divelab/Sys2Bench huggingface dataset:
Question: In a class of 300 students, 150 study Spanish and 100 study French. If a student must study at least one of these two languages, what percent of the students study French but NOT Spanish?
Options:
A)50%
B)40%
C)30%
D)20%
E)10%
Rationale: No of students study french= 300- No of students study spanish = 300-150=150
% of the students study french but not spanish = (150/300)*100 % = 50 %
Answer: A
Answer: A
Question: Martin bought 5 packet milk at an average price (arithmetic mean) of 20¢. If Martin returned two packet to the retailer, and the average price of the remaining millk packet was 12¢, then what is the average price, in cents, of the two returned milk packets?
Options:
A)30
B)31
C)32
D)33
E)34
Rationale: Total price of 5 packet milk=5*20=100
Total price of 3 packet milk=3*12=36
Total price of 2 packet returned milk=100-36=64
Average price of 2 packet milk=64/2=32
Correct option Answer:C
Answer: C
Question: If log8p = 2.5, log2q = 5, then p in terms of q is?
Options:
A)3√q
B)2q
C)q
D)q/2
E)None of these
Rationale: log8p = 5/2
=> p = 85/2 = 23(5/2) = (25)3/2
log2q = 5
=> q = 25
Therefore, p = q3/2.
ANSWER:A
Answer: A
Question: A straight line in the xy-plane has a slope of 2 and a y-intercept of 2. On this line, what is the x-coordinate of the point whose y-coordinate is 520 ?
Options:
A)259
B)498
C)676
D)823
E)1,002
Rationale: slope of 2 and a y-intercept of 2
y-coordinate is 520
y = 2x + 2
518 = 2x
x = 259
Answer:
A. 259
Answer: A
Question: At a certain high school, the senior class is twice the size of the junior class. If 3/8 of the seniors and 1/4 of the juniors study Japanese, what fraction of the students in both classes study Japanese?
Options:
A)1/2
B)2/3
C)1/4
D)1/3
E)3/4
Rationale: Start by deciding on a number of students to represent the number of students in the senior class. For this example I will choose 200 students. That would make the number of students in the junior class 100. Then we can find out how many students are taking Japanese in each grade and add them together. (3/8)*200=75 and (1/4)*100=25. 75+25=100. There are a total of 300 students in the junior class and senior class combined (100+200=300), and there are 100 total students in Japanese, so 100 students in Japanese / 300 total students equals 1/3 of the students in both classes that study Japanese.
Answer: D
Answer: D
Question: Evaluate: |8 - 8(3 - 12)| - |5 - 11| = ?
Options:
A)40
B)74
C)60
D)70
E)80
Rationale: According to order of operations, inner brackets first. Hence
|8 - 8(3 - 12)| - |5 - 11| = |8 - 8*(-9)| - |5 - 11|
According to order of operations, multiplication within absolute value signs (which may be considered as brackets when it comes to order of operations) next. Hence
= |8 + 72| - |5 - 11|
= |80| - |-6|
= 80 - 6 = 74
correct answer B)74
Answer: B
Question: A ship sails out to a mark at the rate of 23 kmph. and sails back at the rate of 16 kmph. The average rate of sailing is ?
Options:
A)5 km/hr
B)12 km/hr
C)12.5 km/hr
D)19 km/hr
E)None
Rationale: Answer
Average = ( 2uv / u +v ) km/hr
= ( 2 x 23 x 16 ) / (23 +16 ) km/hr.
= 19 km/hr.
Correct Option: D
Answer: D
Question: 1 man or 2 women or 3 boys can do a work in 44days. Then in how many days will 1man, 1woman and 1 boy do the work?
Options:
A)20days
B)24days
C)30days
D)15days
E)10days
Rationale: number of days = 44*1*2*3/(1*2 + 2*3 + 1*3) = 24days
Answer is B
Answer: B
Question: If 150!/10^n is an integer, what is the largest possible value of n?
Options:
A)38
B)47
C)32
D)36
E)37
Rationale: The question actually asks the highest power of 10 which divides 150! ( For a number to be an integer - Without any remainder all the trailing zeroe's must be divided by the denominator)
10 = 2 x 5
150 factorial will have 37 as -
150/5 = 30
30/5 = 6
6/5 =1
So answer will be (E) 37
Answer: E
Question: A car traveled 75% of the way from town A to town B at an average speed of 80 miles per hour. The car travels at an average speed of S miles per hour for the remaining part of the trip. The average speed for the entire trip was 40 miles per hour. What is S ?
