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# If positive integer a is multiplied by integer b and the result is les

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Math Expert
Joined: 02 Sep 2009
Posts: 53801
If positive integer a is multiplied by integer b and the result is les  [#permalink]

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19 Feb 2019, 01:18
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15% (low)

Question Stats:

100% (00:54) correct 0% (00:00) wrong based on 20 sessions

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If positive integer a is multiplied by integer b and the result is less than a, then it must be true that b is

A. equal to 1
B. greater than 0
C. greater than a
D. greater than 1
E. less than 1

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Joined: 31 Dec 2018
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Re: If positive integer a is multiplied by integer b and the result is les  [#permalink]

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19 Feb 2019, 01:32
ab<a
then b<a
for all int, till a=1, ab=a
then b must be less than 1 to satisfy the condition

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Joined: 09 Mar 2018
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Re: If positive integer a is multiplied by integer b and the result is les  [#permalink]

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19 Feb 2019, 02:50
Bunuel wrote:
If positive integer a is multiplied by integer b and the result is less than a, then it must be true that b is

A. equal to 1
B. greater than 0
C. greater than a
D. greater than 1
E. less than 1

Given a> 0
ab < a

now ab - a < 0
a (b-1) < 0

only one case wins here b < 1 & a > 0

E
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Re: If positive integer a is multiplied by integer b and the result is les  [#permalink]

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19 Feb 2019, 03:19
Bunuel wrote:
If positive integer a is multiplied by integer b and the result is less than a, then it must be true that b is

A. equal to 1
B. greater than 0
C. greater than a
D. greater than 1
E. less than 1

Notes:

1. a is positive integer.
2. b is an integer. but we don't know it's sign.
3. Multiplication yields a result that is less than a.

scenarios;

a and b both positive integers.

a = 2
b = 2
ab= 4.

4 is greater than a.

a = 1
b=1

ab = 1.

equal to a.

a positive b is negative:

a =2
b--1.

ab = -2.

-2<2.

conform the condition stated in the question.

Thus . b is negative integer.

Option E) b is less than 1.

As b is an integer and negative , it must be less than 1.

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Re: If positive integer a is multiplied by integer b and the result is les  [#permalink]

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19 Feb 2019, 04:24
Bunuel wrote:
If positive integer a is multiplied by integer b and the result is less than a, then it must be true that b is

A. equal to 1
B. greater than 0
C. greater than a
D. greater than 1
E. less than 1

a +ve integer when multiplied by another integer results in value less than original means other value is -ve or is a fraction 0 to 1 ..
IMO E
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Re: If positive integer a is multiplied by integer b and the result is les   [#permalink] 19 Feb 2019, 04:24
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