
D. pq is even --> p=2 and q=3;
E
Answer: E
Question: Maney bought shares for a total value of $1000. Next day, the price of shares is reduced by 10%. With the same $1000, he could now buy 10 more shares. Which of the following is closest to the original price per share?
Options:
A)$10
B)$11
C)$12
D)$13
E)$14
Rationale: From the given information,we can conclude that Maney bought x number of shares for $1000. With a 10% reduction in price, he could buy the same x number of shares for 1000*.90 = $900 . With the remaining money ($1000 - $900 = $100), he can buy 10 more shares. So, the reduced price per share = $100/10 = $10.
Therefore, if the reduced price of $10 equals the original price * 9/10, then the original price is approximately $11=B
Answer: B
Question: The closest approximation of W(69.28 × 0.004)/0.03 is
Options:
A)0.092
B)0.92
C)9.2
D)92
E)920
Rationale: W(69.28 × 0.004)/0.03
1. 0.004 = 4 × 10^(-3)
2. 0.03 = 3 × 10^(-2)
3. (a × b)/c = a × (b/c)
4. 0.004/0.03 = 4 × 10^(-3)/ (3 × 10^(-2)) = 4 × 10^( -3 - (-2))/3 = 4 × 10^(-1) / 3 = (4/3) × 10^(-1) = 1.333 × 10^(-1)
Therefore,
(69.28 × 0.004)/0.03 = 69.28 × (0.004/0.03) = 69.28 × 1.33 × 10^(-1) = 69.28 × 1.33/10 = 6.928*1.33
Now,
7 × 2 = 14
7 × 1 = 7
or better:
6.9 × 1 = 6.9
6.9 × 2 = 13.8
hence,
6.9 <6.928 × 1.33 < 13.8
9.2 is the only answer that satisfies this condition.C
Answer: C
Question: Simplify: 99^48/49 * 245.
Options:
A)23345
B)26695
C)24495
D)25575
E)None of them
Rationale: Given expression = (100-1/49) * 245=(4899/49) * 245 = 4899 * 5=24495.
Answer is C.
Answer: C
Question: If x and y are integers and x=50y + 59, which of the following must be odd?
Options:
A)xy
B)x +2y
C)x + y
D)3x-1
E)3x+1
Rationale: x = 50y + 59, since y is integer, 50y will always be even hence 50y + 59 will be odd hence x = odd
you don't know whether Y is even or odd, so you need to try.
A: odd * even = even ; odd*odd= odd ->not true
C: odd + odd = even ; odd+even = odd -> not true
B: odd + 2*odd = odd ; odd + 2*even = odd -> TRUE, .
D&E WILL BE EVEN IF X IS ODD
Answer B
Answer: B
Question: By selling an article at Rs.600, a profit of 25% is made. Find its cost price?
Options:
A)Rs.482
B)Rs.429
C)Rs.480
D)Rs.408
E)Rs.428
Rationale: SP = 600
CP = (SP)*[100/(100+P)]
= 600 * [100/(100+25)]
= 600 * [100/125] = Rs.480
Answer:C
Answer: C
Question: The diagonal of a rhombus are 62 m and 80 m. Its area is:
Options:
A)1940
B)2480
C)2460
D)2500
E)1980
Rationale: Area of the rhombus = 1/2 d1d2 = ( 1/2 Ã— 62 Ã— 80) Cm(power)2
= 62 Ã— 40 = 2480 Cm(power)2
Answer is B.
Answer: B
Question: What is the value of 10^6 - 6^4?
Options:
A)9,97,111
B)9,97,322
C)9,98,704
D)9,98,851
E)9,98,900
Rationale: As 10^n will always have last digit as 0 AND 6^n will always as last digit 6.. hence difference of such sum should always be ending with 4 and there is only on option ..
Answer C
Answer: C
Question: There is 60% increase in an amount in 6 years at simple interest. What will be the compound interest of $ 12,000 after 3 years at the same rate?
Options:
A)$2160
B)#3120
C)$3972
D)$6240
E)NONE OF THESE
Rationale: Let P = $ 100. Then, S.I. $. 60 and T = 6 years.
R = 100 x 60 = 10% p.a.
100 x 6
Now, P = $ 12000. T = 3 years and R = 10% p.a.