Options:
A)16
B)20
C)25
D)30
E)37.5
Rationale: Total distance = 100 miles (easier to work with %)
75% of the distance = 75 miles
25% of the distance = 25 miles
1st part of the trip → 75/80 = 0.9375
2nd part of the trip → 25/S = t
Total trip → (75+25)/40 = 0.9375 + t » 100/40 = 0.9375 + t » 2.5 = 0.9375 + t » t = 1.5625
Back to 2nd part of the trip formula: 25/S = 1.5625 » S = 16
Ans A
Answer: A
Question: The average age of an adult class is 40years. 17 new students with an avg age of 32years join the class. Therefore decreasing the average by 4year. Find what was theoriginal strength of class?
Options:
A)8
B)12
C)15
D)17
E)18
Rationale: Let original strength = y
Then , 40y + 17 x 32 = ( y + 17) x 36
â‡’ 40y + 544= 36y + 612
â‡’ 4y = 68
âˆ´ y = 17
D
Answer: D
Question: find the number
if 1 = 2
2 = 10
3 = 30
4 = 68
5 = ?
Options:
A)110
B)120
C)130
D)140
E)150
Rationale: 1^3+1=2
2^3+2=10
3^3+3=30
4^3+4=68
so 5 = 5^3+5=130
ANSWER:C
Answer: C
Question: A tank contains 7,000 gallons of a solution that is 5 percent sodium chloride by volume. If 2,500 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?
Options:
A) 4.77%
B) 5.77%
C) 6.77%
D) 7.77%
E) 8.77%
Rationale: We start with 7,000 gallons of a solution that is 5% sodium chloride by volume. This means that there are 0.05 x 7,000 = 350 gallons of sodium chloride.
When 2,500 gallons of water evaporate we are left with 4,500 gallons of solution. From here we can determine what percent of the 4,500 gallon solution is sodium chloride.
(sodium chloride/total solution) x 100 = ?
(350/4,500) x 100 = ?
0.077 x 100 = ?
= 7.7%
Answer is D.
Answer: D
Question: A starts 3min after B for a place 4.5 km distant B on reaching his destination immediately returns and after walking a km meets A. If A can walk 1km in 18min, then what is B's speed?
Options:
A)5kmph
B)4kmph
C)6kmph
D)3.5kmph
E)4.5kmph
Rationale: If speed of B is x kms/min, then
(4.5+1)/x= [3.5/(1/18)] +3
x=1/12 km/min= 5 kms/hr
ANSWER:A
Answer: A
Question: In how many ways 4 Indians and 5 Englishmen can be seated in a row so that they are alternate?
Options:
A)1200
B)9600
C)3240
D)4250
E)2880
Rationale: number of ways = 4!*5! = 2880
Answer is E
Answer: E
Question: 45 men can complete a work in 17 days. Six days after they started working, 30 more men joined them. How many days will they now take to complete the remaining work?
Options:
A)6.6
B)10
C)15
D)7
E)8
Rationale: 45*17 men can complete the work in 1 day
1 man's 1 day work = 1/765
45 men 6 days work = 6*1/17 = 6/17
remaining work = 1-6/17 = 11/17
75 men's 1 day's work = 75/765 = 5/51
11/17 work is done by them in 51/5 * 11/17 = 6.6 days
Answer is A
Answer: A
Question: Johnny borrows $30,000 from Tony at 3% daily interest compounded daily. How much does Johnny owe Tony after 4 weeks?
Options:
A)30000*0.02^56
B)30000*1.12
C)30000*2.12
D)30000*1.03^28
E)(30000*1.02)^56
Rationale: A=A= P(1+r100)^n
So, A=30000(1+3/100)^7âˆ—4
So, A=A= 30000(1.03)^28
Hence answer will be (D)
Answer: D
Question: A goods train runs at the speed of 72 km/hr and crosses a 250 m long platform in 22 sec. What is the length of the goods train?
Options:
A)299
B)190
C)276
D)270
E)281
Rationale: Speed = 72 * 5/18 = 20 m/sec.
Time = 22 sec.
Let the length of the train be x meters.
Then, (x + 250)/22 = 20
x = 190 m.
