MU-NLPC/Calc-aqua_rat huggingface dataset:
List of salaries of 8 employees are listed below. What is the median salary? $40,000, $29,000, $35,500, $31,000, $43,000, $30,000, $27,000, $32,000	Choose the correct choice from the following options: A) $28,000 B) $29,500 C) $30,500 D) $30,000 E) $31,500

Solution: Ordering the data from least to greatest, we get:   $27,000, $29,000, $30,000, $31,000, $32,000, $35,500, $40,000, $43,000   Since there is an even number of items in the data set, we compute the median by taking the mean of the two middlemost numbers.   $31,000 + $32,000 = $63,000   The median salary is $31,500.   $31,500
Answer: E
If f(x) = 1 - x if x > 0
= 1/(1 - x) if x≤≤0. Choose one:  A) 1102  B) 2767  C) 2667  D) 1998  E) 1122

Solution: Let x≤≤0   f(x) = 11−x11−x   f(f(x)) = 1 - 11−x11−x (1102s 11−x11−x x≥0x≥0   = −x1−x−x1−x (Observe −x1−x−x1−x is Positive for x is negitive)   f3(x)f3(x) = 1−−x1−x=1−x−(−x)1−x=11−x1−−x1−x=1−x−(−x)1−x=11−x   So f1(x)=f3(x)=f5(x)=.....f101(x)f1(x)=f3(x)=f5(x)=.....f101(x)   f101(x)=f1(x)=11−x=11−(−101)=1102   1102nswer:1102
Answer: A
The sum of first 45 natural numbers is?  Choose one.
A) 1030	B) 1034	C) 1035	D) 1037	E) 1040

Solution: Let Sn =(1 + 2 + 3 + ... + 45). This is an A.P. in which a =1, d =1, n = 45.   Sn =	n	[2a + (n - 1)d]	=	45	x [2 x 1 + (45 - 1) x 1]	= 45	x 46 = (45 x 23)   2	2	2   = 45 x (20 + 3)   = 45 x 20 + 45 x 3   = 900 + 135= 
900 + 135 = 1_035
1035.   1035)
Answer: C
A shipment of 250 smartphones contains 84 that are defective. If a customer buys two smartphones at random from the shipment, what is the approximate probability that both phones are defective?
A.
B.
C.
D.
E.	Pick: A) 1/250 B) 1/84 C) 1/11 D) 1/9 E) 1/3

Solution: Probability of choosing one defective phone from a lot of 250 which ontains 84 defective phones is = (84/250)   Probability of choosing one defective phone from a lot of 249(we already picked one) which ontains 83(we already picked one) defective phones is = (83/249)   Combined probability of series of events = product of the probabilities = (84/250)*(83/249)   84/250 is close to (1/3) and (83/249)= (1/3)   so answer is (1/3)*(1/3) = (1/9)   ANSWER:1/9
Answer: D
In a mixture of 45 litres, the ratio of acid to base is 3 : 2. How much base must be added to make the ratio 9: 11? Pick:
A) 10 lts
B) 15 lts
C) 17 lts
D) 20 lts
E) 22 lts

Solution: Let M = 3K,W = 2K   Thus, 3K + 2K = 45   => K=9   => acid = 27 litres and base = 18 litres.   Now suppose x litres of base is added to the mixture such that   27/(18 + X) = 9/11   =>162 +9X = 297   => 9X = 135   => X = 15   ANSWER:15 lts
Answer: B
The bankers discount and the true discount of a sum at 10% per annum simple interest for the same time are Rs.100 and Rs.80 respectively. What is the sum and the time?  Choose the correct choice from the following answers:
A) Sum = Rs.400 and Time = 5 years
B) Sum = Rs.200 and Time = 2.5 years
C) Sum = Rs.400 and Time = 2.5 years
D) Sum = Rs.200 and Time = 5 years
E) None of these

