mathewhe/aqua_rat huggingface dataset:
Question: How much greater is the combined area in square inches of the front and back of a rectangular sheet of paper measuring 11 inches by 19 inches than that of a rectangular sheet of paper measuring 9.5 inches by 11 inches?
(A) 50%
(B) 87%
(C) 100%
(D) 187%
(E) 200%
Rationale: Let's just look at the dimensions (no calculation needed).
With dimension 11 the same, the other dimension 19 is twice 9.5
Then the area will be double which means 100% greater.
The answer is C.
Answer: (C) 100%
Question: n^(n/2)=2 is true when n=2 in the same way what is the value of n if n^(n/2) =4?
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Rationale: n^(n/2)=4
Apply log
N/2logn=log4
nlogn=2log4=log4^2=log16
Logn=log16
Now apply antilog
n=16/n
Now n=4.
ANSWER:C
Answer: (C) 4
Question: A man sold an article offering a discount of 5% and earned a profit of 23.5%. What would have been the percentage of profit earned if no discount was offered?
(A) 20%
(B) 35%
(C) 30%
(D) 37%
(E) 39%
Rationale: C
30%
Let C.P. be $100.
Then, S.P. = $123.50
Let marked price be $x. Then, 95/100 x = 123.50
x = 12350/95 = $130
Now, S.P. = $130, C.P. = $100
Profit % = 30%.
Answer: (C) 30%
Question: The average of 11numbers is 60. Out of 11numbers the average of first 6no. is 58, and last 6numbers is 65 then find 6th number?
(A) 78
(B) 65
(C) 58
(D) 62
(E) 48
Rationale: 6th number = sum of 1st 6no.s + sum of last 6no.s - sum of 11no.s
answer = 6*58+6*65-11*60 = 78
Answer is A
Answer: (A) 78
Question: John was 22 years old when he married Betty. They just celebrated their fifth wedding anniversary, and Betty's age is now 7/9 of John's. How old is Betty?
(A) 24
(B) 26
(C) 28
(D) 21
(E) 32
Rationale: Assume Betty's age on marriage = x years.
John's age on marriage = 22
John's age after 5 years = 27 years.
Betty's age after 5 years = x + 5
Given: x + 5 = 7/9 (27) = 21
Therefore Betty's current age = 21
Option D
Answer: (D) 21
Question: If a particular is never chosen, in how many ways can a cricketbe chosen out of 15 players?
(A) 245
(B) 250
(C) 364
(D) 389
(E) 398
Rationale: A particular players is never chosen, it means that 11 players are selected out of 14 players.
=> Required number of ways = 14C11
= 14!/11!x3! = 364
C
Answer: (C) 364
Question: A jogger running at 9 km/hr along side a railway track is 240 m ahead of the engine of a 110 m long train running at 45 km/hr in the same direction. In how much time will the train pass the jogger?
(A) 19 sec
(B) 87 sec
(C) 36 sec
(D) 16 sec
(E) 35 sec
Rationale: Speed of train relative to jogger = 45 - 9 = 36 km/hr.
= 36 * 5/18 = 10 m/sec.
Distance to be covered = 240 + 110 = 350 m.
Time taken = 350/10 = 35 sec.
Answer: E
Answer: (E) 35 sec
Question: Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 28 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is?
(A) 457 km
(B) 444 km
(C) 547 km
(D) 588 km
(E) 653 km
Rationale: 1h ----- 5
? ------ 60
12 h
RS = 28 + 21 = 49
T = 12
D = 49 * 12 = 588
Answer:D
Answer: (D) 588 km
Question: Stock / Number of shares
V ------------ 68
W ---------- 112
X ------------ 56
Y ------------ 94
Z ------------ 45
The table shows the number of shares of each of the 5 stocks owned by Mr Sami. If Mr. Sami was to sell 20 shares of Stock X and buy 26 shares of stock Y, what would be the increase in the range of the numbers of shares of the 5 stocks owned by Mr. Sami?