C.I.	= $ 12000 x 1 +	10 3	- 1
100
= $ 12000 x	331
1000	=3972
ANSWEWR : C 3972
Answer: C
Question: When 1/10 percent of 2,000 is subtracted from 1/10 of 2,000, the difference is
Options:
A)1980
B)1998
C)198
D)200
E)20
Rationale: (1/10)*2000 - (1/10)%*2000 =
200 - (1/1000)*2000 =
200 - 2 = 198
The answer is C.
Answer: C
Question: The price of a jacket is reduced by 25%. During a special sale the price of the jacket is reduced another 25%. By approximately what percent must the price of the jacket now be increased in order to restore it to its original amount?
Options:
A)32.5
B)77.78
C)48
D)65
E)67.5
Rationale: 1) Let the price of jacket initially be $100.
2) Then it is decreased by 25% , therefore bringing down the price to $75.
3) Again it is further discounted by 10%, therefore bringing down the price to $56.25
4) Now 56.25 has to be added byX %in order to equal the original price.
56.25 + ( X% ) 56.25 = 100.
Solving this eq for X, we get X = 77.78
Ans is B.
Answer: B
Question: A single discount equivalent to the discount series of 20%, 15% and 8% is?
Options:
A)37.4
B)31.8
C)31.6
D)31.3
E)31.1
Rationale: 100*(80/100)*(85/100)*(92/100)
= 62.6
100 - 62.6 = 37.4
Answer:A
Answer: A
Question: Natasha climbs up a hill, and descends along the same way she went up. It takes her 4 hours to reach the top and 2 hours to come back down. If her average speed along the whole journey is 2 kilometers per hour, what was her average speed (in kilometers per hour) while climbing to the top?
Options:
A)1.5
B)2.5
C)3.75
D)5
E)7.5
Rationale: Let the distance to the top be x, so the total distance traveled by Natasha is 2x.
The total time is 4 + 2 = 6 hours
The average speed = total distance/total time taken = 2x/6 = x/3
The average speed of the complete journey is 2 km/hour
x/3 = 2
x = 6 km
The average speed while climbing = distance/time = 6/4 = 1.5 km/h
The answer is A.
Answer: A
Question: In a mixture of milk and water, the proportion of milk by weight was 80%. If, in a 200-gram mixture, 50 grams of pure milk is added, what would be the percentage of milk in the resulting mixture?
Options:
A)84%
B)85%
C)86%
D)87%
E)88%
Rationale: The amount of milk is 0.8(200) + 50 = 210 grams.
The proportion is 210/250 = 0.84 which is 84%
The answer is A.
Answer: A
Question: On multiplying a number X by 153, the result obtained was 102325. However, it is found that both the 2's are wrong. Find the correct result.
Options:
A)104345
B)107375
C)108385
D)109395
E)105355
Rationale: The only thing you actually know about the correct number X is that it is divisible by 153 and has 5 as a factor.
You should immediately try to find the factors of 153 and look for them in the options.
153 = 9*17
Divisibility by 9 is easy to check. Only (D) satisfies.
Answer: D
Question: A train 260 m long is running at a speed of 45 km/hr. In what time will it pass a bridge 140 m long?
Options:
A)40
B)32
C)26
D)21
E)14
Rationale: Speed = 45 * 5/18 = 25/2 m/sec
Total distance covered = 260 + 140 = 400 m
Required time = 400 * 2/25 = 32 sec
Answer:B
Answer: B
Question: The cost price of a radio is Rs.2400 and it was sold for Rs.1980, find the loss %?
Options:
A)17%
B)12%
C)22%
D)24%
E)21
Rationale: 2400 ---- 420
100 ---- ? => 17%
Answer:A
Answer: A
Question: 107 Ã— 107 + 93 Ã— 93 = ?
Options:
A)20198
B)20098
C)20000
D)20088
E)20085
Rationale: Explanation :
(a + b)2 + (a âˆ’ b)2 = 2(a2 + b2)
(Reference : Basic Algebraic Formulas)
1072 + 932 = (100 + 7)2 + (100 âˆ’ 7)2 = 2(1002 + 72) = 2(10000 + 49) = 20098. Answer : Option B
Answer: B
Question: Solve the given two equations and find the inequality of X and Y.(a) x^2-7x+12=0 and (b) y^2-12y+32=0
Options:
A)If x>y
B)If x>=y
C)If x < y
D)If X<= Y
E)x=y or relationship cannot be established
Rationale: Solution:-
X=3,4 and Y= 4,8
X<= Y
D
Answer: D
Question: The smallest prime number is:
Options:
A)1
B)6
C)3
D)4
E)2
Rationale: E
2
Answer: E
Question: Jonathan can type a 30 page document in 40 minutes, Susan can type it in 30 minutes, and Jack can type it in 24 minutes. Working together, how much time will it take them to type the same document?