Solution: Explanation :   BD = Rs.100   TD = Rs.80   R = 10%   F = BD ×TD/(BD – TD)=100×80/(100–80)=100×80/20=Rs. 400   BD = Simple Interest on the face value of the bill for unexpired time =FTR/100   ⇒100 = (400×T×10)/100   ⇒100 = 4 × T × 10 ⇒10 = 4 × T   ⇒ T = 10/4= 
10/4 = 5/2 = around 2.5
2.5 years Answer : Option Sum= Rs.400 and Time = 2.5 years
Answer: C
There are two sets A and B. The range of set A is 7, and the range of set B is 13. If the two sets are combined and get a new set Q, which cannot be the range of the set Q?  Choices:
A) 8
B) B.11
C) C.14
D) D.17
E) E.21

Solution: Let Set A has 1,8 as elements   B has 1,14 as elements.. So Range for Combined set Q becomes  14-1= 
 14-1 = 13
13   For range to be 14,   A= 1,8   B= 2,15 (Range=14)   For range to be 17   A=1,8   B= 5,18   For range to be 21:   A=1,8   B= 9 ,22   So we are left with A and B.   Now consider A has elements A= -1,-8 and Thus Range =-1-(-8)= 
-1-(-8) = 7
7   So for Range of combined set to be 11, B needs to have largest elementxso that x- (-8)=11 or x=3...But if x=3, the largest element in Combined Set then smallest element in the combined set will be 3-y=13 or y=-10....And the range of combined set 3-(-10)=13...   Consider Option A   A=-1,-8   B= y,x where y and x are smallest and largest element in Set B   Elements of Combined Set: -8,-1,y and x   Now x-(-8)= 
-(-8) = 8
8 or x=0, then x-y=13 or y=-13...   Range of Combined Set: 0-(-13)= 13...   I don't see how range can be 8 or 11...Can you please post the source and explanation for the OA in spoiler...=B.11
Answer: B
Bob is attempting to feed his pets. He feeds his pets as follows:
- No dog receives more food than any other dog
- No cat receives any less food than any other cat
- The cats, as a group, receive exactly as much food as a single dog
If Bob has seven dogs and four cats, approximately what percentage of the food bag does a cat receive?	Answers:	A) 25.0%	B) 8.3%	C) 3.1%	D) 2.7%	E) 1.0%

Solution: C. Each cat gets 1/4 as much food as a dog. A dog gets 1/8 of the food. 1/4 of 1/8 is 1/32, which is about 3.1%, so the answer is 3.1%.
Answer: C
If a person walks at 12 km/hr instead of 10 km/hr, he would have walked 20 km more. The actual distance traveled by him is:	Pick
A) 50 km B) 100 km C) 60 km D) 70 km E) 80 km

Solution: Let the actual distance travelled be x km.   x/10 = (x+20)/12   12x = 10x + 200   2x = 200   x = 100 km.   answer :100 km
Answer: B
Solve for x: 2x â€“ y = (3/4)x + 7.
Select:
A) (y + 6)/5
B) 4(y + 7)/5
C) (y + 6)
D) 4(y - 6)/5
E) 5/4(y-6)

Solution: Solution:   2x â€“ y = (3/4)x + 7.   or, 2x - (3/4)x = y + 7.   or, (8x -3x)/4 = y + 7.   or, 5x/4 = y + 7.   or, 5x = 4(y + 7).   or, 5x = 4y + 28.   or, x = (4y + 28)/5.   Therefore, x = 4(y + 7)/5.   correct answer 4(y + 7)/5
Answer: B
When positive integer R is divided by 6 the remainder is 3. Which of the following CANNOT be an even integer?	Choose the correct option:
A) a. k + 1
B) b. k -11
C) c. 4k + 2
D) d. (k-3)/3 +2
E) e. R/3

Solution: When positive integer R is divided by 6 the remainder is 3   So, R could equal 3, 9, 15, 21, etc   let's TEST R =3   a.3+ 1 = 4 (EVEN)   b.3-11 = -8 (EVEN)   c. 4(3) + 2 = 14 (EVEN)   d. (3-3)/3 +2 = 2 (EVEN)   At this point, we can already see the answer must be E.   Let's check e. R/3 forfun   e.3/3 = 1 (ODD)   Great!   Answer: e. R/3
Answer: E
A hemispherical bowl is made of 0.5 cm thick steel. Inner radius of the bowl is 4 cm. The volume of steel used in making the bowl is
Options.
A) 55.83 cm3 B) 56.83 cm3 C) 113.67 cm3 D) 58.83 cm3 E) None of these