Answer: B
Answer: B
Question: A and B invests Rs.10000 each, A investing for 8 months and B investing for all the 12 months in the year. If the total profit at the end of the year is Rs.20000, find their shares?
Options:
A)s.8000, Rs.12000
B)s.8000, Rs.12700
C)s.10000, Rs.12090
D)s.8000, Rs.12003
E)s.10000, Rs.12200
Rationale: The ratio of their profits A:B
= 8:12 = 2:3
Share of A in the total profit
= 2/5 * 20000
= Rs.8000 Share of A in the total profit = 3/5 * 20000
= Rs.12000
Answer: A
Answer: A
Question: Let y = 2g + x^2 and g = 4x + 1.
If g^2 = 625, then which of the following can be a value of 2y + 3g?
Options:
A)100
B)130
C)141
D)142
E)247
Rationale: 800score Official Solution:
First note that g can either be 25 or -25. We are going to have to use both to find all solutions before we can choose a final answer. We begin by substituting g = 25 and then g = -25. If g = 25, then x = 6. If g = -25, then x = -26/4. Since all of our solutions are whole numbers, we can dismiss -26/4. We use g = 25 and x = 6 to determine the value of y: y = 2(25) + 36 = 86. Finally, we substitute the values for y and g into the last expression to determine its value : 2(86) + 3(25) = 172 + 75 = 247;the correct answer is (E).
Answer: E
Question: For what value(s) of x is the following equation satisfied: 5x-9-4x = -4x+6+5x
Options:
A)a. -5
B)b. 0 only
C)c. 5/2 only
D)d. No value
E)e. Any value
Rationale: 5x-9-4x = -4x+6+5x
k - 9 = k + 6
-9 = 6, which is false.
So, no k satisfies given equation.
Answer: D.
Answer: D
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?
Options:
A)18:11
B)22:13
C)23:12
D)11:9
E)11:10
Rationale: 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
Question: An bus covers a certain distance at a speed of 240 kmph in 5 hours. To cover the samedistance in 1hr, it must travel at a speed of?
Options:
A)700 km/hr
B)720 km/hr
C)780 km/hr
D)800 km/hr
E)890 km/hr
Rationale: Distance = (240 x 5) = 1200 km.
Speed = Distance/Time
Speed = 1200/(5/3) km/hr. [We can write 1 hours as 5/3 hours]
Required speed = 1200 x 3 km/hr = 720 km/hr.
B
Answer: B
Question: Certain stocks in April were 10% less than they were in May and 20% Lesser than they were in June. What was the percentage decrease in the stocks from May to June?
Options:
A)5%
B)10%
C)20%
D)28%
E)50%
Rationale: Let stocks value in Feb = 100 => In Jan = 90 and March = 90 * 80/100 = 72
Thus, percent decrease in stocks from Feb to March = 100 - 72 = 28%
Hence Answer is D
Answer: D
Question: Lottery balls numbered consecutively from one through one hundred are placed in a spinner. If one ball is drawn at random, what is the probability that it will have the number 1 on it?
Options:
A)9/100
B)1/10
C)11/100
D)19/100
E)1/5
Rationale: Probability = No of balls with 1 / total number of balls
= {1,10,11,12 to 19, 21,31,41,51,61,71,81,91,100}/100
= 20/100=1/5
Answer is E
Answer: E
Question: find the remainder (32)^33^34 when divided by 11?
Options:
A)9
B)10
C)11
D)12
E)13
Rationale: unit digit of 33^34 = 9 i.e odd no.
(32)^33^34 / 11
= (11*3-1)^(-------9) / 11
= (-1)^(odd) / 11
= -1/10
=> rem = -1+11 = 10
ANSWER:B
Answer: B
Question: 4 + 4 + 4 + 4 + 3 x 4^2 + 3 x 4^3 + 3 x 4^4 + 3 x 4^5 + 3 x 4^6 =
Options:
A) 4^24
B) 4^20
C) 4^16
D) 4^12
E) 4^7
Rationale: Let's see that 4 + 4 + 4 +4 is 4^2, then: 4^2 + 3 x 4^2 becomes 4 x 4^2 that is 4^3. You follow with the next element: 4^3 + 3 x 4^3 is equal to 4 x 4^3 that is 4^4. Then is assumed right before 3 x 4^6: 4^6 + 3 x 4^6 becomes 4 x 4^6 that is 4^7. Thus, the correct answer is the option E, 4^7.
