divelab/Sys2Bench huggingface dataset:
Question: In a three digit number, the hundred digit is 2 more than the tens digit and the units digit is 2 less than the tens digit. If the sum of the digits is 30, find the number?
Options:
A)11201
B)12102
C)12081
D)12108
E)10126
Rationale: D
12108
Let the three digit numbers be 100a + 10b + c
a = b + 2
c = b - 2
a + b + c = 3b = 30 => b = 10
So a = 12 and b = 8
Hence the three digit number is: 12108
Answer: D
Question: Tough and Tricky questions: Statistics.
Set X consists of prime numbers {3, 11, 7, F, 17, 19}. If integer Y represents the product of all elements in set X and if 11Y is an even number, what is the range of set X?
Options:
A) 14
B) 16
C) 17
D) 20
E) 26
Rationale: Since 11Y = Even therefore Y has to beEVENsince 11 is a odd integer (Even * Odd = Even)
Similarly, Y is the product of all integers in set X But all integers in Set X are odd except the unknown F and since X contains only prime numbers, F has to equal to 2... ( 2 is the only even prime number and the product of all prime numbers in set X has to be Even, Even * Odd = Even)
Since you know value of F you can calculate the range = Largest integer in the set minus Smallest integer in the set = 19-2 =17
Answer is C
Answer: C
Question: Dylan is on a road trip. He planned on arriving at his destination, 2150 miles away, in 6 days. In the first day, he traveled 310 miles. In the next three days, he travels 1140 miles. How many miles, on average, does Dylan need to travel in the next two days to reach his destination?
Options:
A)330
B)340
C)350
D)360
E)370
Rationale: He still has to travel 2150 - 300 - 1130 = 720 miles
720 miles / 2 days = 360 miles per day.
Correct answer D
Answer: D
Question: man is 36 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:
Options:
A)14years
B)26 years
C)17 years
D)34 years
E)22 years
Rationale: Let the son's present age be x years. Then, man's present age = (x + 20) years.
(x + 36) + 2 = 2(x + 2)
x + 38 = 2x + 4
x = 34.
answer :D
Answer: D
Question: If n is a positive integer and n^2 is divisible by 212, then the largest positive integer that must divide n is
Options:
A)6
B)12
C)24
D)36
E)48
Rationale: The question asks aboutthe largest positive integer that MUST divide n, not COULD divide n. Since the least value of n for which n^2 is a multiple of 72 is 12 then the largest positive integer that MUST divide n is 12.
Complete solution of this question is given above. Please ask if anything remains unclear.
I spent a few hours on this one alone and I'm still not clear. I chose 12 at first, but then changed to 48.
I'm not a native speaker, so here is how I interpreted this question:the largest positive integer that must divide n=the largest positive factor of n. Since n is a variable (i.e. n is moving), so is its largest factor. Please correct if I'm wrong here.
I know that if n = 12, n^2 = 144 = 2 * 72 (satisfy the condition). When n = 12, the largest factor of n is n itself, which is 12. Check: 12 is the largest positive number that must divide 12 --> true
However if n = 48, n^2 = 48 * 48 = 32 * 72 (satisfy the condition too). When n = 48, the largest factor of n is n itself, which is 48. Check: 48 is the largest positive number that must divide 48 --> true
So, I also notice that the keyword isMUST, notCOULD. The question is, why is 48 notMUST divide 48, but instead onlyCOULD divide 48? I'm not clear right here. Why is 12MUST divide 12? What's the difference between them?
Only restriction we have on positive integer n is that n^2 is divisible by 72. The least value of n for which n^2 is divisible by 72 is 12, thus nmustbe divisible by 12 (n is in any case divisible by 12). For all other values of n, for which n^2 is divisible by 72, n will still be divisible by 12. This means that n is always divisible by 12 if n^2 is divisible by 72.
Now, ask yourself: if n=36, is n divisible by 48? No. So, n is not always divisible by 48.
D
Answer: D
Question: In a 280 meters race A beats B by 56 m or 7 seconds. A's time over the course is:
Options:
A)22 seconds
B)12 seconds
C)10 seconds
D)18 seconds
E)28 seconds
Rationale: B runs 56 m in 7 sec.
=> B runs 280 m in 7/56*280 = 35 seconds
Since A beats B by 7 seconds, A runs 280 m in (35-7) = 28 seconds
Hence, A's time over the course = 28 seconds
ANSWER:E
Answer: E
Question: Find the average of the series : 212, 152, 142, 132 and 112?