Solution: inner r= 4   outer R=4.5   formula= 2/3*22/7(R^2-r^2)   (2/3) * (22/7) *(4.5*4.5*4.5 - 4*4*4)   =56.83   ANSWER:56.83 cm3
Answer: B
7 people average age is 30. youngest person age is 4. find average of the people when youngest was born.	Choose one:	A) 23	B) 24	C) 25	D) 26	E) 27

Solution: average age of people =30   so have total age =210   before 7 years we have to deduct each person age by seven years 210-32=182   so average age would be 182/7= 
182/7 = 26
26   ANSWER:26
Answer: D
A tradesman by means of his false balance defrauds to the extent of 20%? in buying goods as well as by selling the goods. What percent does he gain on his outlay? Choose the correct choice from the following answers.
A) 13% B) 14% C) 44% D) 66% E) 77%

Solution: g% = 20 + 20 + (20*20)/100= 
20 + 20 + (20*20)/100 = 44
44%   Answer: 44%
Answer: C
Who come next in the series ?
JAZ, LEX, NIV, POT	Choose the correct choice from the following choices:
A) RUR
B) QUR
C) RUS
D) SUR
E) PUR

Solution: 1st letter increases by 2   J+2=L, L+2=N,N+2=P, P+2=R   2nd letter increases by 4 for 1st 2 words, nd inc by 6 for next 2 words   RUR+4=E, E+4=I,I+6=O, O+6=U   3rd letter decreases by 2   Z-2=X, X-2=V, V-2=T, T-2=R   So the next word is RUR   RURNSWER:RUR
Answer: A
A ball is bought for Rs.400 and sold at a gain of 25% find its selling price?
Select:
A) A)Rs.480/-	B) B)Rs.490/-	C) C)Rs.500/-	D) D)Rs.520/-	E) E)Rs.540/-

Solution: 100 % ------> 400 (100 * 4 = 400)   125 % ------> 500 (125 * 4 = 500)   Selling price = Rs.500/-   Rs.500/-
Answer: C
A no. leaves a remainder 3 on division by 14, and leaves a remainder k on division by 35. How many possiblevalues can k take?	Pick
A) 3
B) 5
C) 8
D) 9
E) 10

Solution: A number leaves a remainder of 3 on division by 14, or it can be written as 14n + 3   On division by 70, the possible remainders can be 3, 17 (3 + 14), 31 (3 + 28), 45 (3 + 42), or 59 (3 + 56). The number can be of the form   70n + 3   70n + 17   70n + 31   70n + 45   70n + 59   Now, we need to divide this number by 35   70n + 3 divided by 35, the remainder will be 3.   70n + 17 divided by 35, the remainder will be 17.   70n + 31 divided by 35, the remainder will be 31.   70n + 45 divided by 35, the remainder will be 10.   70n + 59 divided by 35, the remainder will be 24.   On division by 35, the possible remainders are 3, 17, 31, 10 or 24. There are 5 possible remainders   Correct Answer: 5   5
Answer: B
When sold at a 60% discount, a sweater nets the merchant a 35% profit on the wholesale cost at which he initially purchased the item. By what % is the sweater marked up from wholesale at its normal retail price?	Choose the correct choice:	A) 20%	B) 40%	C) 50%	D) 70.38%	E) 100%

Solution: we should be careful about what are we measuring % on/what is the base..   let the Marked up price =100..   Selling price= 100-60%of 100=40..   profit= 35%..   therefore the wholesale purchase cost= x.... 1.35x=40   or x=29.62...   marked price was 100 so ...   so answer is 70.38%..   70.38%
Answer: D
The total age of A and B is 16 years more than the total age of B and C. C is how many years younger than A?	Choose one
A) 16 B) 24 C) C is elder than A D) Data inadequate E) None

