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It is given that xx and yy are integers such that   ∣x+3∣ < 7 and ∣y − 4∣ < 8. What is the difference of maximum and minimum value of x + xy + y ?
    Correct answer is '144'. Can you explain this answer?
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    It is given thatxxandyyare integers such that x+3 < 7and y − ...
    Let us look at the inequality
    |x+3| < 7 or -7 <  x + 3 < 7 or -10 < x < 4 ...(I)
    Similarly |y-4| < 8, -8 < y-4 < 8 or -4 < y < 12 $$ ...(II)
    Coming to the equation,
    x + xy  + y = x + xy + y + 1 − 1
    x+ xy +  y = (x + 1) (y + 1) -1
    The value will be max when both (x+1) and (y+1) are either positive or negative. for it to be minimum, one has to be positive and other has to be negative
    From (I) and (II) we can say that,
    -9 < x+1 < 5 and −3 <y + 1 < 13
    Therefore (x+1) = [-8,-7,-6,-5,......2,3,4] and (y+1) = [-2,-1,0,....11,12] as xx and yy are integers
    (x+1)(y+1) will have max value of 48 and min value -96
    (x+1)(y+1)-1  will have max value of 47 and min value -97
    Difference = 47-(-97) = 47+97 = 144
    This question is part of UPSC exam. View all CAT courses
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    It is given thatxxandyyare integers such that x+3 < 7and y − ...
    It seems like the question is incomplete. Can you please provide the full question or additional information?
    Community Answer
    It is given thatxxandyyare integers such that x+3 < 7and y − ...
    Let us look at the inequality
    |x+3| < 7 or -7 <  x + 3 < 7 or -10 < x < 4 ...(I)
    Similarly |y-4| < 8, -8 < y-4 < 8 or -4 < y < 12 $$ ...(II)
    Coming to the equation,
    x + xy  + y = x + xy + y + 1 − 1
    x+ xy +  y = (x + 1) (y + 1) -1
    The value will be max when both (x+1) and (y+1) are either positive or negative. for it to be minimum, one has to be positive and other has to be negative
    From (I) and (II) we can say that,
    -9 < x+1 < 5 and −3 <y + 1 < 13
    Therefore (x+1) = [-8,-7,-6,-5,......2,3,4] and (y+1) = [-2,-1,0,....11,12] as xx and yy are integers
    (x+1)(y+1) will have max value of 48 and min value -96
    (x+1)(y+1)-1  will have max value of 47 and min value -97
    Difference = 47-(-97) = 47+97 = 144
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    InstructionsComprehension:Three pouches (each represented by a filled circl e) are kept in each of the nine slots in a 3 × 3 grid, as shown in the figure. Every pouch has a certain number of one-rupee coins. The minimum and maximum amounts of money (in rupees) among the three pouches in each of the nine slots are given in the table. For example, we know that among the three pouches kept in the second column of the first row, the minimum amount in a pouch is Rs. 6 and the maximum amount is Rs. 8.There are nine pouches in any of the three columns, as well as in any of the three rows. It is known that the average amount of money (in rupees) kept in the nine pouches in any column or in any row is an integer. It is also known that the total amount of money kept in the three pouches in the first column of the third row is Rs. 4.Q.What is the number of slots for which the average amount (in rupees) of its three pouches is an integer? Correct answer is '2'. Can you explain this answer?

    Three pouches (each represented by a filled circl e) are kept in each of the nine slots in a 3 × 3 grid, as shown in the figure. Every pouch has a certain number of one-rupee coins. The minimum and maximum amounts of money (in rupees) among the three pouches in each of the nine slots are given in the table. For example, we know that among the three pouches kept in the second column of the first row, the minimum amount in a pouch is Rs. 6 and the maximum amount is Rs. 8.There are nine pouches in any of the three columns, as well as in any of the three rows. It is known that the average amount of money (in rupees) kept in the nine pouches in any column or in any row is an integer. It is also known that the total amount of money kept in the three pouches in the first column of the third row is Rs. 4.Q. What is the number of slots for which the average amount (in rupees) of its three pouches is an integer? Correct answer is '2'. Can you explain this answer?

    Three pouches (each represented by a filled circl e) are kept in each of the nine slots in a 3 × 3 grid, as shown in the figure. Every pouch has a certain number of one-rupee coins. The minimum and maximum amounts of money (in rupees) among the three pouches in each of the nine slots are given in the table. For example, we know that among the three pouches kept in the second column of the first row, the minimum amount in a pouch is Rs. 6 and the maximum amount is Rs. 8.There are nine pouches in any of the three columns, as well as in any of the three rows. It is known that the average amount of money (in rupees) kept in the nine pouches in any column or in any row is an integer. It is also known that the total amount of money kept in the three pouches in the first column of the third row is Rs. 4.Q. What is the number of slots for which the average amount (in rupees) of its three pouches is an integer? Correct answer is '2'. Can you explain this answer?

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    It is given thatxxandyyare integers such that x+3 < 7and y − 4 < 8. What is the difference of maximum and minimum value of x + xy + y?Correct answer is '144'. Can you explain this answer?
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    It is given thatxxandyyare integers such that x+3 < 7and y − 4 < 8. What is the difference of maximum and minimum value of x + xy + y?Correct answer is '144'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about It is given thatxxandyyare integers such that x+3 < 7and y − 4 < 8. What is the difference of maximum and minimum value of x + xy + y?Correct answer is '144'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for It is given thatxxandyyare integers such that x+3 < 7and y − 4 < 8. What is the difference of maximum and minimum value of x + xy + y?Correct answer is '144'. Can you explain this answer?.
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