Options:
A)129
B)150
C)267
D)207
E)174
Rationale: Average = (212+152+142+132+112)/5
= 750/5
= 150
Answer: B
Answer: B
Question: There are two numbers. If 20% of the first number is added to the second number, then the second number increases to its five-fourth. Find the ratio of the first number to the second number?
Options:
A)5/4
B)5/7
C)5/3
D)5/8
E)5/1
Rationale: Let the two numbers be x and y.
20/100 * x + y = 5/4y
=> 1/5 x = 1/4 y => x/y
= 5/4
Answer: A
Answer: A
Question: In a hostel, the number of students decreased by 15% and the price of food increased by 20% over the previous year. If each student consumes the same amount of food then By how much should the consumption of food be cut short by every student, so that the total cost of the food remains the same as that of the previous year?
Options:
A)19%
B)15%
C)25%
D)40%
E)1.96%
Rationale: Cost of food (C) = Food consumed per student (F) * Number of students (N) * Price of food (P)
Originally,
C = FNP
When number of students decrease by 15%, and the price of food increases by 20%,
C = F(new) * (0.85N) * (1.2P)
=> F(new) = F/(0.85*1.2)
=> F(new) = 0.9804F
Therefore the new cost of food must be 98.04% of the old cost, or the cost of food must decrease by 1.96% (option E)
Answer: E
Question: 7.51 8.22 7.86 8.36
8.09 7.83 8.30 8.01
7.73 8.25 7.96 8.53
A vending machine is designed to dispense 8 ounces of coffee into a cup. After a test that recorded the number of ounces of coffee in each of 1000 cups dispensed by the vending machine, the 12 listed amounts, in ounces, were selected from the data above. If the 1000 recorded amounts have a mean of 8.1 ounces and a standard deviation of 0.2 ounces, how many of the 12 listed amounts are within 1.5 standard deviation of the mean?
Options:
A)Four
B)Six
C)Nine
D)Ten
E)Eleven
Rationale: Mean = 8.1
Standard Deviation = 0.2
within 1.5 standard deviation of the mean
i.e. 1.5 standard deviation ABOVE the mean = 8.1+1.5*0.2 = 8.4
and 1.5 standard deviation BELOW the mean = 8.1-1.5*0.2 = 7.8
hence, 9 values fall within 1.5 SD from Mean
Answer: Option C
Answer: C
Question: The speeds of 3 cars in the ratio 2:3:4. The ratio between time taken by them to travel the same distance is?
Options:
A)2:3:4
B)6:4:3
C)8:7:5
D)11:12:15
E)9:2:5
Rationale: Ratio of time taken is = 1/2 : 1/3 : 1/4 = 6:4:3
Answer is B
Answer: B
Question: What will come in place of the x in the following Number series? 65536, 32768, 16384, 8192, x
Options:
A)4090
B)4098
C)4094
D)4092
E)4096
Rationale: Go on dividing by 2 to the next number
Answer : E
Answer: E
Question: A train 100 meters long completely crosses a 350-meter long bridge in 40 seconds. What is the speed of the train in km/h?
Options:
A)37.5 km/h
B)40.5 km/h
C)43.5 km/h
D)46.5 km/h
E)49.5 km/h
Rationale: speed = distance / time = (100 + 350)/40 = 450/40 (m/s) * 3600/1000 = 40.5 km/h
The answer is B.
Answer: B
Question: The average age of 3 boys is 15 years and their ages are in the proportion 1:2:3. The age of the youngest boy is?
Options:
A)10 years
B)12 years
C)15 years
D)18 years
E)7.5 years
Rationale: Total age of 3 boys = 15*3 = 45
ratio of their ages = 1:2:3
Age of the youngest = 45*1/6 = 7.5 years
Answer is E
Answer: E
Question: Rohan ranked eleventh from the top and twenty-seventh from the bottom among the students who passed the annual examination in a class. If the number of students who failed in the examination was 12, how many students appeared for the examination?
Options:
A)48
B)49
C)50
D)Cannot be determined
E)None of these
Rationale: here .. from top its 11th and from bottom its 27th that means at top 10 members are there and bottom 26 members are there so 26+10+1=37. 37 memebers are passed, in above question 12 members are failed in examination so therefore 37+12=49.
ANSWER:B
Answer: B
Question: If -13 < 7a + 1 < 29 and 19 < 2 - b < 23, what is the maximum possible integer value of a + b?