Solution: Solution   [(A+B) - (B+C)]	= 16   â€¹=â€ºA - C   = 16.   16nswer 16
Answer: A
Find the number of ways of arranging the letters of the word "MATERIAL" such that all the vowels in the word are to come together?  Options.
A) 1448 B) 1440 C) 1478 D) 1477 E) 1432

Solution: In the word, "MATERIAL" there are three vowels A, I, E.   If all the vowels are together, the arrangement is MTRL'AAEI'.   Consider AAEI as one unit. The arrangement is as follows.   M T R L A A E I   The above 5 items can be arranged in 5! ways and AAEI can be arranged among themselves in 4!/2! ways.   Number of required ways of arranging the above letters = 5! * 4!/2!   = (120 * 24)/2= 
(120 * 24)/2 = 1_440
1440 ways.   Answer: 1440
Answer: B
Which of the numbers below is the odd one out
2,6,15,31,56,59,92.	Choices.
A) 6	B) 31	C) 56	D) 92	E) 59

Solution: 59 is the odd man.. diff between successive no.s is a perfect square   ANSW59R:59
Answer: E
a+b=4,ab=3,find the sum of receiprocals of a and b  Select:
A) 4/3
B) 3/4
C) 5/3
D) 3/5
E) 1/5

Solution: 1/a+1/b=a+b/ab,   so 1/a+1/b=a+b/ab   =4/3   4/3NSWER:4/3
Answer: A
An oil cylinder was 3/4th full. When THREE bottles of oil is poured into it, it is 4/5th full. How many bottles of oil
can the full cylinder hold?  Choose the correct answer:
A) 60
B) 15
C) 40
D) 30
E) 35

Solution: (4/5 -3/4) cylinder is filled by 3 bottles     0.8 -0.75= 
  0.8 -0.75 = 0.05
0.05 cylinder is filled by 3 bottles   1 cylinder is filled by   3/0.05= 
  3/0.05 = 60
60 bottles   60NSWER:60
Answer: A
A wooden box of dimensions 8 m x 7 m x 6 m is to carry rectangularboxes of dimensions 8 cm x 7 cm x 6 cm. The maximum number ofboxes that can be carried in the wooden box, is
Options
A) 9800000  B) 1000000  C) 7500000  D) 1200000  E) None of these

Solution: Explanation: Number = (800*700*600)/8*7*6 = 1000000 Answer: 1000000
Answer: B
Due to construction, the speed limit along an 9-mile section of highway is reduced from 55 miles per hour to 35 miles per hour. Approximately how many minutes more will it take to travel along this section of highway at the new speed limit than it would have taken at the old speed limit ? Choose the correct choice.
A) 5
B) 7
C) 10
D) 15
E) 24

Solution: 9/35 - 9/55 = 9/5 * ( 11 - 7)/77   = 9/5 * 4/77 * 60 min   = 9 * 12 * 4/77   = 432/77 ~ 5.6   Answer - 7
Answer: B
The largest number of four digits exactly divisible by 77 is	Select the correct option:
A) 9768
B) 9933
C) 9988
D) 9944
E) 9955

Solution: Explanation: Find the remainder when 10000 is divided by 77. Then subtract that remainder from 10000.   77) 10000 (12   77   230   154   760   693   67   So 10000 â€“ 67 = 9933 is exactly divisible by 77.   ANSWER IS 9933
Answer: B
There are 280 doctors and nurses at a hospital. If the ratio of doctors to nurses is 5 to 9, how many nurses are at the hospital?  Choose the correct choice from the following answers:
A) 165 B) 170 C) 175 D) 180 E) 185

Solution: The number of nurses at the hospital is (9/14)*280= 
(9/14)*280 = 180
180.   The answer is 180.
Answer: D
Riya and Priya set on a journey. Riya moves eastward at a speed of 24kmph and Priya moves westward at a speed of 35 kmph.How far will be priya from Riya after 45 minutes	Choose the correct choice from the following answers:
A) 25kms B) 10kms C) 50kms D) 30kms E) 44kms

