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If a is positive integer, can a be expressed as the product of two int
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26 Dec 2016, 10:00
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If a is positive integer, can a be expressed as the product of two integers, each of which is greater than 1? (1) a is even. (2) 7 < a < 11
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If a is positive integer, can a be expressed as the product of two int
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Updated on: 27 Dec 2016, 00:51
i) since a is even  it can only be a +ve integer. if a = 2 = 2*1 but x,y have to be >1 therefore not A
ii) a is a +ve integer let a = 9 =3*3, but x,y have to be >1 (false) let a = 8 = 4*2 or 8*1 (false)
B
Originally posted by MG1788 on 26 Dec 2016, 22:12.
Last edited by MG1788 on 27 Dec 2016, 00:51, edited 2 times in total.



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Re: If a is positive integer, can a be expressed as the product of two int
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26 Dec 2016, 22:22
MG1788 wrote: i) since a is even  it can only be a +ve integer. if a = 2 = 2*1 but x,y have to be >1 therefore not A
ii) a can be a decimal or integer let a = 8.1 = 0.3*27 but x,y have to be >1 let a = 10.1 = 10.1*1 but x,y have to be >1 therefore not B
i) + ii) a = even and lies between 7 & 11 =? a = 8,10. these can be represented as x*y with x,y>1
I think itc C I agree till last line , but i think it is E a = 8 or 10 : 8 = 4 * 2 here both are >1 8 = 8*1 here one integer is equal to 1



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Re: If a is positive integer, can a be expressed as the product of two int
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27 Dec 2016, 00:05
Question: Is 'a' composite integer?
If 'a' is prime it cannot be expressed as a product of 2 integers, each of which is greater than 1.
St1: a is even > If a = 2 then a is prime and cannot be expressed as a product of 2 integers which are greater than 1. If a = 4 then 4 = 2*2 and can be expressed as product of 2 integers. Not Sufficient.
St2: a = 8, 9, 10 > a is not prime. a can be expressed as product of 2 integers which are greater than 1. Sufficient.
Answer: B



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If a is positive integer, can a be expressed as the product of two int
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27 Dec 2016, 07:55
IMO E
Given  a >0, a>integer asked can a = b*c with b,c>1 and b,c integers
1) since a is even Possible solutions (i) b=2, c=1 a=even a = 2*1 = 2 ( c not greater than 1 ) NO (ii) b=2, c=3 a=even a = 2*3 = 6  YES
2) a = { 8,9,10 } Possible Solutions (i) b = 5 c = 2 a= 5*2 = 10  YES ( B,C integers, >1 ) (ii) b= 5/2 c=4 a = 5/2 * 4 =10  NO ( B,C >1 but B is not an integer. But A still meets the criteria )
Therefore, Not A, not B
Combine (1) and (2) statements
Possible Solutions (i) b = 5 c = 2 a= 5*2 = 10  YES ( B,C integers, >1 ) (ii) b= 5/2 c=4 a = 5/2 * 4 =10  NO ( B,C >1 but B is not an integer)
A is even and a lies {8,9,10} But we still have YES and NO answers.
Hence E.



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Re: If a is positive integer, can a be expressed as the product of two int
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27 Dec 2016, 08:55
jojo1 wrote: IMO E
Given  a >0, a>integer asked can a = b*c with b,c>1 and b,c integers
1) since a is even Possible solutions (i) b=2, c=1 a=even a = 2*1 = 2 ( c not greater than 1 ) NO (ii) b=2, c=3 a=even a = 2*3 = 6  YES
2) a = { 8,9,10 } Possible Solutions (i) b = 5 c = 2 a= 5*2 = 10  YES ( B,C integers, >1 ) (ii) b= 5/2 c=4 a = 5/2 * 4 =10  NO ( B,C >1 but B is not an integer. But A still meets the criteria )
Therefore, Not A, not B
Combine (1) and (2) statements
Possible Solutions (i) b = 5 c = 2 a= 5*2 = 10  YES ( B,C integers, >1 ) (ii) b= 5/2 c=4 a = 5/2 * 4 =10  NO ( B,C >1 but B is not an integer)
A is even and a lies {8,9,10} But we still have YES and NO answers.
Hence E. Hi jojo1, Question is not asking us to test whether a or b is a non integer. We have to check whether the integer can be expressed as a product of two integers greater than 1.