Options:
A)-23
B)-18
C)-14
D)-13
E)-12
Rationale: -13 < 7a + 1 < 29 and 19 < 2 - b < 23
-14 < 7a < 28 and 17 < - b < 21
-2 < a < 4 and -17 > b > -21
Max(a+b ) <4+(-17)
Max(a+b ) <(-13)
Max(a+b ) = -14
Answer: Option C
Answer: C
Question: In a weight-lifting competition, the total weight of Joe's two lifts was 600 pounds. If twice the weight of his first lift was 300 pounds more than the weight of his second lift, what was the weight, in pounds, of his first lift?
Options:
A)225
B)275
C)300
D)350
E)400
Rationale: This problem is a general word translation. We first define variables and then set up equations.
We can define the following variables:
F = the weight of the first lift
S = the weight of the second lift
We are given that the total weight of Joe's two lifts was 600 pounds. We sum the two variables to obtain:
F + S = 600
We are also given that twice the weight of his first lift was 300 pounds more than the weight of his second lift. We express this as:
2F = 300 + S
2F – 300 = S
We can now plug in (2F – 300) for S into the first equation, so we have:
F + 2F – 300 = 600
3F = 900
F = 300
Answer is C
Answer: C
Question: According to the directions on a packet of smoothie mix, 1 3-ounce packet of smoothie mix is to be combined with 12 ounces of water to make a smoothie. How many 2-ounce packets of smoothie mix are required to prepare 150 12-ounce smoothies?
Options:
A) 120
B) 150
C) 180
D) 240
E) 600
Rationale: This question wasn't particularly grueling, but I think it's the first where I had the opportunity to solve it via theory andinspectionthat many on this board suggest as strategy on the GMAT. It actually came to me by accident. Basically, if we thought that the 3 packets of powder were included in the 12 ounces of water, that would mean we would need 150 packets of smoothie mix (along with 12(150) ounces of water for a total of 150 packets. However, we know, after a more careful reading of the stimulus, that the 3 ounces are NOT included in the 12 ounces. As such, the answer has to be LESS than 150 packets, since 150 would be too much powder considering you already have 150(12) ounces of water and need less packets than water to make a smoothie. As such, the only answer less than 150 is 120, A. Does this make sense? Or am I way off base?
C
Answer: C
Question: Mohan paid a sum of money for purchasing 30 pens, which he recovered in full when he sold 15 of them. What was his percentage of profit or loss per pen?
Options:
A)60%
B)70%
C)80%
D)90%
E)100%
Rationale: E
33.33%
If the sum he paid whilst purchasing 30 pens = A,
Then the Cost Price of each pen = A/30.
Since the amount he got whilst selling 15 pens is also = A
Then the Selling Price of each pen = A/15.
Since Selling Price > Cost Price, he made a profit.
Profit per pen = Selling Price - Cost Price = A/15 - A/30 = A/30.
Profit percentage per pen = Profit per pen / Cost per pen x 100 = (A/30) / (A/30) x 100 = 100% Answer :E
Answer: E
Question: If 5^10 x 2^10 = 10^n what is the value of n?
Options:
A)16
B)14
C)12
D)10
E)18
Rationale: 5^10*2^10 = 10^n
or 10^10 =10^n
n=10
D
Answer: D
Question: In how many different ways can the letters of the word 'OPTICAL' be arranged so that the vowels always come together?
Options:
A)620
B)640
C)690
D)710
E)720
Rationale: The word 'OPTICAL' has 7 letters. It has the vowels 'O','I','A' in it and these 3 vowels should always come together. Hence these three vowels can be grouped and considered as a single letter. That is, PTCL(OIA).
Hence we can assume total letters as 5 and all these letters are different.
Number of ways to arrange these letters
=
5
!
=
5
×
4
×
3
×
2
×
1
=
120
=5!=5×4×3×2×1=120
All the 3 vowels (OIA) are different
Number of ways to arrange these vowels among themselves
=
3
!
=
3
×
2
×
1
=
6
=3!=3×2×1=6
Hence, required number of ways
=
120
×
6
=
720
E)
Answer: E
Question: Pipe A can fill a tank in 7 hours, pipe B in 14 hours and pipe C in 42 hours. If all the pipes are open,in how many hours will the tank be filled ?
Options:
A)4
B)4.2
C)4.5
D)4.3
E)4.1
Rationale: 1/7+1/14+1/42=10/42=1/4.2. so 4.2 hrs
ANSWER:B
Answer: B
Question: A 1200 m long train crosses a tree in 120 sec, how much time will I take to pass a platform 700 m long?