Solution: total eastward distance= 24kmph*3/4hr=18 km   total westward distance= 35kmph*3/4hr=26 km   total distn betn them= 18+26= 
18+26 = 44
44km   ans 44km   ANSW44kmsR:44kms
Answer: E
At the end of the day, February 14th, a florist had 150 roses left in his shop, all of which were red, white or pink in color and either long or short-stemmed. A third of the roses were short-stemmed, 20 of which were white and 15 of which were pink. The percentage of pink roses that were short-stemmed equaled the percentage of red roses that were short-stemmed. If none of the long-stemmed roses were white, what percentage of the long-stemmed roses were red? Choose one:
A) 50%	B) 25%	C) 250%	D) 75%	E) 80%

Solution: R + W + P = 150   S + L = 150   1/3 * 150= 
1/3 * 150 = 50
50   Short-Stemmed White= 20   Short-Stemmed Pink = 15   => Short-Stemmed Red =15   15/P = 15/R   => R = P   So Total Long Stemmed = 100   50%nd Long Stemmed Red + Long Stemmed Pink = 100   So Long Stemmed Red/Long Stemmed = ?   Total White = 20 (50%s no Long stemmed white)   => R + R + 20 = 150   => R = 130 and R = 65   Long Stemmed R = 65 - 15= 
65 - 15 = 50
50   So Long Stemmed Red/R= 50/100 = 50%   50%nswer - 50%
Answer: A
The price of 2 saris and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ? Choose the correct option.
A) Rs. 2400
B) Rs. 2490
C) Rs. 2500
D) Rs. 2550
E) Rs. 2600

Solution: Let the price of a saree and a shirt be Rs. x and Rs. y respectively.   Then, 2x + 4y = 1600 .... (i)   and x + 6y = 1600 .... (ii)   Divide equation (i) by 2, we get the below equation.   => x + 2y = 800. --- (iii)   Now subtract (iii) from (ii)   x + 6y = 1600 (-)   x + 2y = 800   ----------------   4y = 800   ----------------   Therefore, y = 200.   Now apply value of y in (iii)   => x + 2 x 200 = 800   => x + 400 = 800   Therefore x = 400   Solving (i) and (ii) we get x = 400, y = 200.   Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.   Rs. 2400
Answer: A
One pipe can fill a tank three times as fast as another pipe. If together the two pipes can fill the tank in 36 minutes, then the slower pipe alone will be able to fill the tank in Choose the most appropriate option:	A) 144 mins	B) 140 mins	C) 136 mins	D) 132 minw	E) None of these

Solution: Explanation:   Let the slower pipe alone fill the tank in x minutes   then faster will fill in x/3 minutes.   Part filled by slower pipe in 1 minute = 1/x   Part filled by faster pipe in 1 minute = 3/x   Part filled by both in 1 minute =   1/x+3/x=1/36   =>4/x=1/36   x=36∗4=144mins   Option 144 mins
Answer: A
7 points are marked on a straight line and another 6 points are marked on a second straight line with no points in common. How many triangles can be constructed with vertices from among the above points? Choices.
A) 281  B) 91  C) 168  D) 196  E) 364

Solution: Solution: select 2 from 7 and one from 6 + select 2 from 6 and 1 from 7   7C2*6C1 + 6C2*7C1   = 281   281nswer : 281
Answer: A
40 men shake hands with each other. Maximum no of handshakes without cyclic handshakes.
Choose the correct option.
A) 780 B) 200 C) 210 D) 220 E) 230

Solution: or, if there are n persons then no. of shakehands = nC2 = 40C2 = 780   780NSWER:780
Answer: A
Find the C.I. on a sum of Rs.10000 for 6 months at 20% per annum, interest being compounded halfyearly?
Select the correct option:
A) 3010 B) 2010 C) 1000 D) 3100 E) 2100

Solution: 1000.I.= 10000(11/10)^1-10000   = 1000   Answer: 1000
Answer: C
A music store has 90 different CD's. If an average price is $12 per CD and 20 of the most expensive ones are $20 each, what is the average price of the remaining CD's?  Choose the correct choice from the following answers.
A) 8.33  B) 8.75  C) 9.23  D) 9.71  E) 10.07

