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Both (1) & (2) are true

I am new here n to gmat prep, why I see "D" mentioned by few folks when there are no options.. are A,B,C,D standard?


B

Correcting myself, its C for PS question

Apologies, its B

C is not possible as that will result in b < 3 which isn’t possible so eliminated

DS Question 1 - Mar 20

If a and b are positive integers, is a^4−b^4 divisible by 4?

1) a + b is divisible by 4

2) The remainder is 2 when a^2 + b^2 is divided by 4

Source: Math Revolution | Difficulty: Hard

PS Question 1 - Mar 20

What is the largest prime factor of the expression 3^8 − 2^12?

A. 2
B. 3
C. 5
D. 17
E. 29

Source: VeritasPrep | Difficulty: Hard

PS Question 1 - Mar 20 Ans - 29

DS i guess statment 1 sufficient... For the 2nd one don’t know

E. 29 (Using the expansion property of a^2-b^2)

DS (1)

2 is incorrect

D?

Statement 1 is pretty simple. Sufficient.

Statement 2 we can take a^2+b^2 = 4k + 2 where k>0 is the divisor and then use this to simplify the question stem. Sufficient.

Both cases we’re getting a "Yes"

Can you elaborate this "and then use this to simplify the question stem" ?

a^4 - b^4 = (a^2 - b^2)(a^2+b^2) --- (1)

Using statement 2 -> a^2+b^2 = 4k + 2 -> a^2 = 4k +2 - b^2

Using the value of a^2 in (1), -> (4k + 2 - b^2 - b^2) ( 4k + 2 ) [ As b^2 gets cancelled]

-> (4k + 2 - 2b^2) ( 4k+2) (Now we take 2 as common from both)

-> 2 * 2 ( 2k + 1 - b^2) ( 2k + 1)

Hence it’s divisible by 4. Sufficient.

E


D


Can someone tell me how S2 is sufficient ? I thought if a,b,c are numbers then a+b+c = 3b (only this case satisfy what question stem is asking)

DS Question 1 - Mar 21

A bank account earned 2% annual interest, compounded daily, for as long as the balance was under $1,000, starting when the account was opened. Once the balance reached $1,000, the account earned 2.5% annual interest, compounded daily until the account was closed. No deposits or withdrawals were made. Was the total amount of interest earned at the 2% rate greater than the total amount earned at the 2.5% rate?

(1) The account earned exactly $25 in interest at the 2.5% rate.
(2) The account was open for exactly three years.

Source: Official Guide | Difficulty: Medium

PS Question 1 - Mar 21

The sum of x and y is at least 2 but no more than 5. If the total of twice x and three times y is non-negative and no more than 40, which of the following expresses all possible values of y?

A. −4 ≤ y ≤ 36

B. −10 ≤ y ≤ 30

C. −10 ≤ y ≤ 36

D. 0 ≤ y ≤ 40

E. 2 ≤ y ≤ 5

Source: Princeton Review | Difficulty: Hard

stem: Is, interest @2% p.a. > interest @2.5% p.a. ?
or I1 > I2 ?

if "m" is the principal amount to start with and for "n" days the account operated

$1000 will be the new amount at the end of 2% interest scenario.

1000 = m(1+2/(100*365))^t , assuming this goes on for "t" days
we get value of "m" if we have "t"

then interest, I1 = m(1+2/(100*365))^t - m

another case where 2.5% is interest rate., 1000 is the principal to start with
then, total interest earned, I2= 1000(1+2.5/(100*365))^n-t - 1000

WE need value of t,n to make a comparison;

both statements individually are not sufficient;
statement1: we get to know I2 = 25, so, "n-t" can be known
statement2: we get time of 3 years, that is we can say "n" is given in years. so we can get "t"

combine both, we have all the info we need, so option C

here, 2 <= x + y <= 5
so, 4 <= 2x+2y <= 10
hence, -4 >= -2x-2y >= -10
or the same as, -10 <= -2x-2y <= -4

and another inequality, 0 <= 2x + 3y <= 40

add both inequalities

therefore -10 <= y <= 36 ... option C ?

DS Question 1 - March 22

If m and n are positive integers greater than 1, is m + n odd?

(A) m is a divisor of 16

(B) The units digit of 12^m + 28^n is 6.

Source: GMATWhiz | Difficulty: Hard

PS Question 1 - March 22

If the sum of the first 11 terms of an arithmetic progression consisting 16 terms is zero, then which of the following COULD be true ? (An arithmetic progression is a sequence of numbers such that the difference between the consecutive terms is constant)

I. 11th smallest term is zero
II. 6th largest term is zero
III. All terms are non negative

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

Source: GMAT Club Tests | Difficulty: Hard

DS Qn - clearly m is even & m can be (2,4,8,16) given m,n great than 1... But it’s not sufficient so answer m+n... Statement 2 individual also not sufficient to answer... With together 1 & 2 we can say n also even... So m+n even & Answer= together sufficient to answer the question

PS Q1 - D

As III doesnt seem possible, for sum to be 0 of 11 terms, they have to offset so half would be positive and half negative

DS Question 1 - Mar 24

For every dollar of sales charged to a certain bank credit card, a department store must pay $0.003 to the bank that issued the credit card. What percentage of the department store’s sales transactions last month were credit card transactions?

(1) The store made 2,000 sales last month.

(2) The store took in a total of $250,000 last month and paid $300 to the bank that issued the credit card.

Source: Princeton Review | Difficulty: Hard

PS Question 1 - Mar 24

For a certain set of numbers, if x is in the set, then both -x^2 and -x^3 are also in the set. If the number 1/2 is in the set, which of the following must also be in the set ?

I. -1/64
II. 1/64
III. 1/2^(1/3)

A. I only,
B. II only,
C. III only,
D. I and II only
E. I, II and III

Source: GMAT Club Tests | Difficulty: Hard