Options:
A)288
B)190
C)188
D)188
E)12
Rationale: L = S*T
S= 1200/120
S= 10 m/Sec.
Total length (D)= 1900 m
T = D/S
T = 1900/10
T = 190 Sec
Answer:B
Answer: B
Question: An integer n between 1 and 99, inclusive, is to be chosen at random. What is the probability that n(n+1) will be divisible by 3 ?
Options:
A)1/9
B)1/3
C)1/2
D)2/3
E)5/6
Rationale: n(n+1) to be divisible by 3 either n or n+1 must be a multiples of 3.
In each following group of numbers: {1, 2, 3}, {4, 5, 6}, {7, 8, 9}, ..., {97, 98, 99} there are EXACTLY 2 numbers out of 3 satisfying the above condition. For example in {1, 2, 3} n can be: 2, or 3. Thus, the overall probability is 2/3.
Answer: D.
Answer: D
Question: The wheels revolve round a common horizontal axis. They make 15, 20 and 48 revolutions in a minute respectively. Starting with a certain point on the circumference down wards. After what interval of time will they come together in the same position?
Options:
A)1 min
B)2 min
C)3 min
D)4 min
E)None
Rationale: Time for one revolution = 60/15 = 4
60/ 20 = 3
60/48 = 5/4
LCM of 4, 3, 5/4
LCM of Numerators/HCF of Denominators = 60/1 = 60
ANSWER:A
Answer: A
Question: The HCF and LCM of two numbers m and n are respectively 6 and 210. If m + n = 60, then 1/m + 1/n is equal to
Options:
A)1/35
B)3/35
C)1/21
D)2/35
E)None
Rationale: Answer
We have, m x n = 6 x 210 = 1260
âˆ´ 1/m + 1/n = (m + n)/mn = 60/1260 = 1/21
Correct Option: C
Answer: C
Question: On what dates of April, 2001 did Wednesday fall?
Options:
A)2nd, 9th, 16th, 23rd
B)4th, 11th, 18th, 25th
C)3rd, 10th, 17th, 24th
D)1st, 8th, 15th, 22nd, 29th
E)None of these
Rationale: Explanation :
We need to find out the day of 01-Apr-2001
01-Apr-2001 = (2000 years + period from 1-Jan-2001 to 01-Apr-2001)
We know that number of odd days in 400 years = 0
Hence the number of odd days in 2000 years = 0 (Since 2000 is a perfect multiple of 400)
Days from 1-Jan-2001 to 01-Apr-2001 = 31 (Jan) + 28 (Feb) + 31 (Mar) + 1(Apr) = 91
91 days = 13 weeks = 0 odd day
Total number of odd days = (0 + 0) = 0 odd days
0 odd day = Sunday. Hence 01-Apr-2001 is Sunday.
Hence first Wednesday of Apr 2011 comes in 04th and successive Wednesdays
come in 11th, 18th and 25th
Answer : Option B
Answer: B
Question: The sticks of same length are used to form a triangle as shown below.If 87 such sticks are used then how many triangles can be formed?
Options:
A)43
B)44
C)45
D)465
E)47
Rationale: First triangle is formed by using 3 sticks, but any subsequent triangle may be formed by using 2 sticks. Therefore, If 1st triangles uses 3 sticks, Remaining sticks = 87 - 3 = 84. With these 84, we can form 42 triangles. So total = 42 + 1 = 43
Answer:A
Answer: A
Question: A coin has two sides. One side has the number 1 on it and the other side has the number 2 on it. If the coin is flipped three times what is the probability that the sum of the numbers on the landing side of the coin will be greater than 5?
Options:
A)3/8
B)1/16
C)1/8
D)1/2
E)1/4
Rationale: One approach to solve the problem is to list the different possibilities for a toss of coin three times. Because there are two outcomes and the coin is tossed three times, the table will have 2*2*2 or 8 rows.
Next add the resulting rows together to find the sum (the fourth column in the table below).
Toss 1 | Toss 2 | Toss 3 | Sum
1 ---------- 1 -------- 1 ------ 3
1 ---------- 1 -------- 2 ------ 4
1 ---------- 2 -------- 1 ------ 4
1 ---------- 2 -------- 2 ------ 5
2 ---------- 1 -------- 1 ------ 4
2 ---------- 1 -------- 2 ------ 5
2 ---------- 2 -------- 1 ------ 5
2 ---------- 2 -------- 2 ------ 6
From the table we see that there are 1 situations where the sum of the tosses will be greater than 5. And there are 8 possible combinations resulting in a probability of
1/8 or a probability of 1/8.