(A) 4
(B) 6
(C) 9
(D) 17
(E) 20
Rationale: Based on the original number of shares, the range would be: 112 - 45 = 67
However, the prompt tells us that two of the values in the table are going to change. After the changes, the values will be:
V 68
W 112
X 36
Y 120
Z 45
Now the range is 120 - 36 = 84
The INCREASE in the range requires us to compare thenewrange to theoldrange: 84 - 67 = 17
D
Answer: (D) 17
Question: If n is a positive integer and the product of all the integers from 1 to n, inclusive, is a multiple of 1000, what is the least possible value of n?
(A) 12
(B) 11
(C) 14
(D) 13
(E) 15
Rationale: 1000 = 2*2*2*5*5*5, so we need 3 factors of 2 and 3 factors of 5. Therefore, the smallest value of n is 15, so the answer is E.
Answer: (E) 15
Question: Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $500 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $555 as interest. What was the value of his total savings before investing in these two bonds?
(A) 2,000
(B) 2,500
(C) 4,000
(D) 5,000
(E) 6,000
Rationale: So, we know that Shawn received 20% of the amount he invested in a year. We also know that in one year Shawn received $250, thus 0.2x = $250 --> x = $1,250.
Since, he invested equal sums in his 2 bonds, then his total savings before investing was 2*$1,250 = $2,500.
Answer:B
Answer: (B) 2,500
Question: IF GO=32& SHE=49 the SOME will be equal to?
(A) 56
(B) 58
(C) 62
(D) 64
(E) 66
Rationale: If we count letters till the end of the alphabet including that letter in reverse order then
G = 20 and O = 12 totaling 32
S = 8, H = 19 and E = 22 totaling 49
So
SOME = 8 + 12 + 14 + 22 = 56
ANSWER:A
Answer: (A) 56
Question: If the positive integer y is divisible by 4, 8, and 12, then which of the following must y be divisible by?
I. 24
II. 36
III. 48
(A) III only
(B) II only
(C) I only
(D) II and III only
(E) I, II, and III
Rationale: Answer = C
LCM of 4, 8, 12 = 24
Answer = 24
Answer: C
Answer: (C) I only
Question: Of the books standing in a row on a shelf, an atlas is the 30th book from the left and the 33rd book from the right. If 3 books to the left of the atlas and 4 books to the right of the atlas are removed from the shelf, how many books will be left on the shelf?
(A) 55
(B) 57
(C) 58
(D) 61
(E) 63
Rationale: 100%. There are total of 30+33-1=62 books and 3+4=7 books are removed, thus 62-7=55 books are left.
Answer: A.
Answer: (A) 55
Question: John, James and Jim' investment ratio in a business is 4:7:9. If total total investment is 80000. Find Jim's investment?
(A) 35000
(B) 40000
(C) 16000
(D) 36000
(E) 60000
Rationale: let the investment of John James and Jim is 4x 7x and 9x
4x+7x+9x = 80000
20x = 80000
x = 4000
Jim' investment = 9*4000 = 36000
Answer : D
Answer: (D) 36000
Question: clay brought 4 chocolates for 4 guests. 1 of the guest arrive early and eat 3 chocolates each. How many chocolates are left over if the other guests all have the same number of chocolates?
(A) 0
(B) 1
(C) 6
(D) 5
(E) 2
Rationale: clay made 4*4 chocolates = 16 chocolates. 1 guests eat 2 chocolates, leaving 13 remaining for 3 guests.
1+3=4.
4 is not divisible by 3. The 3 guests ate a cumulative number of chocolates divisible by 3, because the number is the same.
13-12=1.
B is the correct answer
Answer: (B) 1
Question: If the selling price is trippled,the profit is quadrupled, what is the percentage of profit??
(A) 50%
(B) 100%
(C) 150%
(D) 200%
(E) 250%
Rationale: we can make two equations from the given info..
let selling price be S and cost price be C..
so profit=P=S-C...
if S is doubled profit is tripled..
so 4P=3S-C..
or S=3P...
therefore C=P..