Answer: E
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.961. Find the cost of each ice-cream cup?
Options:
A)25
B)66
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) = 961
96 + 225 + 490 + 6x = 961
6x = 150 => x = 25.
Answer: A
Answer: A
Question: In Town X, 64 percent of the population are employed, and 40 percent of the population are employed males. What percent of the employed people in Town X are females?
Options:
A)16%
B)24%
C)38%
D)40%
E)52%
Rationale: We are asked to find the percentage of females in employed people.
Total employed people 64%, out of which 40 are employed males,hence 24% are employed females.
(employed females)/(total employed people)=24/64=38%
Answer: C.
Answer: C
Question: A boat can move upstream at 35 kmph and downstream at 75 kmph, then the speed of the current is?
A. 5 kmph
Options:
A)15
B)12
C)17
D)13
E)20
Rationale: US = 35
DS = 75
M = (75- 35)/2
= 20
Answer:E
Answer: E
Question: What is the sum of all 3 digit positive integers that can be formed using the digits 1, 5, and 8, if the digits are allowed to repeat within a number?
Options:
A)126
B)1386
C)3108
D)308
E)13986
Rationale: There can be 27 numbers. Every digit has three possibilities because question permits repetition. So it becomes a very good summation problem.
If there are 27 digits. There are 27 hundred digits, 27 tens digit and 27 ones digit to be summed. Of 27 hundred digits, 9 of them are 1, 9 of them are 5 and the last 9 are 8. Same is true for the other two digits.
Thus the sum is:
9x100+9x500+9x800+9x10+9x50+9x80+9x1+9x5+9x8=
999x(1+5+8)=999x14=13986
E
Answer: E
Question: Sunil invested $ 1800 fir 4 years and $ 1300 for 2 years at the same rate of Simple Interest. If the total interest from these investments is $ 1900, what is the rate of interest?
Options:
A)18 3/4%
B)5 1/3%
C)19 1/4%
D)16%
E)18 2/4%
Rationale: (1800x4xR)/100+(1300x2xR)/100=1900
98R=1900
R= 19 1/4%
Answer is C
Answer: C
Question: Sreenivas sells a table to Shiva at 10% profit and Shiva sells it to Mahesh at 10% loss. At what price did Sreenivas purchase the table if Mahesh paid Rs. 2178?
Options:
A)2277
B)2669
C)2200
D)2766
E)2998
Rationale: Let the cost price of table for Sreenivas be Rs. x and given that, cost price of table for Mahesh = Rs. 2178.
=> (90%) of (110%) of x = Rs. 2178.
=> (90/100)(110/100)x = 2178
=> x = (2178 * 100)/(9 * 11)
=> x = Rs. 2200
Answer: C
Answer: C
Question: Pipe A fills a tank in 42 minutes. Pipe B can fill the same tank 6 times as fast as pipe A. If both the pipes are kept open when the tank is empty, how many minutes will it take to fill the tank?
Options:
A)3
B)4
C)5
D)6
E)7
Rationale: A's rate is 1/42 and B's rate is 1/7.
The combined rate is 1/42 + 1/7 = 1/6
The pipes will fill the tank in 6 minutes.
The answer is D.
Answer: D
Question: A large box contains 18 small boxes and each small box contains 25 chocolate bars. How many chocolate bars are in the large box?
Options:
A)230
B)320
C)450
D)540
E)110
Rationale: The number of chocolate bars is equal to
18 *25 = 450
correct answer C
Answer: C
Question: A small water pump would take 3 hours to fill an empty tank. A larger pump would take 1/4 hour to fill the same tank. How many hours would it take both pumps, working at their respective constant rates, to fill the empty tank if they began pumping at the same time?
Options:
A)3/13
B)1/5
C)1/10
D)1/3
E)1/7
Rationale: Rate of the small pump is 1/3 tank/hour
Rate of the larger pump is 1/(1/4) or 4 tank/hour;
Combined rate of the two pumps is 1/3+4=13/3 tank/hour, together they will fill the empty tank in 1/(13/3)= 3/13 hours (time=job/rate).
Answer: A
Answer: A
Question: Susan, John, Tim, Matt and Kim need to be seated in 5 identical chairs in straight line so that Susan is seated always left to Tim. How many such arrangements are possible ?