SO the correct answer is C.
Answer: C
Question: If x = –2, what is the value of 4x^3?
Options:
A)–32
B)–24
C)–8
D)8
E)32
Rationale: 4x^3 = 4(−2)34(−2)3 = 4 * - 8 = -32.
Answer is -32
ANSWER:A
Answer: A
Question: Adam has s pairs of shoes, which is 1/2 as many as Katherine and twice as many as Julie. In terms of s, how many pairs of shoes do the three of them have combined?
Options:
A)7/2*s
B)11s
C)2s
D)5/2*s
E)13/4*
Rationale: == s +2s + s/2 ==> 3s + 1/2 s = 7/2*s
Ans .A
Answer: A
Question: A table is bought for Rs.800/- and sold at Rs.600/- find gain or loss percentage
Options:
A)25% gain
B)20% loss
C)20% gain
D)25% loss
E)None
Rationale: Formula = (Selling price ~ Cost price)/Cost price * 100
= (600 - 800)/800 = 25% loss
D
Answer: D
Question: Two numbers are less than third number by 34% and 37% respectively. How much percent is the second number less than by the first
Options:
A)8%
B)10%
C)9%
D)11%
E)22%
Rationale: Let the third number is x.
then first number = (100-34)% of x
= 66% of x = 66x/100
Second number is (63x/100)
Difference = 66x/100 - 63x/100 = 3x/100
So required percentage is, difference is what percent of first number
(3x/100 * 100/63x * 100 )% = 22% ANSWER :E
Answer: E
Question: The average of first 10 prime numbers is?
Options:
A)12.9
B)12.6
C)12.3
D)512.4
E)12.1
Rationale: Sum of 10 prime no. = 129
Average = 129/10 = 12.9
Answer: A
Answer: A
Question: The speed of a boat in still water is 12 kmph. What is the speed of the stream if the boat can cover 32 km downstream or 16 km upstream in the same time?
Options:
A)5 kmph
B)6 kmph
C)7 kmph
D)4 kmph
E)10 kmph
Rationale: X = the speed of the stream
(12 + X) / (12 - X) = 2/1
12+ X = 24 - 2X
3X = 12
X = 4 km/hour
If the speed of the stream is 4km/hour, then the 'downstream' speed of the boat is 12+4 = 16km/hour and the 'upstream' speed of the boat is 12-4 = 8km/hour. In that way, if the boat traveled for 2 hours, it would travel 2x8 = 16km downstream and 2x16 = 32km/hour upstream.
Answer : D
Answer: D
Question: The value of a machine depreciates at the rate of 10% every year. It was purchased 3 years ago. If its present value is Rs. 8748, its purchase price was :
Options:
A)12000
B)10000
C)15000
D)20000
E)25000
Rationale: Purchase = 8748/(1-10/100^3) = 12000
ANSWER A
Answer: A
Question: A man is 20 mins late to the office if he walks at 20 kmph, and 15 mins earlier if he walks at 30 kmph. How much time will he be early/late if he walks at 25 kmph?
Options:
A)early 1 min
B)early 2 min
C)late 1 min
D)late 2 min
E)none
Rationale: let distance be x,then
time1= x/20*60,
t2=x/30*60
difference b/w both time is 35min then
x/20-x/30=35 so x=35
now for 25kmph
35/25*60= 84 min
for 20kmph time=105 min
for 30kmph time= 70min
in 30 kmph he is early by 15 min then actual time is 85 min
so the anser is he is early by 1 min
ans=early 1 min
t=35/25*60
ANSWER:A
Answer: A
Question: Calculate the value of 8.14 x 10^3 ?
Options:
A)81400000
B)8140000
C)814000
D)8140
E)814
Rationale: 8.14 x 10^6 = 8.14 x 1000 = 8140.
Answer = D
Answer: D
Question: The ratio of two numbers is 4 : 5 and their H.C.F. is 4. Their L.C.M. is
Options:
A)48
B)22
C)80
D)27
E)35
Rationale: Explanation:
Let the numbers be 4x and 5x. Then, their H.C.F. = x. So, x = 4.
So, the numbers 16 and 20.
L.C.M. of 16 and 20 = 80.
Answer: Option C
Answer: C
Question: A certain debt will be paid in 52 installments from January 1 to December 31 of a certain year. Each of the first 12 payments is to be $410; each of the remaining payments is to be $65 more than each of the first 12 payments. What is the average (arithmetic mean) payment that will be made on the debt for the year?