% of profit=P/P=100%
B
Answer: (B) 100%
Question: A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:
(A) 20 days
(B) 22 1/2 days
(C) 25 days
(D) 30 days
(E) 40 days
Rationale: Ratio of times taken by A and B = 1 : 3.
The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day.
If difference of time is 2 days, B takes 3 days.
If difference of time is 60 days, B takes = 3/2 x 60 = 90 days.
So, A takes 30 days to do the work.
A’s 1 day’s work = 1/30
B’s 1 day’s work = 1/90
A’s and B’s one day work = 1/30 + 1/90 = 2/45.
Therefore, A and B together can do the work in = 45/2 = 22 1/2 days.
ANSWER:B
Answer: (B) 22 1/2 days
Question: Two cars cover the same distance at the speed of 60 and 64 kmps respectively. Find the distance traveled by them if the slower car takes 1 hour more than the faster car
(A) 960 km
(B) 968 km
(C) 960 km
(D) 980 km
(E) 964 km
Rationale: 60(x + 1) = 64x
X = 15
60 * 16 = 960 km
Answer: C
Answer: (C) 960 km
Question: 4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 6 mat-weavers in 6 days?
(A) 25
(B) 9
(C) 39
(D) 61
(E) 16
Rationale: Let the required number of bottles be x.
More weavers, More mats (Direct Proportion)
More days, More mats (Direct Proportion)
Wavers	4	:	6 :: 4 : x
Days	4:6
4 * 4 * x = 6 * 6 * 4
x =	(6 * 6 * 4)/(4 x 4)
x = 9.
Answer is B.
Answer: (B) 9
Question: What is the largest power of 3 contained in 200!
(A) 88
(B) 48
(C) 66
(D) 97
(E) 39
Rationale: In real basic terms, we're asked to find all of the '3s' in 200!
We can figure out that 200/3 = 66, so we know that there are at least 66 '3s' in 200! While that answer is among the 5 choices, it seems a bit too 'easy', so let's do a bit more work and list out the first few numbers that we know have a '3' in them:
3 = 3x1
6 = 3x2
9 = 3x3
Notice how both 3 and 6 have just one 3 in them, but 9 has TWO 3s (there's an 'extra' 3 that we have to account for). This implies that there are probably other numbers that include 'extra 3s' that we have to figure out:
To find those extra 3s, we have to look at numbers that contain 'powers of 3'...
3^2 = 9
3^3 = 27
3^4 = 81
3^5 = 243, but that's too big (we're only going up to 200). Keep in mind that a multiple of 81 is also a multiple of 9 and 27, so we don't want to count any of those values more than once.
200/9 = 22, so we know that there are at least 22 extra 3s (and certainly more because of the 27 and 81). With the 66 3s that we already have, those 22 extra 3s increase the total to 88. With the other extra 3s, we'll end up with MORE than 88 3s. There's only one answer that fits that logic...
ANSWER:D
Answer: (D) 97
Question: A bank offers 5% C.I. calculated on half-yearly basis . A customer deposits Rs. 1600 each on 1st January and 1st July of a year. At the end of the year, the amount he would have gained by way of interest is?
(A) 126
(B) Rs.121
(C) 165
(D) 134
(E) 123
Rationale: Amount = [1600 * (1 + 5/(2 * 100)2 + 1600 * (1 + 5/(2 * 100)]
= [1600 * 41/40(41/40 + 1)
= [(1600 * 41 * 81)/(40 * 40)]
= Rs. 3321.
C.I. = 3321 - 3200 = Rs.121.
Answer:B
Answer: (B) Rs.121
Question: 12,31,68,129,?,347,516
(A) 129
(B) 240
(C) 347
(D) 220
(E) 520
Rationale: 2*2*2 + 4 = 12
3*3*3 +4 = 31
4*4*4 + 4 = 68
5*5*5 + 4 = 129
7 *7 *7 + 4 = 347
8 *8 *8 + 4 = 516.
