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shivam7
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SATYAM7777
what is the rightmost non zero digit in the integer value of 12!?
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It is a unit digit question, remove 2, 5, and 10 because this gives unit digit as 0. Then remove group of numbers which gives unit digit as 6. then 11 will be left. when you multiply 11 with 6 you get unit digit as 6.
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aryannn_1712
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If a and b are positive integers, what is the units digit of b ?

(1) b is 25% greater than a.

(2) If b is decreased by 50%, the result is not an integer.

can someone explain this plz?
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Ontherox
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From 1: b is a multiple of 5 (units digit can be 0/5) - not sufficient

From 2: b is odd (not sufficient)

1&2: units digit is 5, so both together are sufficient
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HaCh369
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Isn’t the answer E ?

Because from 1: b =5a/4 => a is even => b is even

From 2: b is odd

So there in no single solution

Please feel free to correct me if I’m wrong here

My bad, there’s an error on my end
Please ignore
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aryannn_1712
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answer is D

I got B

sorry C

C is the answer but i got B

I know B isnt correct so its either E or C

but I cant see C being right
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HaCh369
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It’s C

From 2: we know b is odd

From 1: we get a = 4b/5

So for a to be an integer > 0, be has to be an integer divisible by 5

So the unit’s digit is either 0 or 5
But since we know from 2 that b is odd, the unit’s digit can only be 5

Hope this helps
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AsiaticLion
If PQ > 0 and |P|^Q = 1, then what is the value of P? (1) |P| = P (2) |Q| = Q
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(1) Since |P| = P, P^Q = 1. Ln both sides, so Q ln P = 0. Q or ln P = 0. Since PQ>0, Q cannot be 0. Thus P = 1. Sufficient

(2) Since |Q| = Q, P^Q =1. Same as before, apply ln both sides and reject Q=0. So again, ln P = 0 which means P =1. Sufficient

D
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aryannn_1712
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If the probability is 0.7 that event X will occur and 0.85 that event Y will occur, what is the least possible value of the probability that both events will occur?

(A) 0.15
(B) 0.55
(C) 0.595
(D) 0.7
(E) 0.85

Can someone help with this one
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Tukkebaaz
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sourabhmulik
An automobile rental agency purchases new cars from manufacturer in lots of 5 and releases the oldest cars in lots of 3. Last year the number of cars owned by the agency increased by 14. If a purchase of a lot and release of a lot each count as one transaction, which of the following is least number of transactions that could have occurred last year? a) Three b) Four c) Five d) Six e) Seven
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D =20-6= added 4 lots and sold 2 lots

AsiaticLion
If PQ > 0 and |P|^Q = 1, then what is the value of P? (1) |P| = P (2) |Q| = Q
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D

SATYAM7777
what is the rightmost non zero digit in the integer value of 12!?
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12!= 12*11*10****2*1 split into Prime factors = 2^10 * 3^5 * 5^2 * 7^1 * 11^1 now exclude 0’s i.e. 5*2 for non 0 digit = 2^8* 3^5 *7^1 * 11^1 = 4*3*7*1 = 4 (Ans)
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aryannn_1712
If the probability is 0.7 that event X will occur and 0.85 that event Y will occur, what is the least possible value of the probability that both events will occur? (A) 0.15 (B) 0.55 (C) 0.595 (D) 0.7 (E) 0.85
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Should be C. As P(X will occur) * P(Y will occur) = 0.70 * 0.85 = 0.595
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papapow69
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aryannn_1712
If the probability is 0.7 that event X will occur and 0.85 that event Y will occur, what is the least possible value of the probability that both events will occur? (A) 0.15 (B) 0.55 (C) 0.595 (D) 0.7 (E) 0.85
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B: 0.55.

P(X) = 0.7
B(Y) = 0.85
P(X and Y) = P(X) + P(Y) - P(X or Y)
P(X and Y) = 0.7 + 0.85 - P(X or Y)
P(X and Y) = 1.55 - P(X or Y)

Now, we know that probability can not be less than 0, and can not be more than 1. Thus, to minimize P(X and Y) we need to maximize P(X or Y). P(X or Y) can be set as much as 1. And thus,

P(X and Y) = 1.55 - 1 = 0.55.

Hence, (B) 0.55 is the answer.
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Tukkebaaz
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IshanSaini
Should be C. As P(X will occur) * P(Y will occur) = 0.70 * 0.85 = 0.595
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Agree B is right, I would solve using sets but yes same concept. The problem here and this is something to always be mindful of in 2 event problems as ppl tend to skip through is - The 2 events are not mentioned as independent [in which case we can take P (A&B)= P(A) * P(B)]. Hope this helps :)
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Is n divisible by 11 with no remainder?

(1) n is divisible by m with integer result
(2) m is divisible by 5.5 with integer result

isn’t it E? E because if n is 5.5, it can be divisible by 5.5 but not divisible by 11. But the answer sheet seems to disagree with me.
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hazeljj
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aryannn_1712
If the probability is 0.7 that event X will occur and 0.85 that event Y will occur, what is the least possible value of the probability that both events will occur? (A) 0.15 (B) 0.55 (C) 0.595 (D) 0.7 (E) 0.85
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I actually used Venn diagram for this which I believe works too. Probability of both events occurring will be the overlapping region. And since it needs to be minimised, prob of X + prob of Y - prob of X and Y occurring = 1.
P(X) + P(Y) - overlapped region = 1
Overlapped region = 1.55 - 1
So B

sldisek783
isn’t it E? E because if n is 5.5, it can be divisible by 5.5 but not divisible by 11. But the answer sheet seems to disagree with me.
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I also thought it’s E. Was there an explanation given? I saw the responses to the post and I don’t quite agree with them either.
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Rohinivish
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If x^2 < |x| and x≠0, which of the following are true?
I. x<0
II. x^2 < 1
III. x^1/2 = integer
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mysterymanrog
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Rohinivish
If x^2 < |x| and x≠0, which of the following are true? I. x<0 II. x^2 < 1 III. x^1/2 = integer
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I) Is false, consider the case of x=1/2

Ii) Is true. For any integer value of x, x^2 must be larger. So x must be some fraction (neg or pos)

III) root(x)=int. Not necessIrly true.

sldisek783
Is n divisible by 11 with no remainder? (1) n is divisible by m with integer result (2) m is divisible by 5.5 with integer result
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1) Clearly ins
2) 5.5=11/2
If m/(11/2)=int then 2m/11=int
M is some multiple of 11, since 2 is jot a factor of 11. Sufficient

B
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sldisek783
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hazeljj
I also thought it’s E. Was there an explanation given? I saw the responses to the post and I don’t quite agree with them either.
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The answer is C in fact. The question asks if n is divisible by 11 with no remainder, not if n is divisible by 11 with an integer result and with no remainder.
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mysterymanrog
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sldisek783
The answer is C in fact. The question asks if n is divisible by 11 with no remainder, not if n is divisible by 11 with an integer result and with no remainder.
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Good catch! It is not given that m is an int, making 2 ins.
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Tukkebaaz
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mysterymanrog
1) Clearly ins 2) 5.5=11/2 If m/(11/2)=int then 2m/11=int M is some multiple of 11, since 2 is jot a factor of 11. Sufficient B
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Say n = m = 5.5- yeah so? So S1 n/m =1 is true. S2 m/5.5 = 1 is also true but now your answer to the Qn stem is: False. In case n= m = 11x ( x is an integer) your answer is true. Based on these 2 points. Ans should be E. What is the source of this question??
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IS coordinate Geometry is a part of Gmat focus?
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