Solution: The sum of the prices of all CD's is (90 * $12 = $1,080).   The sum of the prices of the most expensive CD's is $400. So, ($1,080 - $400 = $680) is left for 70 remaining CD's. Thus the average price is (frac{$680}{70} = $9.71)
Answer: D
While camping, 3 people are to be seated around a stool. two seating arrangement are considered different only when the position of the people are different relative to each other. what is the total number of possible seating arrangement for the group?	Choose the correct choice from the following answers:	A) a.2	B) b.10	C) c.8	D) d.32	E) e.600

Solution: for 3 people seating arrangement around a circular stool = (3-1)= 
(3-1) = 2
2!= 2*1= 
2*1 = 2
2   Oa.2 is a.2
Answer: A
In what time will a railway train 40 m long moving at the rate of 36 kmph pass a telegraph post on its way? Choose the correct choice from the following answers.
A) 5 sec	B) 4 sec	C) 3 sec	D) 6 sec	E) 1 sec

Solution: T = 40/36 * 18/5= 
40/36 * 18/5 = 4
4 sec   Answer: 4 sec
Answer: B
The speeds of 3 trains in the ratio 2:6:16 The ratio between time taken by them to travel the same distance is?	Options: A) 6:4:3 B) 1:2:3 C) 24:8:3 D) 26:5:2 E) 24:8:7

Solution: Ratio of time taken is = 1/2 : 1/6 : 1/16 = 24:8:3   Answer is 24:8:3
Answer: C
Crazy Eddie has a key chain factory. Eddie managed to decrease the cost of manufacturing his key chains while keeping the same selling price, and thus increased the profit from the sale of each key chain from 20% of the selling price to 50% of the selling price. If the manufacturing cost is now $50, what was it before the decrease?
Choose the correct answer
A) $20 B) $40 C) $50 D) $80 E) $100

Solution: cost+profit=income (selling price)   profit now = 0.5x or x-50   0.5x=x-50   50=0.5x   x=100$ is selling price   so, profit before was  0.2*100= 
 0.2*100 = 20
20$   cost=100-20= 
100-20 = 80
80$   ANSWER:$80
Answer: D
On increasing the number of lines in a page by 80, they become 240. What is the % of increase in the no. of lines in the page? Choose one
A) 30%
B) 40%
C) 50%
D) 70%
E) 80%

Solution: Explanation : Number of pages increased = 80   Now , the number of pages of book = 240   Number of pages of the books before increase = 240 – 80 = 160   % increase in the number of pages in the book = 80 160   x 100% = 50%   50%
Answer: C
A customer asks the clerk for a paintbrush and a bucket of whitewash for a total price of B dollars. If the paintbrush costs 100 cents less than twice the price of a bucket of whitewash, what is the price of half a bucket of whitewash in dollars?  Select
A) (B + 200)/2.  B) (B + 2)/6.  C) (2B + 200)/3.  D) (B + 2)/3.  E) (B - 2)/6.

Solution: P = 2w - 200   thus total price in cents as given should be   2w-200 +w = 100B   3w - 200 = 100 B   3w = 100 B+200   3w =b+2 (in dollars)   w/2 = (b+2)/6   (B + 200)/2.ns:(B + 200)/2.
Answer: A
The compound ratio of 2/3, 6/7, 1/3 and 1/8 is given by?
Choose the correct option.
A) 1/49  B) 1/42  C) 1/09  D) 1/77  E) 1/12

Solution: 2/3 * 6/7 * 1/3 * 1/8   = 1/42   Answer: 1/42
Answer: B
Eight people are planning to share equally the cost of a rental car. If one person withdraws from the arrangement and the others share equally the entire cost of the car, then the share of each of the remaining persons increased by:
Choose the correct choice from the following answers:	A) 1/7	B) 2/7	C) 3/7	D) 4/7	E) None of them