6*6*6 + 4 = 220
ANSWER : D
Answer: (D) 220
Question: Find the value of 72519 x 9999 = m.
(A) 233243413
(B) 354545451
(C) 343435451
(D) 565656767
(E) 725117481
Rationale: 72519 x 9999	= 72519 x (10000 - 1)
= 72519 x 10000 - 72519 x 1
= 725190000 - 72519
= 725117481
E
Answer: (E) 725117481
Question: Each week, Harry is paid x dollars per hour for the first 30 hours and 1.5x dollars for each additional hour worked that week. Each week, Annie is paid x dollars per hour for the first 40 hours and 2x dollars for each additional hour worked that week. Last week Annie worked a total of 47 hours. If Harry and Annie were paid the same amount last week, how many hours did Harry work last week?
(A) 40
(B) 42
(C) 44
(D) 46
(E) 48
Rationale: Annie earned 40x + 7(2x) = 54x
Let H be the number of hours that Harry worked.
Harry earned 30x + 1.5x(H-30) = 54x
(1.5x)(H) = 69x
H = 46 hours
The answer is D.
Answer: (D) 46
Question: In a garden man has to pick some flowers ans has to pass thru 3 doors. Each door has a guard. Man has to give half of the flowers he had to the guard and in return guard returns the man him one flower back. how many flower should man pick so that at the end he is left with same number of flowers he has picked?
(A) 1
(B) 2
(C) 3
(D) 4
(E) 5
Rationale: suppose man pick up x flowers.
He gives half flowers he had to guard and guard in return gives 1 flower to man.
so,
after 1st door remained flowers towards guard=(x/2)+1
i.e(x+2)/2
after 2nd door remained flowers towards guard=[(x+2)/4]+1
after 3rd door remained flowers towards guard=[(x+6)/8]+1
i.e.(x+14)/8
at the end he is left with same number of flowers he has picked.
so(x+14)/8=x
8x-x=14
x=2
Hence he should pick up 2 flowers.
ANSWER:B
Answer: (B) 2
Question: A boy wants to go abroad by boat and return by flight. He has a choice of 4 different boat to go and 5 flight to return. In how many ways, can the boy perform his journey?
(A) 20
(B) 25
(C) 30
(D) 40
(E) 50
Rationale: Ans.(A)
Sol. Number of choices to go by ship = 4 Number of choices to return by airline = 5 From, fundamental principle, total number of ways of performing the journey = 4 x 5 = 20 ways
Answer: (A) 20
Question: Tane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks. If they both work together, how many weeks will it take for them to produce 15 handcrafted drums?
(A) 30
(B) 36
(C) 70
(D) 80
(E) 150
Rationale: Method I: the rates solution
“Tane can make a handcrafted drum in 4 weeks. Zane can make a similar handcrafted drum in 6 weeks.” Tane’s rate is (1 drum)/(4 weeks) = 1/4. Zane’s rate is (1 drum)/(6 weeks) = 1/6. The combined rate of Tane + Zane is
R = 1/4 + 1/6 = 3/12 + 2/12 = 5/12
That’s the combined rate. We need to make 15 drums — we have a rate and we have an amount, so use the “art” equation to solve for time:
T = A/R = 15/(5/12) = 15*(12/5) = (15/5)*12 = 3*12 = 36
BTW, notice in the penultimate step, the universal fraction strategy: cancelbeforeyou multiply (Tip #3:http://magoosh.com/gmat/2012/can-i-use- ... -the-gmat/. Tane and Zane need 36 weeks to make 15 drums.
Answer = B.
Answer: (B) 36
Question: The difference between the ages of two person is 10 years. Fifteen years ago, the elder one was twice as old as the younger one. The present age of the elder person is
(A) 15
(B) 25
(C) 35
(D) 45
(E) 30
Rationale: x>y;
x-y=10;
x-15=2*(y-15);
Finally, x=35.