Options:
A)A)60
B)B)120
C)C)80
D)D)240
E)E)60
Rationale: Total number of arrangements = 5! = 120
In exactly half, Susan will be to the left of Tim, which gives us 60 arrangements
Option (A)
Answer: A
Question: On the xy co-ordinate plane, point C is (4,-2) and point D is (-1,2.5). The point on line segment CD that is twice as far from C as from D is:
Options:
A)(1,-1)
B)(1,1)
C)(2,0.25)
D)(3,0.5)
E)(3,1)
Rationale: We want the point on the line that is twice as far from C as it is from D. We can examine the x and y coordinates separately since they are independent.
*It should be noted that there are two solutions to this problem, one point between C and D, and another point with D in the middle of C and the point. We can quickly look at the answer choices and see that all the points are between C and D, therefore we can search for that point using the following method:
Taking the x-coordinate first, the distance between C and D is |(x-coordinate of C) - (x-coordinate of D)|= |5 - (-1)| = 6
The x-coordinate that is twice as far from C as it is from D (and in between C and D) will be 4 units from C and 2 units from D. So the x coordinate of the point we're looking for is 5-4 = 1, or (-1)+2 = 1.
Now looking at the y-coordinate, we do the same thing. The distance between C and D is |(-2) - 2.5| = 4.5
The y-coordinate that is twice as far from C as it is from D (and in between C and D) will be 3 units from C and 1.5 units from D. So the y coordinate of the point we're looking for is (-2)+3 = 1, or 2.5-1.5 = 1.
So now we have our coordinates of the point on the line that is twice as far from C as it is from D: (3,1)
Answer: E
Answer: E
Question: A man two flats for $675958 each. On one he gains 14% while on the other he loses 14%. How much does he gain or lose in the whole transaction?
Options:
A)1.96%
B)2.56%
C)3.12%
D)4.65%
E)5.12%
Rationale: In such a case there is always a loss
Loss% = (14/10)^2 = 49/25 = 1.96%
Answer is A
Answer: A
Question: James can hit a target once in 4 shots. If he fires 4 shots in succession, what is the probability that he will hit his target?
Options:
A)365/784
B)415/784
C)175/256
D)256/175
E)263/541
Rationale: James will hit the target if he hits it once or twice or thrice or all four times in the four shots that he takes.
So, the only possibility when the man will not hit the target is when he fails to hit the target in even one of the four shots that he takes.
The event of not hitting the target even once is the complement of the event of hitting the target at least once.
The probability that he will not hit the target in any given shot = 1 – 1/4 = ¾
Therefore, the probability that he will not hit the target in any of the four shots =3/4*3/4*3/4*3/4=81/256
The probability that he will hit the target at least in one of the four shots=1-81/256
=175/256
Ans: C
Answer: C
Question: If 10 people contributed a total of $30.00 toward a gift and each of them contributed at least $2.00, then the maximum possible amount any one person could have contributed is
Options:
A) $1.00
B) $1.25
C) $12.00
D) $6.00
E) $20.00
Rationale: C for me
9 people with 2$ each -> maximum = 12
Answer: C
Question: The speed of a bus increases by 2 kmph after every one hour. If the distance travelled in the first one hour was 35 km, what was the total distance travelled in 12 hours?
Options:
A)550
B)500
C)552
D)560
E)580
Rationale: Dist 1st hr = 35 km
speed of bus by 2 kmph 2nd hr = 37 km
3rd hr = 39 km
tot = 35+37+39+....(12 terms)
12/2(2*35+(12-1)2]
=6*92
= 552
ANSWER C
Answer: C
Question: A rectangular-shaped carpet that measures x feet by y feet is priced at $25. What is the cost of the carpet, in dollars per square yard? (1 square yard = 9 square feet)
Options:
A)9/(25xy)
B)xy/225
C)225/(xy)
D)225xy
E)25xy/9
Rationale: The area of the carpet in feet is xy.
The area in square yards is xy / 9.
The price per square yard is 25 / (xy/9) = 225/(xy).
The answer is C.
Answer: C
Question: How many words can be formed from the letters of the word ‘EXTRA’ so that the vowels are never together?
Options:
A)9
B)15
C)32
D)56
E)72
Rationale: Sol. The given word contains 5 different letters.
Taking the vowels EA together, we treat them as one letter.
Then, the letters to be arranged are XTR (EA).