Solution: Original share of 1 person = 1/8   New share of 1 person = 1/7   Increase = (1/7 - 1/8	= 1/56)   Therefore, Required fraction = (1/56)/(1/8)	= (1/56)x (8/1)	= 1/7   1/7nswer is 1/7.
Answer: A
A retailer bought a machine at a wholesale price of $90 and later on sold it after a 10% discount of the retail price. If the retailer made a profit equivalent to 20% of the whole price, what is the retail price r of the machine?
Choices
A) 81
B) 100
C) 120
D) 135
E) 160

Solution: Since the wholesale price was $90 and the profit was 20% of the wholesale price ([.2][90] = $18), the retail price would have to be above $108, but not that much greater than that.   Let's start by TESTing Answer C: $120....   If.....   Retail Price r= $120   10% discount off = $120 - (.1)(120) = 120 - 12= 
120 - 12 = 108
108   20% profit on wholesale price= 90 + (.2)(90) = 90 + 18= 
90 + 18 = 108
108   These two numbers MAT120H, so this MUST be the answer!   Final Answer:   [Reveal]Spoiler:   120
Answer: C
A certain Social Security recipient will receive an annual benefit of $12,000 provided he has annual earnings of $9,360 or less, but the benefit will be reduced by $1 for every $3 of annual earnings over $9,360. What amount of total annual earnings would result in a 60 percent reduction in the recipient's annual Social Security benefit? (Assume Social Security benefits are not counted as part of annual earnings.)
Choose one:
A) $15,360
B) $17,360
C) $18,000
D) $23,760
E) $27,360

Solution: For every $3 earn above $9360, the recipient loses $1 of benefit.   OR   For every $1 loss in the benefit, the recipient earns $3 above $9360   If earning is; 9360+3x   Benefit = 12000-x   Or the vice versa   If benefit is 12000-x, the earning becomes 9360+3x   He lost 50% of the benefit;   Benefit Received= 12000-0.6*12000 = 12000-7200= 
12000-7200 = 4_800
4800   Earning becomes 9360+3x=9360+3*4800= 
9360+3*4800 = 23_760
23760   Ans:$23,760
Answer: D
If x^5y^4z^2 <0 , which of the following must be true?
I. xy <0
II. yz <0
III. xz <0 Choose the correct option:	A) I	B) II	C) III	D) I and II	E) None

Solution: Ans:- x^5y^4z^2 <0   x must be negative. x<0 ; y and z can be either negative or positive as even powers is always positive.   I. xy <0 :- x<0 but y can be - or + hence xy < 0 when y>0 or xy >0 when y <0. So not always true.   II. yz <0 :- As both y and z can be + or - ; yz < 0 or yz >0 are possible   II. xz <0 :- x<0 but z can be - or + hence xz < 0 when z>0 or xz >0 when z <0. So not always true.   Ans :- None
Answer: E
The smallest value of n, for which 2n+3 is not a prime number, is
Choose the correct choice:	A) 4,5	B) 3,4	C) 2,6	D) 5,6	E) 2,3

Solution: (2Ã—1 + 3) = 5.   (2Ã—2 + 3) = 7.   (2Ã—3 + 3) = 9.   (2Ã—4 + 3) = 15.   which is not prime , n=3,4.   ANSWER:3,4
Answer: B
The workforce of Company X is 60% female. The company hired 24 additional male workers, and as a result, the percent of female workers dropped to 55%.How many employees did the company have after hiring the additional male workers? Choose the correct choice from the following:  A) 160  B) 220  C) 288  D) 360  E) 420

Solution: Let's xx be total quantity of employees   0.6x=females before adding men   0.55(x+24)=females after adding men   as quantity of women doesn't change we can make an equation:   0.6x=0.55(x+24)   0.05x=13.2   x=264 - this is quantity of employees before adding 24 men   So after adding it will be 288   Answer is 288
Answer: C
On the number line, the number p is twice as many units from -2 as -2 is from 7. If p is less than –2, what is the value of p ?  Pick one
A) –20 B) –10 C) –6 D) 10 E) 14

Solution: Distance between -2 and 7 = 9   Since number p is twice as many units from -2 as -2 is from 7   , therefore p can be -20 Since , p is less than -2 ,   the value of p = -20   –20nswer –20
Answer: A