ANSWER:C
Answer: (C) 35
Question: How many 4 digit numbers are there, if it is known that the first digit is odd, the second is even, the third is prime, the fourth (units digit) is divisible by 3, and the digit 2 can be used only once?
(A) 20
(B) 150
(C) 225
(D) 300
(E) 380
Rationale: 4 options for the first digit:1, 3, 5, 7, 9;
5 options for the second digit: 0, 2, 4, 6, 8;
4 options for the third digit: 2, 3, 5, 7;
4 options for the fourth digit: 0, 3, 6, 9.
Four digit # possible without the restriction (about the digit 2): 5*5*4*4=400
Numbers with two 2-s, 2X2X 5*1*1*4=20.
Thus there are 400-20=380 such numbers.
Answer: E.
Answer: (E) 380
Question: A cricket team played 200 games and won 80 percent of them. How many games did it win?
(A) 80
(B) 94
(C) 160
(D) 114
(E) 124
Rationale: 80% of 200 =x
0.80 x 200 = x
160=x
answer :C
Answer: (C) 160
Question: Teams A, B, C,D and E were in a baseball tournament. Each team played each other team once. Team A beat team D. Teams A, B and C won the exact same number of games. How many games did team D lose?
(A) 5 games
(B) 4 games
(C) 3 games
(D) 2 games
(E) 1 game
Rationale: There are 4 teams and each team played each other team once. That tells us 2 facts:
 Each team played 3 games
 4 teams played a total of 6 games.
Since there are only 6 games, only 6 total wins are possible. Since A, B and C won the exact same number of games, they either all won 1 game or all won 2 games. Let’s examine both scenarios:
Scenario #1: A, B and C each won 1 game. In this scenario, D must have won all 3 games it played. That contradicts with the fact that A beat D. So, scenario 1 is not possible. So, it has to be scenario #2.
Scenario #2: A, B and C each 2 games. In this scenario, D won 0 games. That means D lost all 3 games it played.
correct answer C
Answer: (C) 3 games
Question: At Company X, senior sales representatives visit the home office once every 12 days, and junior sales representatives visit the home office once every 8 days. The number of visits that a junior sales representative makes in a 2-year period is approximately what percent greater than the number of visits that a senior representative makes in the same period?
(A) 10%
(B) 25%
(C) 33%
(D) 50%
(E) 67%
Rationale: Each 24-day period, senior representatives visit the home office 2 times while junior representatives visit 3 times, thus 50% more.
The answer is D.
Answer: (D) 50%
Question: Pipe A can fill a tank in 15 hours, pipe B in 10 hours and pipe C in 3 hours. If all the pipes are open, in how many hours will the tank be filled?
(A) 2
(B) 2.5
(C) 3
(D) 5
(E) None
Rationale: Sol.
Part filled by (A + B + C) in 1 hour = (1/15 + 1/10 + 1/3) = 1/2.
âˆ´ All the three pipes together will fill the tank in 2 hours.
Answer A
Answer: (A) 2
Question: If x/y= 4 and y is not '0' what % of x is 2x-y
(A) 150%
(B) 175percent
(C) 200%
(D) 250%
(E) 350%
Rationale: let z be the percentt
x*z/100=2x-y
zx=7y*100
z=700y/4y
z=350/2
z= 175%
ANSWER:B
Answer: (B) 175percent
Question: A sum of money invested for a certain number of years at 8% p.a. simple interest grows to Rs.180. The same sum of money invested for the same number of years at 4% p.a. simple interest grows to Rs.120 only. For how many years was the sum invested?
(A) 25years
(B) 15years
(C) 20years
(D) 22years
(E) None of these
Rationale: Explanation:
From the information provided we know that,
Principal + 8% p.a. interest on principal for n years = 180 …….. (1)
Principal + 4% p.a. interest on principal for n years = 120 ……… (2)
Subtracting equation (2) from equation (1), we get
4% p.a. interest on principal for n years = Rs.60.
