16. If x and y are integers and xy^2 is a positive odd integer, which of the following must be true?
1. xy is positive
2. xy is odd.
3. x + y is even.
(A) 1 only
(B) 2 only
(C) 3 only
(D) 1 and 2
(E) 2 and 3
17. The dimensions of a rectangular box is (l*b*h) 20 in * 8 in * 2 in.That is to be completely wrapped with paper. If a single sheet of paper is to be used without patching, then the dimensions of the paper could be
(A) 17 in by 25 in
(B) 21 in by 24 in
(C) 24 in by 12 in
(D) 24 in by 14 in
(E) 26 in by 14 in
19. If M and N are positive integers that have remainders of 1 and 3, respectively, when divided by 6, which of the following could NOT be a possible value of M+N?
(A) 86
(B) 52
(C) 34
(D) 28
(E) 10
wat is d soln
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Q. 16 - if the squared value is postiive and odd, it means:
1) XY (product of x and y) is odd
a) that means that X and Y are also odd (as the product of 2
odd number is odd, else its even, if one of the numbers is
even)
b) if both X and Y are odd their sum is even
2) XY (product of A and y) could be +ve or -ve, as the square of a value is always positive, we cannot be sure if the product was -ve or +ve.
From the above, Option "e" will be a fit
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q. 17 Without going too much into the calculations, only option B has both dimensions as more than 20. If we are wrapping on the smaller sides, we will need atleast, 8+2+8+2 = 20 or more and the other side is already 20, so this alone gives us sufficient information that option "b" will be a fit.
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Q. 18 - When divied by the same number, the sum of 2 numbers will give the remainder which will be equal to the sum of individual remainders. Based on this, any of the answer choises when divided by 6 doesnt leave a remainder of 4 is the answer to this question. In the case of this question, option A - 86, leaves a remainder of 2 and all others leave 4 as remainder.
So option "a" will be a fit.
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1) XY (product of x and y) is odd
a) that means that X and Y are also odd (as the product of 2
odd number is odd, else its even, if one of the numbers is
even)
b) if both X and Y are odd their sum is even
2) XY (product of A and y) could be +ve or -ve, as the square of a value is always positive, we cannot be sure if the product was -ve or +ve.
From the above, Option "e" will be a fit
-----------------------------------------------
q. 17 Without going too much into the calculations, only option B has both dimensions as more than 20. If we are wrapping on the smaller sides, we will need atleast, 8+2+8+2 = 20 or more and the other side is already 20, so this alone gives us sufficient information that option "b" will be a fit.
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Q. 18 - When divied by the same number, the sum of 2 numbers will give the remainder which will be equal to the sum of individual remainders. Based on this, any of the answer choises when divided by 6 doesnt leave a remainder of 4 is the answer to this question. In the case of this question, option A - 86, leaves a remainder of 2 and all others leave 4 as remainder.
So option "a" will be a fit.
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pls help in solvin dis ...
7. A certain elevator has a safe weight limit of 2,000 pounds. What is the greatest possible number of people who can safely ride on the elevator at one time with the average (arithmetic mean) weight of half the riders being 180 pounds and the average weight of the others being 215 pounds?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
7. A certain elevator has a safe weight limit of 2,000 pounds. What is the greatest possible number of people who can safely ride on the elevator at one time with the average (arithmetic mean) weight of half the riders being 180 pounds and the average weight of the others being 215 pounds?
(A) 7
(B) 8
(C) 9
(D) 10
(E) 11
Is the answer D by any chance ?
Its given that avg weight of half the riders = 180 and the other half = 215.
Which means that if 'x' stands for half the np of riders then
180x + 215x < 2000.We have to find the max no.of people that can ride with the weight as close as possible to 2000.
Plugging in and checking each answer will lead to 'D'.
Its given that avg weight of half the riders = 180 and the other half = 215.
Which means that if 'x' stands for half the np of riders then
180x + 215x < 2000.We have to find the max no.of people that can ride with the weight as close as possible to 2000.
Plugging in and checking each answer will lead to 'D'.
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For 19, the answer should be E.
Let M = 7 and N = 9
9 + 7 = 16, so it cannot be 10.
Let M = 7 and N = 9
9 + 7 = 16, so it cannot be 10.