Options:
A)5 minutes
B)10 minutes
C)15 minutes
D)18 minutes
E)20 minutes
Rationale: You may set up common equation like this:
job/A+job/B+job/C=job/x
Memorize this universal formula, you will need it definitely for GMAT.
and find x from this equation
In this specific case, the equation will look like this:
30/40+30/30+30/24=30/x
If you solve this equation, you get the same answer B (10)
Answer: B
Question: In how many years Rs 200 will produce the same interest at 10% as Rs. 1000 produce in 2 years at 12%
Options:
A)13
B)9
C)11
D)12
E)10
Rationale: Explanation:
Clue:
Firstly we need to calculate the SI with prinical 1000,Time 2 years and Rate 12%, it will be Rs. 240
Then we can get the Time as
Time = (100*240)/(200*10) = 12
Option D
Answer: D
Question: The amount of an investment will double in approximately 70/ p years, where p is the percent interest, compounded annually. If Thelma invests $ 60,000 in a long-term CD that pays 5 percent interest, compounded annually, what will be the approximate total value of the investment when Thelma is ready to retire 42 years later?
Options:
A)$ 280,000
B)$ 320,000
C)$ 360,000
D)$ 480,000
E)$ 540,000
Rationale: The amount of an investment will double in approximately 70/ p years, where p is the percent interest, compounded annually. If Thelma invests $ 60,000 in a long-term CD that pays 5 percent interest, compounded annually, what will be the approximate total value of the investment when Thelma is ready to retire 42 years later?
The investment gets doubled in 70/p years. Therefore, the investment gets doubled in 70/5= every 14 years. After 42 years, the investment will get doubled 42/14= 3 times.
So the amount invested will get doubled thrice.
So, 60000 *2^3 = 480000
Hence, the answer is D.
Answer: D
Question: A invested some money in 8% stock at 96.If B wants to invest in an equally good 10% stock ,he must purchase a stock worth of :
Options:
A)Rs. 120
B)Rs. 60
C)Rs. 128
D)Rs. 130
E)Rs. 140
Rationale: Solution
For an income of Rs. 8, investment = Rs. 96.
For an income of Rs. 10, investment = Rs.(96/8x10) = Rs. 120
Answer A
Answer: A
Question: The fourth proportional to 18, 14 and 18 is?
Options:
A)14
B)66
C)77
D)88
E)99
Rationale: (14*18)/18 = 14
Answer: A
Answer: A
Question: 17200 x 223 + 17200 x 77 = ?
Options:
A)2736900
B)2738800
C)2658560
D)5160000
E)None of them
Rationale: =17200 x (223+77) (by distributive law)
=17200 x 300
=5160000
Answer is D
Answer: D
Question: Aishwarya was first to board to her flight to delhi.
She forgot her seat number and picks a random seat for herself.
After this, every single person who get to the flight sits on his seat if its available else chooses any available seat at random.
Abhishek is last to enter the flight and at that moment 99/100 seats were occupied.
Whats the probability what Abhishek gets to sit in his own seat ?
Options:
A)1/2
B)3/2
C)3/2
D)2/2
E)5/2
Rationale: A
1/2
one of two is the possibility
1. If any of the first 99 people sit in Abhishek seat, Abhishek will not get to sit in his own seat.
2. If any of the first 99 people sit in Aishwarya's seat, Abhishek will get to sit in his seat.
Answer: A
Question: A person want to give his money of $15800 to his 4 children A,B,C,D in the ratio 5:9:6:5. What is the A+C share?
Options:
A)$4000
B)$2890
C)$3005
D)$6952
E)$6003
Rationale: A's share = 15800*5/25= $3160
C's share = 15800*6/25 = $3792
A+C = $6952
Answer is D
Answer: D
Question: Pipe A can fill a tank in 3 hours, pipe B in 4 hours, and pipe C in 12 hours. If all the pipes are open, in how many hours will the tank be filled?