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If a is positive integer, can a be expressed as the product of two int
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18 Jun 2019, 04:45
Bunuel wrote: If a is positive integer, can a be expressed as the product of two integers, each of which is greater than 1?
(1) a is even. (2) 7 < a < 11 Hi, the question asks if a "can" be expressed as..... And in both the cases, of course, a can be expressed as asked. Shouldn't the answer be D?
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Re: If a is positive integer, can a be expressed as the product of two int
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18 Jun 2019, 16:52
OhsostudiousMJ wrote: Bunuel wrote: If a is positive integer, can a be expressed as the product of two integers, each of which is greater than 1?
(1) a is even. (2) 7 < a < 11 Hi, the question asks if a "can" be expressed as..... And in both the cases, of course, a can be expressed as asked. Shouldn't the answer be D? Well the first statement is not valid when a = 2. Ideally we say a statement is true when it is valid for all the values, so here in this case say Can 2 be expressed as product of 2 ints both greater than 1? The answer is no , hence s1 is false.
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Re: If a is positive integer, can a be expressed as the product of two int
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19 Jun 2019, 00:41
laddaboy wrote: OhsostudiousMJ wrote: Bunuel wrote: If a is positive integer, can a be expressed as the product of two integers, each of which is greater than 1?
(1) a is even. (2) 7 < a < 11 Hi, the question asks if a "can" be expressed as..... And in both the cases, of course, a can be expressed as asked. Shouldn't the answer be D? Well the first statement is not valid when a = 2. Ideally we say a statement is true when it is valid for all the values, so here in this case say Can 2 be expressed as product of 2 ints both greater than 1? The answer is no , hence s1 is false. Okay, I get it now. Thanks.
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Re: If a is positive integer, can a be expressed as the product of two int
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19 Jun 2019, 01:11
I think the answer is B. Statement 1 tells us that A has to be even, but an even integer allows for both scenarios: Case 1: 2*3 = 6 = Product of two integers that are not 1 Case 2: 1*2 = 2 = Not possible to be formed by multiplying two positive integers that are not 1 Statement two tells us that a is not prime (no primes between 7 and 11) Therefore, we know that "a" can be formed by multiplying two integers other than one.
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Re: If a is positive integer, can a be expressed as the product of two int
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19 Jun 2019, 08:55
Given a = + ve integer Que = a can be expressed as c *b or not
1. A is even ,lets start with 2 = 2* no feasible value as value should be > 1 with 4 = 2 * 2 = feasible NOT SUFFICIENT 2. 7 < a < 11 a = 2*4 , 2*5 , 4 * 2 , 5 *2 feasible SUFFICIENT'
Answer is B



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Re: If a is positive integer, can a be expressed as the product of two int
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15 Jan 2020, 00:39
Given : a=mn, where m & n are greater than 1 (m&n>1) from st1 > a is even i.e a = 2,4,6,8,10..... lets take it one by one : a = 2 > mn = 2 > 2*1 = 2 (not valid > condition is m & n >1) a = 4 > mn = 4 > 2*4 = 2 (valid) from these solutions, we can see there is no consistency, so NOT SUFFICIENT
from st2 > 7 < a < 11, which means values of a are {8,9,10} lets take it one by one : 8 = possible factors = 1,2,4,8 = (1*8);(2*4);(4*2);(8*1) = 1 being factor of 8, makes it against the cond & so not valid 9 = possible factors = 1,3,9 = (1*9);(3*3);(9*1) = 1 being factor of 9, makes it against the cond & so not valid 10 = possible factors = 1,2,5,10 = (1*10);(2*5);(5*2);(10*1) = 1 being factor of 10, makes it against the cond & so not valid so a ={8,9,10} results a STRICTLY NO
Note : In DS, either STRICTLY YES or STRICTLY NO results a SUFFIECIENT RESULT
Therefore B is Suffient.
Please correct me if my approach or my answer is wrong.
Thank and kudos in advance




Re: If a is positive integer, can a be expressed as the product of two int
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