Options:
A)443
B)450
C)460
D)468
E)475
Rationale: Total number of installments = 52
Payment per installment for the first 12 installments = 410
Payment per installment for the remaining 32 installments = 410+65=475
Average = (12*410 + 40*475)/52 = 460
Answer C
Answer: C
Question: One out of every 5000 computer chips is defective. If 2 out of every 30 defective chips have defective processors and there are 30 defective processors in the first batch, how many computer chips are there in the first batch?
Options:
A)450
B)900
C)90,000
D)2250,000
E)900,000
Rationale: (D) Read the whole question to get the feel of what they are asking you to find. Then start with the smallest amount and work your way outwards. We are told that two out of every 30 defective chips have a defective processor. Let x be the total number of defective processors in the batch. Because we know 2 out of every 30 defective chips will have defective processors, and the total number of defective processors in the batch is 30, we can write out an equation: (2/30)x = 30. This can be simplified to (1/15)x = 30. Multiplying each side by 15, we arrive at x = 450. This tells us that there are 450 defective chips in the whole batch. Because we know that 1 out of every 1000 chips is defective, we can set up a proportion. If 1 out of every 5000 chips is defective, then 450 out of y chips would be defective, where y is the total number of chips in the batch. This can be set up as an equation as follows: 1/5000 = 450/y. Solve for y and you will get the total number of chips in the batch: 2250,000.
The answer is (D).
Answer: D
Question: If Solomon distributes his toys in the ratio of 1/4 : 1/6 : 1/10 : 1/9 between his four friends A, B, C and D, then find the total number of toys Solomon should have?
Options:
A)111.7
B)118.7
C)113.7
D)218.7
E)418.7
Rationale: Here, A : B : C : D = 1/4 : 1/6 : 1/10 : 1/9
1) L.C.M of 4 : 6 : 10 : 9 is 180
2) Find the number of pens each friend received --------- (To find no. of pens each friend has, multiply the ratio with the L.C.M. calculated)
A = (1/4) x 180 = 45
B = (1/6) x 180 = 30
C = (1/10) x 180 = 18
D = (1/7) x 180 = 25.7
3) Total number of toys = (45 x + 30 x + 18 x + 25.7 x) = 118.7 x
Minimum number of pens (x) = 1
Therefore, total number of pens = 118.7 pens.
Correct option :B
Answer: B
Question: Anil spends 40% of his income on rent, 30% of the remaining on medicines and 20% of the remaining on education. If he saves Rs. 840 every month, then find his monthly salary?
Options:
A)RS.3500
B)Rs.1500
C)Rs.4500
D)Rs.2500
E)Nill
Rationale: Answer: Option D
Let's anil's salary be Rs. 100.
Money spent on Rent = 40% of 100 = Rs. 40.
Money spent on medical grounds = 30% of (100 - 40) = 3/10 * 60 = Rs. 18.
Money spent on education = 20% of (60 - 18) = 1/5 * 42 = Rs. 8.40
anil saves 100 - (40 + 18 + 8.40) i.e., Rs. 33.60
for 33.6 ---> 100 ; 840 ---> ?
Required salary = 840/33.6 * 100 = Rs. 2500
Answer: D
Question: When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a constant amount each year for the next 6 years. At the end of the 6th year, the tree was 1/4 taller than it was at the end of the 4th year. By how many feet did the height of the tree increase each year?
Options:
A)1
B)2/5
C)1/2
D)2/3
E)6/5
Rationale: Say, the tree grows by x feet every year.
Then, 4 + 6x = (1+1/4)(4+4x)
or, x = 1
Answer A
Answer: A
Question: Ravi purchased a refrigerator and a mobile phone for Rs. 15000 and Rs. 8000 respectively. He sold the refrigerator at a loss of 4 percent and the mobile phone at a profit of 10 percent. Overall he make a.
Options:
A)223
B)277
C)288
D)200
E)812
Rationale: Let the SP of the refrigerator and the mobile phone be Rs. r and Rs. m respectively.
r = 15000(1 - 4/100) = 15000 - 600
m = 8000(1 + 10/100) = 8000 + 800
Total SP - Total CP = r + m - (15000 + 8000) = -600 + 800 = Rs. 200
As this is positive, an overall profit of Rs. 200 was made.
Answer: D
Answer: D
Question: If y > 0, (1y)/20 + (3y)/10 is what percent of y?
Options:
A)35%
B)50%
C)60%
D)70%
E)80%
Rationale: can be reduced to y/20+3y/10 =7y/20=35%
A
Answer: A