These letters can be arranged in 4! = 24 ways.
The vowels EA may be arranged amongst themselves in 2! = 2 ways.
Number of words, each having vowels together = (24x2) = 48 ways.
Total number of words formed by using all the letters of the given words
= 5! = (5x4x3x2x1) = 120.
Number of words, each having vowels never together = (120-48) = 72.
Ans: E
Answer: E
Question: The probability that B can shoot a target two out of two times is 0.5. What is the probability that the target will be missed by B immediately after such two shots?
Options:
A)0.25
B)0.5
C)0.75
D)0.4
E)0.8
Rationale: Suppose there are total 'x' shots.
B shoots 2 out of 2 times. means out of x shots (x>2) B shots 2 out of 2 ----> B shots at least 2 out of x.
therefore, 2/x = 0.5 (given)
the target will be missed by B immediately after such two shots : this means he can shot just twice ...the third shot cannot happen which means he missed (x-2) shots.
thus, the probabilty of missing just after 2 shots is (x-2)/x.
(x-2)/x = 1 - 2/x
= 1 - 0.5
= 0.5
Answer : B
Answer: B
Question: In the x-y plane, the area of the region bounded by the graph of |x+y| + |x-y| = 12 is
Options:
A)8
B)12
C)16
D)1296
E)24
Rationale: I've never seen such kind of question in GMAT before.
OK there can be 4 cases:
|x+y| + |x-y| = 12
A. x+y+x-y = 12 --> x=6
B. x+y-x+y = 12 --> y=6
C. -x-y +x-y= 12 --> y=-6
D. -x-y-x+y=12 --> x=-6
The area bounded by 4 graphs x=6, x=-6, y=6, y=-6 will be square with the side of 4 so the area will be 36*36=1296
Answer:D
Answer: D
Question: In how many ways, a committee of 5 members can be selected from 6 men and 5 ladies, consisting of 3 men and 2 ladies?
Options:
A)200
B)120
C)245
D)320
E)147
Rationale: (3 men out 6) and (2 ladies out of 5) are to be chosen.
Required number of ways = (6c3x5c2)
= [6x5x4/3x2x1] x [5x4/2x1] = 200.
Ans: A
Answer: A
Question: Statements: Government has spoiled many top ranking financial institutions by appointing bureaucrats as Directors of these institutions. Assumptions: 1) Government should appoint Directors of the financial institutes taking into consideration the expertise of the person in the area of finance. 2) The Director of the financial institute should have expertise commensurate with the financial work carried out by the institute.
Options:
A)Only conclusion I follows
B)Only conclusion II follows
C)Either I or II follows
D)Neither I nor II follows
E)Both I and II follow
Rationale: According to the statement, Government has spoiled financial institutions by appointing bureaucrats as Directors. This means that only those persons should be appointed as Directors who are experts in finance and are acquainted with the financial work of the institute. So, both I and II follow.
E
Answer: E
Question: Two trains of length 100 m and 200 m are 100 m apart. They start moving towards each other on parallel tracks, at speeds 54 kmph and 72 kmph. After how much time will the trains meet?
Options:
A)12 sec
B)3 sec
C)4 sec
D)10 sec
E)5 sec
Rationale: They are moving in opposite directions, relative speed is equal to the sum of their speeds.
Relative speed = (45 + 72)*5/18 = 32.5 mps.
The time required = d/s = 100/32.5 = 3 sec.
ANSWER:B
Answer: B
Question: At a particular pizza shop, a pizza can be created from any combination of 7 different types of spice, 7 different types of meat, among which are pepperoni and anchovies, and 4 different types of cheese. If a customer at the shop decides to order a pizza with 1 type of spice, 2 types of cheese, and 4 types of meat but without pepperoni and anchovies together, how many possible ways to garnish the pizza are available to the customer?
Options:
A)6
B)35
C)120
D)450
E)1050
Rationale: Number of possible ways to select 1 type of spice = 7c1 = 7
Number of possible ways to select 2 types of cheese = 4c2 = 6
Number of possible ways to select 4 types of meat but without pepperoni and anchovies together
= Total number of ways without any restriction - Total number of ways in which pepperoni and anchovies together
= 7c4 - 5c2
=35 - 10
=25
Possible ways to garnish the pizza are available to the customer = 7*6 * 25
=1050
Answer E
Answer: E