Options:
A)1.1
B)1.3
C)1.5
D)1.7
E)1.9
Rationale: The part filled by A + B + C in 1 hour is 1/3 + 1/4 + 1/12 = 2/3
All the three pipes together will fill the tank in 1.5 hours.
The answer is C.
Answer: C
Question: If 10 litres of an oil of Rs.50 per litres be mixed with 5 litres of another oil of Rs.68 per litre then what is the rate of mixed oil per litre?
Options:
A)Rs.49.17
B)Rs.51.03
C)Rs.56
D)Rs.55.33
E)None of the above
Rationale: 50*10 = 500
68*5 = 340
840/15 = 56
ANSWER:C
Answer: C
Question: The difference between compound and simple interest on a certain sum of money for 3 years at 6 2/3% p.a is Rs.184. Find the sum?
Options:
A)22887
B)28779
C)27677
D)13500
E)17971
Rationale: P = (184*106) / [6 2/3 * 6 2/3 *(300*6 2/3)]
P = 13500
Answer:D
Answer: D
Question: Ashley and Betty start a business with $9000 each, and after 3 months, Betty adds another $5000. How should they share the profits at the end of the 24 months?
Options:
A)72:107
B)4:5
C)17:23
D)3:4
E)68:95
Rationale: Ashley invests $9000 for 24 months, but Betty invests $9000 for the first 3 months and then adds $5000. So, the investment of Betty for remaining 21 months is $14000.
Ashley:Betty
9000*24 : (9000*3) + (14000*21)
216000 : 321000
A:B = 72:107
Answer: A
Answer: A
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?
Options:
A)2 3/2 hours
B)2 1/3 hours
C)2 1/5 hours
D)2 9/2 hours
E)2 1/2 hours
Rationale: Required time
= (5 1/4)/3 + (5 1/4)/7
= 2 1/2 hours.
Answer: E
Answer: E
Question: The profit earned by selling an article for 872 is equal to the loss incurred when the same article is sold for 448. What should be the sale price of the article for making 50 per cent profit?
Options:
A)960
B)990
C)1,200
D)920
E)None of these
Rationale: Let the profit or loss be x
and 872 – x = 448 + x or, x = 424⁄2 = 212
\ Cost price of the article = 872 – x = 448 + x = 660
\ SP of the article = 660 × 150⁄100 = 990
Answer B
Answer: B
Question: x is the product of each integer from 1 to 75, inclusive and y=100^k, where k is an integer . What is the greatest value of k for which y is a factor of x?
Options:
A)8
B)7
C)6
D)9
E)10
Rationale: The number of trailing zeros in the decimal representation of n!, the factorial of a non-negative integer n, can be determined with this formula:
n5+n52+n53+...+n5k, where k must be chosen such that 5k≤n
x = 1*2*3....*75 = 50!
No. of trailing zeros in 75! = 75/5 + 75/5^2 = 15+3 = 18
100^k = 10^2k → k = 18/2 = 9
D
Answer: D
Question: Each of the numbers x1, x2...., xn, n > 4, is equal to 1 or –1.
Suppose, x1x2x3x4 + x2x3x4x5 + x3x4x5x6 + ... + xn–3xn–2xn–1xn + xn–2xn–1xnx1 + xn–1xnx1x2 + xnx1x2x3= 0, then,
Options:
A)n is even
B)n is odd.
C)n is an odd multiple of 3.
D)n is prime
E)None
Rationale: Explanation :
Every term of the eq : x1x2x3x4 + x2x3x4x5 + x3x4x5x6 + ... + xn–3xn–2xn–1xn + xn–2xn–1xnx1 + xn–1xnx1x2 + xnx1x2x3= 0, would either be 1 or -1 (product of 1's and -1's would never be anything else).
Now for the equation to be true number of 1's would have to be equal to number -1's thus there would always be even number of terms in the equation. Now for that to be true n would have to be even.
Say for example n=6: x1x2x3x4 + x2x3x4x5 + x3x4x5x6 + x6x1x2x3.
We see there are 4 terms in the equation, we can have 2 1's and 2 -1's. So , n is even.
Answer : A
Answer: A