Now, we can substitute this value in equation (2),
i.e Principal + 60 = 120
= Principal = Rs.60.
We know that SI = , where p is the principal, n the number of years and r the rate percent of interest.
In equation (2), p = Rs.60, r = 4% p.a. and the simple interest = Rs.60.
Therefore, 60 =(60*n*4)/100
=> n = 100/4 = 25 years.
Answer: A
Answer: (A) 25years
Question: WHEN A PERSON SELLS TWO ITEMS $1150 each, ONE AT A GAIN OF 20% AND OTHER AT A LOSS OF 20%.THEN THE SELLER INCURES A LOSS OR GAIN OF:
(A) 2% gain
(B) no loss no gain
(C) 4% loss
(D) 1% loss
(E) 5% gain
Rationale: When two items are sold at the same price, one at a profit of a% and other at a loss of a% (which means the cost price of one item was lower than the selling price and the cost price of the other item was higher than the selling price), there will always be a loss of (a^2)/100 %. e.g. Here a = 20, so loss % = (20)^2/100 % = 4%.
Answer : C
Answer: (C) 4% loss
Question: Units digit of 7^5^6^13?
(A) 7
(B) 8
(C) 9
(D) 1
(E) 11
Rationale: (7^5) unit digit is 7
7^6 unit digit is 9
9^13 unit digit 9
hence unit digit is 9.
ANSWER:B
Answer: (B) 8
Question: Two trains of length 120 m and 280 m are running towards each other on parallel lines at 42 kmph and 30 kmph respectively. In what time will they be clear of each other from the moment they meet?
(A) 12
(B) 67
(C) 26
(D) 20
(E) 23
Rationale: Relative speed = (42 + 30) * 5/18 = 4 * 5 = 20 mps.
Distance covered in passing each other = 120 + 280 = 400 m.
The time required = d/s = 400/20 = 20 sec.
Answer:D
Answer: (D) 20
Question: E and F work at a hospital with 4 other workers. For an internal review, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that E and F will both be chosen?
(A) A)1/3
(B) B)1/4
(C) C)1/15
(D) D)3/8
(E) E)2/3
Rationale: Total number of people = 6
Probability of selecting E first and then F is 1/6∗1/5=1/30
Probability of selecting F first and then E is 1/6∗1/5=1/30
Therefore probability of selecting E and F for the review is 1/30+1/30=1/15
Answer is C
Answer: (C) C)1/15
Question: If the sides of a triangle are 78 cm, 72 cm and 30 cm, what is its area?
(A) 1030 cm^2
(B) 1380 cm^2
(C) 105 cm^2
(D) 1000 cm^2
(E) 1080 cm^2
Rationale: The triangle with sides 78 cm, 72 cm and 30 cm is right angled, where the hypotenuse is 78 cm.
Area of the triangle
= 1/2 * 72 * 30
= 1080 cm^2
Answer: E
Answer: (E) 1080 cm^2
Question: The labeled price of a table is Rs. 8,500. The shopkeeper sold it by giving 5% discount on the labeled price and earned a profit of 15%. What approximately is the cost price of the table?
(A) Rs. 5758
(B) Rs. 6195
(C) Rs. 6425
(D) Rs. 7021
(E) None of these
Rationale: Explanation:
Labeled price = Rs. 8,500
By giving 5% discount on labeled price, the selling price is
= 95 / 100 * 8500 = Rs. 8075
By earning 15% profit on the selling of price Rs. 8075 the cost price is
= 100 / 115 * 8075 = Rs. 7021.74
Therefore, approximate cost is 7021.74
ANSWER D
Answer: (D) Rs. 7021
Question: Two trains travelling in the same direction at 30 and 22 kmph completely pass off another in 1 minute. If the length of the first train is 125 m, what is the length of the second train?
