If x is a positive integer, the symbol * represents which of

Question

If x is a positive integer, the symbol * represents which of the following operations: addition, subtraction, multiplication, or division?

(1) For all x, 5* x = x * 5
(2) For all x, 2x * 2x = 4x

can someone clarify?

option 1:

5*1=5*1 multiplication-true
5+1=1+5 addition-true
we need a unique operation.
So, BCE

option 2: 2x * 2x = 4x

when x=1 this is also true for muliplication and addiction.

So, CE

and i marked E since we can't find a unique operation even after clubbing 1 and 2.

OA: B

VeritasPrepBrandon · Answer

I like how you assess the statements individually at first, and then in tandem second. That is always the right approach with data sufficiency questions.

In statement 1, you are correct. The order in which the numbers/variables are positioned does not matter for addition or multiplication, so statement 1 could imply either addition or subtraction. It cannot, however, imply subtraction or division, as the positioning of the numbers/variables here does matter.

In statement 2, it can only be addition. This is a great problem for picking numbers. With x=1, you are correct in that both multiplication and addition will yield the same result (4). However, you need to test more than one number. This operation must hold for all positive numbers, not just x=1. So let's try x=10. Addition: 2(10)+2(10) = 40 and 4(10) = 40, so this work. Now let's try multiplication: 2(10)*2(10) = 20*20 = 400 and 4(10) = 40, so multiplication does NOT work. Thus the * symbol must represent addition.

Remember to always pick multiple different kinds of numbers when employing the picking numbers strategy. Different kinds of numbers include positive/negative, odd/even, integers/fractions, large numbers, and the numbers 0 and 1.

I hope this helps!!!

Bunuel · Answer

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saswata4s · Answer

(1) Suppose x = 10. Then:

Addition: 5*x = 5 + 10 = 15; x*5 = 10 + 5 = 15; Same, hence satisfies.
Subtraction:5 - 10 = -5; 10 - 5 = 5; Not same, hence does not satisfy.
Multiplication: 5*10 = 50; 10*5 = 50; Same, hence satisfies.
Division: 5/10 = 1/2; 10/5 = 2; Not same, hence does not satisfy.

SO two possible results: Addition & Multiplication. Hence, insuff.

(2) For all x, 2x * 2x = 4x

Addition: 2x + 2x = 4x; satisfies.
Subtraction: 2x - 2x = 0; does not satisfy.
Multiplication: 2x * 2x = 4x^2; does not satisfy.
Division: 2x / 2x = 1; does not satisfy.

Sufficient.

Ans: B

vivek2k70 · Answer

I think answer should be E
Multiplication: 2x * 2x = 4x^2; does not satisfy
what if x=1?

Bunuel · Answer

(2) says: For  ALL  x, 2x * 2x = 4x.

For  ALL  x, 2x * 2x = 4x to be true "*" can only stand for an addition.

pushkarajnjadhav · Answer

(1) For all x, 5* x = x * 5
lets consider * is addition,
5+x = x+5 ---- true
consider * is subtraction
5-x not equal to x-5
consider * is multiplication
5*x =x*5---- true
consider * is division
5/x not equal to x/5

statement I states that * could be addition or multiplication. Hence Insufficient.

(2)For all x, 2x * 2x = 4x
lets consider * is addition
2x+2x =4x ---- true
for remaining signs the equation does not hold.
 statement II clearly states that * operator is addition operator, hence sufficient.

Answer is Option C.

Kudos if it helps.

bumpbot · Answer

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If x is a positive integer, the symbol * represents which of

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