(A) 7.33 m
(B) 8.33 m
(C) 25.63 m
(D) 28.33 m
(E) 8.93 m
Rationale: RS = 30 – 22 = 8 * 5/18 = 2.22 mps
T = 60 sec
D = 2.22 * 60 = 133.33 m
125
--------
8.33 m
ANSWER:B
Answer: (B) 8.33 m
Question: Find the odd man out. 2, 5, 10, 17, 26, 38, 50, 65
(A) 50
(B) 38
(C) 26
(D) 65
(E) 75
Rationale: Explanation :
The pattern is (1×1)+1 , (2×2)+1 , (3×3)+1 , (4×4)+1 , (5×5)+1 , (6×6)+1 , (7×7)+1 , (8×8)+1
Hence, in place of 38, the right number was (6×6)+1 = 37. Answer : Option B
Answer: (B) 38
Question: A batsman scored 110 runs which included 3 boundaries and 8 sixes. What percent of his total score did he make by running between the wickets?
(A) 45(4/11) %
(B) 45 %
(C) 45(5/11) %
(D) 44(5/11) %
(E) None of these
Rationale: Explanation :
Total runs scored = 110
Total runs scored from boundaries and sixes = 3 x 4 + 8 x 6 = 60
Total runs scored by running between the wickets = 110 - 60 = 50
Required % = (50/110) × 100 = 500/11 = 45(5/11)%
Answer : Option C
Answer: (C) 45(5/11) %
Question: (x —1)(x + 3) > 0
(x +5)(x—4) < 0
Which of the following values of x satisfy both inequalities shown?
I. -6
II. -4
III. 5
IV. 2
(A) I and II only
(B) I and III only
(C) II and III only
(D) II and IV only
(E) I, II, III, and IV
Rationale: (x - 1)(x + 3) > 0 --> x<-3 or x>1.
(x + 5)(x - 4) < 0 --> -5<x<4.
Among choices only -4 and 2 satisfy both inequalities.
Answer: D.
Answer: (D) II and IV only
Question: A salesperson receives a base salary of $1000 per month and a commission of 7.5% of the selling price of each item sold above the first 50 item. If this month she sold 530 items for $150 each, what will her monthly salary be?
(A) $1,500
(B) $1,800
(C) $6,400
(D) $2,500
(E) $2,800
Rationale: Ans : 1000+ 7.5 % * 150 * (530-50) = $ 6400
ANSWER:C
Answer: (C) $6,400
Question: In a day hands of clock will be together
(A) 12 times
(B) 24 times
(C) 20 times
(D) 22 times
(E) 25 times
Rationale: 22 times {The hands of a clock coincide 11 times in every 12 hours (Since between 11 and 1, they coincide only once, i.e., at 12 o'clock) Therefore in a day , It coincides 22 times }
ANSWER:D
Answer: (D) 22 times
Question: Three people of different age groups are to be seated on a bench. How many different sitting arrangements are possible if oldest must always sit next to youngest ?
(A) 2
(B) 4
(C) 6
(D) 8
(E) 10
Rationale: Consider O and Y one. But, in this arrangement they can sit in two different combinations.
O first and Y second or Y first and O second.
Total we have (O and Y) and third person= 2 arrangements to do.
Total arrangements= 2*2= 4
B is the answer
Answer: (B) 4
Question: During the last four years, a large truck company purchased diesel at rates of $1.2, $1.4, $1.6 and $2.1 per gallon. What was the mean cost of diesel over the four-year period if the company spends the same amount of dollars on diesel each year?
(A) $2.5
(B) $2.55
(C) $1.51
(D) $3.25
(E) $3.0
Rationale: finding the Harmonic mean here.
HM = 4/(1/12 + 1/14 + 1/16 + 1/21) = 15.1
C
Answer: (C) $1.51
Question: A man is 26 years older than his son. In two years, his age will be twice the age of his son. The present age of the son is?
(A) 11
(B) 25
(C) 24
(D) 22
(E) 91
Rationale: Let the son's present age be x years.
Then, man's present age = (x + 26) years.
(x + 26) + 2 = 2(x + 2) x + 28 = 2x + 4 => x = 24.
Answer: C
Answer: (C) 24